Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R33/00—Arrangements or instruments for measuring magnetic variables
  • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
  • G01R33/28—Details of apparatus provided for in groups G01R33/44 - G01R33/64
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R33/00—Arrangements or instruments for measuring magnetic variables
  • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
  • G01R33/28—Details of apparatus provided for in groups G01R33/44 - G01R33/64
  • G01R33/38—Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field
  • G01R33/383—Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field using permanent magnets
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R33/00—Arrangements or instruments for measuring magnetic variables
  • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
  • G01R33/28—Details of apparatus provided for in groups G01R33/44 - G01R33/64
  • G01R33/38—Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field
  • G01R33/387—Compensation of inhomogeneities
  • G01R33/3873—Compensation of inhomogeneities using ferromagnetic bodies ; Passive shimming
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R33/00—Arrangements or instruments for measuring magnetic variables
  • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
  • G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
  • G01R33/48—NMR imaging systems
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
  • H01F7/00—Magnets
  • H01F7/02—Permanent magnets [PM]
  • H01F7/0273—Magnetic circuits with PM for magnetic field generation
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
  • H01F7/00—Magnets
  • H01F7/02—Permanent magnets [PM]
  • H01F7/0273—Magnetic circuits with PM for magnetic field generation
  • H01F7/0278—Magnetic circuits with PM for magnetic field generation for generating uniform fields, focusing, deflecting electrically charged particles

Definitions

• the present disclosure relates to designs for magnet arrays and in particular to magnet arrays for use in magnetic resonance applications.
• FIG. 1 shows a cross-sectional view of an idealization of a Halbach cylinder 10, along with a coordinate system that is used to compute and select the orientations of magnetic dipoles, shown as arrows 11 , within a region surrounding a central volume 12.
• a coordinate system that is used to compute and select the orientations of magnetic dipoles, shown as arrows 11 , within a region surrounding a central volume 12.
• integer parameter k 1 for the most prevalent case, which produces a substantially uniform field in the central volume 12.
• 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. 1.
• FIGS. 2A, 2B, and 2C show example prior-art implementations of Halbach-cylinder- based magnet configurations.
• FIG. 2A adapted from Bertora ef al., shows a cylindrical configuration of magnets designated 20 surrounding space 24, that makes efficient use of space but employs many oblique shapes 21 , 22, 23 in its design.
• FIG. 2B adapted from Danieli, is an array 30 that uses simple shapes 31 to enclose space 32 but suffers from low packing density. 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. 2A, that are difficult or expensive to fabricate with high tolerance.
• FIG. 2C 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 Leskowitz er a/., U.S. Patent Application 2011/0137589.
• FIG. 3A shows a sphere 50 enclosing a central cavity 51 and having local magnetic dipole orientations 52.
• the magnetization direction has no z component (along the cylindrical symmetry axis) and is independent of the z coordinate of the dipole's position.
• Such spherical assemblies are generally composed of combinations of magnets having complex shapes, as illustrated in FIG. 3B, adapted from Leupold.
• FIG. 3B it will be seen that the sphere 60 comprises multiple component primary magnets 61 having chosen dipole orientations 62 and surrounding central cavity 63. In order to achieve the desired conformation and field, a large number different primary magnets having different shapes and magnetic orientations is required.
• a magnet array that comprises one or more polyhedral magnets.
• such arrays provide a design context within which practical implementations of Halbach spheres or other compact magnetic configurations are possible.
• the magnets are made of high-coercivity materials and are configured based on a lattice.
• individual ones of the polyhedral magnets are selected from the group consisting of: a truncated cube; a rhombic dodecahedron; a Platonic solid; an Archimedean solid; a Johnson solid; a chamfered polyhedron; and a truncated polyhedron.
• the lattice is a Bravais lattice.
• the lattice is a simple cubic lattice, a body centered cubic lattice, a face centered cubic lattice, or a hexagonal lattice.
• the polyhedral magnets comprise pluralities of first and second polyhedral magnets, the second polyhedral magnets being smaller than the first polyhedral magnets and a plurality of the second polyhedral magnets at least partly define a sample channel.
• the direction ⁇ corresponds to a body diagonal of the magnet array, a face normal axis of the magnet array, or a face diagonal of the magnet array.
• sample channel is oriented along a body diagonal of the magnet array.
• magnetization direction m selected from a finite set of possible values compatible with the array having the desired magnetic field direction v.
• the magnet array further comprises a sample rotator.
• individual ones of the polyhedral magnets are selected from the group consisting of: a truncated cube; a rhombic dodecahedron; a Platonic solid; an Archimedean solid; a Johnson solid; a chamfered polyhedron; and a truncated polyhedron.
• the polyhedral magnets are truncated cubes and wherein the direction v corresponds to a body diagonal of the magnet array or to a face normal axis of the magnet array or a face diagonal of the magnet array.
• the lattice is a Bravais lattice.
• the lattice is simple cubic lattice, a body centered cubic lattice, a face centered cubic lattice, or a hexagonal lattice.
• the method further comprises providing a testing volume within the magnet array and wherein the polyhedral magnets comprise pluralities of first and second polyhedral magnets, the second polyhedral magnets being smaller than the first polyhedral magnets and wherein a plurality of the second polyhedral magnets at least partly define a sample channel.
• a shimming assembly for the magnet assembly according embodiments wherein the shimming assembly comprises polyhedral magnets disposed in a lattice configuration, the magnets movable within the magnet assembly.
• a shimming assembly for the magnet array according to embodiments, the shimming assembly comprising polyhedral shimming magnets comprised within the magnet array, the shimming magnets actuable by a user to move within the magnet assembly.
• the magnet array comprises a plurality of shimming magnets occupying positions within said lattice configuration.
• a method for shimming a magnetic field generated by the magnet array comprising the steps of: a) obtaining a functional representation of the effect of moving the one of the plurality of shimming magnets on the magnetic field; b) repeating step a) for each one of the plurality of shimming magnets; c) deriving a sum function of the results of steps a) and b); and d) monitoring the magnetic field while adjusting the positions of ones of the shimming magnets.
• a magnetic resonance device comprising a magnet array comprising first and second polyhedral magnets arranged in a lattice configuration and at least partly enclosing a testing volume, wherein the first and second polyhedral magnets are truncated cubes and second polyhedral magnets are smaller than the first polyhedral magnets and at least partly define a sample channel extending along a body diagonal of the magnet array.
• FIG. 1 is a cross-sectional view of an idealized Halbach cylinder.
• FIGS. 2A-2C are cross-sectional views of implementations of Halbach-cylinder-based magnet assemblies.
• FIG. 3A depicts an idealized magnetization scheme for a Halbach sphere.
• FIG. 3B shows a practical embodiment of a Halbach sphere.
• FIGS. 4A-4D show unit cells of example point lattices.
• FIGS. 5A-5N show examples of polyhedral shapes.
• FIGS. 6 through 9 illustrate the primary magnet layers of a magnet array of a first embodiment according to FIG. 10 with the frames used to assemble them to form the array.
• FIG. 6A is a plan view of the zeroth, or central layer of an example of a first embodiment in its support frame.
• FIG. 6B is an end view of the frame used to hold the layer according to FIG. 6A.
• FIG. 7A is a plan view of the first layer of the first embodiment in its support frame.
• FIG. 7B is an end view of the frame used to hold the layer according to FIG. 7A.
• FIG. 8A is a plan view of the second layer of the first embodiment in its support frame.
• FIG. 8B is an end view of the frame used to hold the layer according to FIG. 8A.
• FIG. 9 is a plan view of the third layer of the first embodiment in its support frame.
• FIG. 9B is an end view of the frame used to hold the layer according to FIG. 9A.
• FIG. 10 is a corner view of an array assembled from the layers of FIGS. 6 through 9 showing the location of a possible sample channel.
• FIGS. 11A-11C show possible magnetic dipole orientations for individual cubic magnets.
• FIGS. 12A-12C show possible primary magnetic field orientations within a generally cubic magnet array.
• FIG. 13A is an exploded view of a second embodiment based on rhombic dodecahedra.
• FIG. 13B is a plan view of the central layer of the second embodiment according to FIG 13A.
• FIG. 14 is an array structure according to a third embodiment.
• FIG. 15 is an array structure according to a fourth embodiment.
• FIG. 16 is an array structure according to a fifth embodiment.
• FIG. 17 is an array structure according to a sixth embodiment.
• FIGS. 18A-18D are depictions of example space-filling assemblies of regular and semi- regular polyhedra corresponding to further alternative embodiments.
• the recitation of a specified number of elements is understood to include the possibility of any greater number of such elements.
• the recitation that a magnet array, or a layer of a magnet array, comprises two magnets indicates that the array or layer comprises at least two magnets, but may comprise 3, 4, 5 or any number of magnets greater than two.
• reference to individual ones of a group of elements indicates that any single one or more than one of such elements has the specified property or characteristic.
• the term "or” is inclusive rather than exclusive, and a statement indicating one characteristic "or” another will be understood to include the possibility of both characteristics being present. In other words the phrase "A or B" will be understood to contemplate the presence of both of
• magnetic resonance 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).
• NMR nuclear magnetic resonance
• ESR electron spin resonance
• MRI magnetic resonance imaging
• FMR ferromagnetic resonance
• Embodiments may also be applied in ion cyclotron resonance (ICR).
• 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.
• the term "shimming” refers to any method for suppressing a magnetic field inhomogeneity or otherwise modulating an aspect of the field.
• the magnetic field is a primary magnetic field and is generated or maintained within a magnetic resonance device.
• this is an NMR machine, is a spectrometer or is a compact NMR machine.
• shimming is achieved by movement of selected magnets or shimming elements positioned at selected locations within a magnet array or within the lattice configuration of a magnet array. Shimming may also be achieved, in embodiments that comprise electronic current paths included in the design for this purpose, by modulating currents thereon under the control of a shimming algorithm.
• the term "electronic shimming” is used to indicate the use of modulated electronic currents.
• primary magnet refers to one of the magnets forming part of a magnet array or contributing to a primary magnetic field for use in magnetic
• FIGS. 6 through 10 show possible arrangements of magnets according to an example of a first series of embodiments and in embodiments magnets may be truncated cubes.
• shimming magnet or “shimming block” refers to a magnet or other structure within or associated with a magnet array and useable to shim a magnetic field associated with the array.
• certain layers contain a number of shimming magnets or shim locations 120.
• shimming magnets may be controllably moved to modulate the field, and it will therefore be understood that in such a case the shimming magnets are sized to permit such movement.
• pole piece refers to a piece of magnetically permeable material placed in the vicinity of primary magnets for use in contributing to or shaping the primary magnetic field.
• pole pieces are made of any suitable material and design, all of which will be readily understood, selected from and implemented by those skilled in the art.
• pole pieces are made from HipercoTM or soft iron materials. It will be understood that in embodiments pole pieces may be applied to multiple pairs of opposed magnet faces and that in embodiments pole pieces may comprise shim paths to carry shim currents controllable by a user.
• primary field means the magnetic field generated by a magnet array.
• the array is comprised in a magnetic resonance apparatus.
• a field strength in the range of 1.0 to 2.5 Tesla is achieved, however the field strength will depend on the number of layers of lattice sites, the strength of the individual component magnets, the presence or absence and types of pole piece and construction materials used and other variables. Those skilled in the art will understand all such variables and their causes and effects and make suitable allowances therefor.
• field strengths of up to or less than or about 0.1 , 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1 , 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1 , 2.2, 2.3, 2.4, 2.5 or more will be generated.
• the field in the testing volume will depend on many variables including the number of lattice layers used, the nature of the primary magnets, any pole piece materials used and other variables all of which will be readily identified by those skilled in the art.
• the primary field will be between about 1.0 and 2.5 Tesia.
• the magnetic primary magnetic field of an array or the magnetic field within the testing volume is between about 0.1 and 2.5 Tesia, between 1.0 and 2.5 Tesia, between about 1.2 and 2.3 Tesia, or between about 1.5 and 2.0 Tesia
• a "testing volume” refers to a cavity within a magnet array that is designated to hold a sample under test.
• a testing volume is located at a lattice point within a lattice configuration and in embodiments contains within it other materials or susbsystems comprised within the apparatus associated with the magnet assembly, such as shimming means, means to hold or to rotate a sample or to modulate or maintain its temperature or other physical characteristics, means to apply field gradients, or means to apply or detect pulsed or transient magnetic fields.
• shimming means means to hold or to rotate a sample or to modulate or maintain its temperature or other physical characteristics
• means to apply field gradients means to apply or detect pulsed or transient magnetic fields.
• a reference to "modulating" a magnetic field or an inhomogeneity that may be comprised therein refers to imposing one or more desired constraints on the configuration of the field at any point in space. Thus modulating refers generally to the achievement of a desired change.
• “suppressing" an inhomogeneity refers to any adjustment to the geometric components of a magnetic field to correct or smooth out or otherwise overcome undesired irregularities or distortions in the field.
• shim path when used with reference to a shim path, shim current, magnetic field or the like, refers to both the spatial arrangement of components and to the overall position of the structure under consideration.
• the term "lattice” means a regular array of points in space, each of which is displaced from an origin by a sum of integer multiples of vectors, the vectors together constituting a 3-dimensional basis.
• a lattice can be visualized in terms of repeats of its unit cell, the smallest volume of the repeat pattern that can be used to construct the whole lattice.
• Illustrative examples of possible lattices are the simple cubic lattice; the face-centered cubic lattice; the body- centered cubic lattice; and hexagonal lattices such as the simple hexagonal or hexagonal close-packed lattices. The foregoing are illustrated in FIGS. 4A-4D, namely: (4A) simple cubic lattice; (4B) face-centered cubic lattice; (4C) body-centered cubic lattice; (4D) simple hexagonal lattice.
• a lattice may be a distorted version of one of the foregoing lattice types, such as a simple tetragonal lattice, which is a simple cubic lattice lengthened or shortened along one dimension.
• a simple tetragonal lattice which is a simple cubic lattice lengthened or shortened along one dimension.
• Further embodiments incorporate two or more interpenetrating lattices, and without limitation include interpenetrating lattices of the foregoing identified types.
• the term "lattice configuration" or “lattice arrangement” refers to an arrangement of objects wherein individual objects are positioned with their centers substantially coincident with a finite set of points of a lattice. More particularly, where used in reference to a group of magnets or to a magnet array or portion thereof, the term “lattice configuration” or “lattice arrangement” refers to an arrangement wherein individual component magnets are placed with their centers substantially coinciding with a finite set of points defined by a lattice.
• a lattice configuration will necessarily reflect the underlying lattice structure, so that, for example, a Bravais lattice configuration indicates a lattice configuration based on an underlying Bravais lattice.
• a magnet array may be expanded by adding additional magnets according to the underlying lattice pattern, to the extent desired by the user.
• a single location within the lattice configuration occupied by a first polyhedral magnet may be optionally occupied by a suitably modified first polyhedral magnet or by a plurality of second polyhedral magnets, as desired by a user to suit particular purposes.
• magnet array or “magnet assembly” refers to an
• a magnet array comprises individual primary magnets arranged in a lattice configuration.
• the shapes and locations for individual component magnets substantially fill the volume surrounding a designated central volume or testing volume.
• primary magnets forming a magnet array are unitary magnets or are composite magnets, or include both unitary and composite magnets, and in
• embodiments are shaped or arranged to provide access to the interior of the array.
• the shapes, sizes and arrangement of the primary magnets avoid numerous, skewed, or asymmetrical shapes with oblique magnetization axes.
• the primary magnets are polyhedral. It will be understood that since a magnet array comprises a lattice configuration of primary magnets, the size of the array may be expanded by simply extending the portion of the lattice occupied by suitable magnets. It will be understood that in embodiments multiple unit cells of the lattice configuration may be occupied by single primary magnets, and that in alternative embodiments a single unit cell may be occupied by a composite primary magnet comprising a number of smaller second polyhedral magnets.
• a magnet array is generally assembled with the assistance of structural frames to hold the component magnets of the array in position.
• each layer of the magnet array is assembled in a frame, and the frames with their accompanying magnets are then assembled to form the array.
• magnets are
• symmetry is exploited in order to keep the number of separate component part types to a minimum.
• FIG. 12A, B and C Three preferred axes or directions for a magnetic field exist among the infinity of possibilities for such a direction. These are illustrated in FIG. 12A, B and C and are shown schematically.
• body diagonal refers to a straight line or axis of symmetry of a magnet array that extends between geometrically opposed corners of the magnet array and through the center point of the array. This direction is illustrated by an arrow 92 within a portion of the simple cubic lattice 90 in FIG. 12C.
• face normal axis refers to a straight line or axis of symmetry that passes through opposed face centers of a magnet array and through the center point of the array, as shown in a side view 94 of a simple cubic lattice in FIG. 12A.
• face diagonal refers to a straight line or axis of symmetry that passes through opposed edge midpoints of a magnet array and through the center point of the array as shown in the side view 96 of the simple cubic lattice in FIG. 12B.
• the body diagonal, face normal, and face diagonal directions are called the (111), (100), and (110) axes, respectively.
• sample rotator means a device or means for rotating a sample to be tested within the testing volume.
• sample rotator means a device or means for rotating a sample to be tested within the testing volume.
• polyhedron means a solid comprising substantially flat faces and the term “polyhedral magnet” refers to a magnet having a polyhedral shape. It will be seen that in embodiments pluralities of individual polyhedral magnets are arranged to form a magnet array. In embodiments polyhedral shapes may be distorted, such as, by way of example and not limitation, square parallelepipeds. In particular embodiments polyhedra are selected from the following possibilities: chamfered polyhedron; truncated polyhedron (including in preferred embodiments a truncated cube); rhombic dodecahedron; Platonic solid, Archimedean solid, or Johnson solid.
• a Platonic solid - also commonly referred to as a regular polyhedron - has identical vertices and has congruent faces, each of which is a regular polygon.
• An Archimedean solid - also commonly referred to as a semi-regular polyhedron - is a polyhedron that has vertices that are identical.
• a Johnson solid has regular polygonal faces but inequivalent vertices.
• magnets also comprise spherical or circular- cylindrical magnets and in embodiments these are located at lattice points.
• a magnet array is assembled from a plurality of polyhedral magnets. In embodiments all of the polyhedral magnets comprised in an array are of the same shape. In embodiments the polyhedral magnets forming an array are of the same size. In alternative embodiments the polyhedral magnets forming an array are of different sizes or of different shapes or of different shapes and different sizes. In embodiments magnets are unitary or are composite or include both unitary and composite magnets.
• FIG.5 illustrates a number of polyhedral shapes all of which are contemplated in alternative embodiments of polyhedral magnets, namely: (A) cube; (B) tetrahedron; (C) octahedron; (D) cuboctahedron; (E) truncated cube; (F) truncated tetrahedron; (G) truncated octahedron; (H) truncated cuboctahedron (great rhombicuboctahedron); (I) small rhombicuboctahedron; (J) hexagonal prism; (K) square antiprism; (L) square parallelepiped (square prism); (M) chamfered cube; (N) rhombic dodecahedron.
• A cube
• B tetrahedron
• C octahedron
• D cuboctahedron
• E truncated cube
• references to any polyhedra also contemplate and include shapes that are derived from the named polyhedron by rounding or chamfering of edges, by drilling holes, or distorting the dimensions along an axis, or in a variety of other ways readily understood by those skilled in the art. It will be understood that in embodiments the truncation or chamfering or general shape of the packed polyhedral magnets will leave spaces useable to form or partly form channels or openings.
• first polyhedral magnets and “second polyhedral magnets” mean classes of polyhedral magnets that differ in shape or in size, or that differ in shape and size. Generally the overall geometry of the magnet array will be best described or understood in terms of the assembly of such first magnets which will generally be primary magnets.
• second polyhedral magnets is used to indicate polyhedral magnets that are substantially smaller than the first polyhedral magnets and in embodiments such secondary magnets are used to form sample channels in the magnet array or to fill spaces in the array or extend the array.
• the secondary polyhedral magnets of the array will have a diameter that allows a plurality of such second polyhedral magnets to be packed to occupy a space
• Magnets according to particular embodiments are made from or comprise any suitable materials all of which will be readily identified and used by those skilled in the art.
• magnets will be or comprise high coercivity materials.
• magnets are rare-earth based magnets.
• possibilities are neodymium-iron-boron and samarium-cobalt alloys. Those skilled in the art will readily identify and implement a range of possible alternatives.
• individual primary magnets have a diameter of up to, less than, or about 0.1 , 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1 , 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1 , 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.0, 3.1 , 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4.0 or more inches.
• an array comprises a mixture of larger first magnets and smaller second magnets
• the component second magnets forming composite magnets comprised in a magnet array will be suitable increments or portions of the size of the larger first magnets making up the array.
• the truncated cubic primary magnets or first magnets are about 1.25 inches face to face.
• the second magnets which comprise composite magnets of such an array are about 0.50 inches face to face.
• This direction can be selected arbitrarily in principle, but in practice it is often desirable to exploit the symmetry of the lattice and the magnets and to select certain special directions that are related to symmetry elements such as the fourfold or threefold symmetry axes of a cubic unit cell.
• gradient axes will be used to denote gradient tensor components, or principal components or other directional quantities defining the desired field configuration.
• the primary magnetic fields of magnet arrays disclosed herein approximate the field generated by a Halbach sphere.
• Possible magnetic field directions for a generally cubic magnet array include: a direction normal to a face of the lattice's unit cell; a direction along the line joining the center of the lattice's unit cell to the midpoint of an edge; a direction along a body diagonal of the lattice's unit cell as shown schematically in FIG. 12 and further explained elsewhere herein.
• sample channel means an opening in a magnet array useable to access the testing volume, for example to introduce a sample to the testing volume, or to remove a sample therefrom.
• a sample channel will have any desired orientation and by way of example and not limitation in
• a sample channel may extend from a face, corner or edge of a magnet array as is illustrated in FIG. 10.
• a sample channel is defined at least in part by the positioning of second magnets having reduced size or different geometry from the other first magnets making up the array.
• a sample may be introduced in a suitable sample tube.
• a sample tube can be a long glass tube containing a liquid sample, a flow tube, or a small "rotor"- type tube common in solid-state nuclear magnetic resonance (NMR).
• NMR solid-state nuclear magnetic resonance
• the axis along which a sample tube is to be inserted can be chosen.
• full exploitation of symmetry can select certain directions as preferable from among the infinity of possibilities for a sample-tube entry axis, and some of these are listed below.
• Other considerations may be material to the choice of the sample channel axis.
• a particularly useful combination of magnetic field direction and sample tube entry axis is to have the magnetic field direction be normal to a face of a cubic lattice's unit cell and to have the sample tube's entry axis be along the body diagonal.
• the angle between these axes is cos -1 ⁇ / ⁇ /3 « 54.7°, the so-called "magic angle" known to practitioners of solid-state NMR. Rapid rotation of a sample around this axis is known to permit use of certain very useful experimental techniques.
• At least three construction methods are contemplated that will permit a sample or a sample tube to be introduced into the central cavity or testing volume of the magnet array.
• the possibilities include but are not limited to: expanding the lattice to put space between the component magnets; drilling holes through the magnets, which may optionally be carried out in symmetric patterns; and leaving out symmetrically disposed subsets of the magnets or subsets of the component second magnets that make up one or more of the composite magnets.
• the foregoing possibilities may be combined in ways readily understood by those skilled in the art.
• FIGS. 6 through 10 A first series of embodiments is described with general reference to FIGS. 6 through 10 and a more detailed explanation of an example of the first series of embodiments is presented below.
• a magnet array comprising a plurality of polyhedral magnets arranged in a lattice configuration.
• the magnet array has an associated magnetic field with a designated field direction ⁇ .
• the magnet array at least partly encloses a testing volume and in embodiments completely or almost completely encloses the testing volume.
• the magnetization direction m of an individual polyhedral magnet located at a displacement vector r from an origin point in the testing volume is determined by the formula:
• the polyhedral magnets 101 are truncated cubes, and the magnet array is based on a simple cubic lattice, as illustrated in FIG. 10.
• the first embodiment also comprises a method for generating a magnetic field having a field direction v.
• individual ones of the polyhedral magnets are selected from the group consisting of: a truncated cube; a rhombic dodecahedron; a Platonic solid; an Archimedean solid; a Johnson solid; a chamfered polyhedron; and a truncated polyhedron.
• the lattice upon which the array is based is a Bravais lattice and thus the magnets of the array have a Bravais lattice configuration.
• the lattice is a simple cubic lattice, a body centered cubic lattice, a face centered cubic lattice, or a hexagonal lattice and the lattice configuration of the magnets of the array follows such underlying lattice structure.
• the polyhedral magnets making up the array comprise pluralities of first 101 and second 106 polyhedral magnets, the second polyhedral magnets being smaller than the first polyhedral magnets.
• a plurality of the second polyhedral magnets at least partly define a sample channel 107.
• the sample channel is oriented along a body diagonal of the lattice defining the magnet array. This orientation is particularly suited to an array comprised of truncated cubes. It will be understood that with suitable adjustments other orientations are possible and will vary depending on the type of lattice used to construct the array.
• direction v of the magnetic field corresponds to a body diagonal of the magnet array, a face normal axis of the magnet array, or a face diagonal of the magnet array.
• FIG 11 B a cubic magnet is depicted in side view with its
• magnetization terms apply without change to a cubic magnet that is truncated like those used in the lattice configuration of FIG 10 and also generally to a composite magnet or an array that comprises multiple component magnets.
• An individual polyhedral magnet has a finite number of possible orientations within a packed array. In order to facilitate or improve quality-control procedures, or to make them more cost-efficient, it may be desirable to limit the choice of possible
• a single primary magnet may have a dipole oriented in any of the three directions illustrated in FIG. 11 and may be oriented within a lattice with a given face- normal along any one of six directions corresponding to the six faces of the cube, and then may be further oriented in any of four possibilities by rotation around that face normal, giving a finite but large set of possibilities for the magnetization direction.
• the array may be assembled using only three components, namely individual magnets having one of the three dipole orientations shown in FIG. 11. It will be understood that the same principle may be applied to a wide range of other polyhedral shapes. It will also be understood that in embodiments or parts of
• a single magnet may be a unitary magnet or may be a composite magnet.
• the field associated with a single magnet may also be referred to as a dipole.
• the array further comprises a sample rotator.
• the arrays of the first embodiment are comprised in a magnetic resonance device.
• the shapes of the polyhedra are selected so that, when positioned on a lattice, the polyhedra interlock and substantially fill a volume. In embodiments the shapes are selected and arranged so that the assembly as a whole exhibits high symmetry, and, in particular, so that a limited number of individual magnet designs is required to assemble the array. It will be understood that if a relatively limited number of individual magnet designs is sufficient then the number of different types of component parts is small compared to the number of types of parts that would be present if each magnet were unique in its design.
• the array comprises shims, and there are provided methods for shimming the primary magnetic field associated with an array. In embodiments the shimming uses shimming magnets positioned within or around the array. In embodiments the shimming is achieved using electronic shimming structures. In embodiments suitable pole pieces are provided to provide fine shimming of the field.
• first magnets 103 are larger first magnets 103 and others are smaller second magnets 106.
• the smaller second magnets form composite magnets 104 at particular points in the array.
• the use of such smaller second magnets 106 is exploited to provide a sample channel 107, in this case oriented along a body diagonal.
• a magnet array 102 of the embodiment may be formed by forming and positioning individual layers of individual magnets 101.
• a central layer is designated Layer 0 and comprises a vacant space 110 at its center, forming the testing volume.
• FIG. 6 shows a plan view of Layer 0 of the magnet array of a first example of the first embodiment. It will be seen that these magnets are primary magnets and are "first magnets" as explained in the definitions section of the disclosure.
• Layer 0 is assembled in a support frame 150 having faces 151 , 152 and ends 153, 154, shown schematically in cross section in FIG. 6B. It will be appreciated that additional openings will be incorporated as required by a user to provide for wiring and other structures.
• Layer 0 is bounded on a first side by a Layer 1 , followed by a Layer 2, and finally a Layer 3.
• Layer 0 On the opposite side of Layer 0 the same arrangement extends in the opposite direction, with Layer -1 , Layer -2, and Layer -3. It will be understood that the array is generally symmetrical. Each layer is assembled in a frame and the frames will be secured together to form an assembled array 102.
• Layer 1 is shown in FIG. 7, and it will be seen that the central or testing volume is bounded on all sides and is generally cubic.
• the magnet array comprises a plurality of shimming magnets 120 associated with the array.
• the shimming magnets occupy positions within lattice configuration and in embodiments are sized to be moveable within the array.
• the shimming magnets 120 are polyhedral and are comprised within the magnet array.
• the shimming magnets are positioned at lattice points within the array, and in embodiments are positioned outside the magnet array.
• the shimming magnets are actuable by a user to move within the magnet assembly.
• Individual magnets 101 comprising the magnet array are formed into an ordered arrangement, and the arrangement includes shimming magnets 120, and composite magnets 104 comprising smaller second magnets 106.
• the shimming magnets 120 are slightly smaller than the other primary magnets 103, etc., permitting them to be moved as desired by a user, in order to effectively adjust the magnetic field in the testing volume.
• these magnets are individually moveable, or are connected in pairs or in pluralities.
• the possible paths of movement in embodiments are designated by arrows, 125.
• the magnets are mounted in frame 160. Channels 168 in the frame 160 are sized to accommodate shimming magnets 120 and to allow them to be moved.
• Layers 2 The structure of Layers 2 is shown in FIG. 8. It will be seen that the arrangement of this layer in an embodiment comprising primary magnets that are truncated cubes is generally a square having five primary magnets 101 along each side. It will be seen that Layer 2 also comprises, at four positions, shimming magnets 120. In embodiments these are related in pairs to corresponding magnets in adjacent layers. Thus in the embodiment illustrated four shimming magnets in Layer 2 are connected in pairs to corresponding magnets in layer 3 of FIG 9. In these embodiments the pairs of shimming magnets together move into and out of the plane of the figure. It will be appreciated that in the illustrated embodiment, the array comprises seven layers and thus 24 pairs of magnets that are used for shimming.
• shimming magnets or electronic shims are provided in any suitable numbers.
• shimming magnets or electronic shims are generally symmetrically arranged around the testing volume.
• 1 , 2, 3, 4, 5, 6, 7, 8, 9, 10, 1 1 , 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 , 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 , 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 , 42, 43, 44, 45, 46, 47, 48 or more shims or shimming magnets are provided.
• movement of the shimming magnets is coordinated in groups of 1 , 2, 3, 4, 5, 6, 7, 8, 9 or more shimming magnets.
• the method comprises one or more steps.
• the steps comprise: a) obtaining a functional representation of the effect of moving the one of the plurality of shimming magnets on the magnetic field; b) repeating step a) for each one of the plurality of shimming magnets; c) deriving a sum function of the results of steps a) and b); and d) monitoring the magnetic field while adjusting the positions of ones of the shimming magnets.
• the shimming magnets are provided as one means for "coarse” shimming the magnetic field within the testing volume.
• the procedure for shimming comprises one or more or all of the following steps:
• a suitable functional representation might take the form ⁇ , ⁇ , ⁇ , ⁇ , where x, y, and z denote the position coordinates within the testing volume where the field is to be estimated, and where ⁇ represents a coordinate variable along which shim magnet / ' is permitted to move controllably.
• This functional representation can be obtained variously by magnetostatic simulations or by mapping the magnetic field changes that occur, for example with a gaussmeter probe, when magnet / ' is moved along the coordinate 77 ⁇ .
• Alternative functional representations and means for determining them will be readily understood by those skilled in the art.
• this sum function as a representative of the effects on the main magnetic field depends in part on the extent to which the individual effects are independent, / ' . e. on the extent to which the magnetizations of the shim magnets and other magnets are resistant to changes induced by the motions.
• an important physical factor governing this resistance is the coercivity of the magnetic materials used to fabricate both the shim magnets and the other component magnets in the array. It will be appreciated that in embodiments use of high-coercivity magnetic materials is thus preferred.
• the sum function is then decomposed into component functions, in terms of both the spatial variables x, y, z and the magnet-coordinate variables T]j .
• the magnet-coordinate variables can be combined linearly into new variables ⁇ ] , possibly adapted to the symmetry of the shim-magnet positioning, and the sum function expressed in terms of both the spatial variables x, y, z and the symmetry-adapted variables.
• shimming will choose functional forms (polynomials, for example) in the spatial variables x, y, z to suit the particular application.
• a response function of the magnetic field within the testing volume is determined.
• this response function might be a magnetic field map or an NMR parameter, such as a resonance line width or may be other functions which will be readily identified and selected amongst by those skilled in the art.
• a use will adjust or will iteratively adjust the positions of the shim magnets, and monitor changes in the response function, until a desired field configuration is achieved.
• Those skilled in the art of shimming will use
• shimming magnets may be moved coordinately or separately as desired by a user. Those skilled in the art will readily understand the adjustments that are necessary or desirable to optimize the foregoing adjustments to the shimming magnets. Those skilled in the art will recognize and implement a variety of ways to achieve each of the foregoing steps.
• a composite magnet 104 comprising a series of smaller or second magnets 106.
• Layer 2 is mounted in a frame 170, having external face 171 and internal face 172, and sloped edges 173, 174.
• Central region 175 comprises a recessed portion 178 on internal face 172, and the periphery of the frame is thickened 176.
• Recessed portion 178 fits snugly with the thickened central portion 165 of frame 160 holding adjacent layer 1. Openings 177 are provided to allow adjacent frames to be mutually secured, for example, with bolts.
• Layers 3 are shown in plan view in FIG. 9. It will be seen that Layer 3 is a square with three magnets along each side, comprising central primary magnets 101, and four shimming magnets again designated 120, at its corner positions. Again these shimming magnets are slightly smaller than the other primary magnets and can be moved to shim the primary field.
• the layer is assembled in frame 180 having sloped edges 183, 184, an outer face 181 and an inner face 182 which will fit snugly with adjacent frame 170. Openings 187 are again provided to allow adjacent frames to be mutually secured.
• the composite magnet positions comprising composite magnets 104 comprised of secondary magnets 106 allow the formation of a sample channel 107 accessible from a corner of the array.
• FIGS. 6A, 7A, 8A, and 9A show magnets in positions constrained by the frame, which is shown in plan view.
• FIGS. 6B, 7B, 8B, and 9B respectively show cross sectional end views of the respective frames for the layers illustrated.
• the framing materials will be selected by a user from a range of suitable materials and in the exemplary embodiment are made of any suitable material.
• Openings are provided in the frames as necessary or desirable to accommodate wires, mountings, bolts, screws and the like and to permit access to the array as required by a user. It will be understood that in embodiments both primary and shimming magnets are unitary magnets and in alternative embodiments are composite magnets.
• the truncated cubic primary magnets or first magnets are about 1.250 inches face to face.
• the second magnets, which comprise composite magnets, are about 0.500 inches face to face.
• the testing volume of the array is about the same size as one of the larger first or primary magnets. It will be understood that a range of sizes may be used and that the specific ratio of sizes of the first and second magnets will be adjusted by a user to suit particular purposes.
• FIGS. 6 through 10 A first example of the first embodiment is explained with particular reference to FIGS. 6 through 10 and is merely illustrative of embodiments and is in no way limiting of the subject matter claimed herein.
• the primary magnets 101 are in the shape of truncated cubes. Some are unitary magnets 103 generally referred to herein as first magnets, and others are composite magnets 104 comprising multiple smaller second magnets 106.
• the truncated cubes are disposed with their centers placed at the points of a simple cubic lattice as shown in FIG. 4A. If the lattice sites are labeled with triads of integers, e. g.
• the set of these several orientations is made far more numerous by the fact that the component magnets are polyhedra of high symmetry rather than wedges or other oblique shapes. Consequently the array can be constructed using a limited number of component magnet
• a single primary magnet may have a dipole oriented in any of the three directions illustrated in FIG. 11 and may be oriented in several different ways within a cubic lattice.
• the array may be assembled using only three components, namely individual magnets having one of the three dipole orientations shown in FIG. 1. It will be understood that the same principle may be applied to a wide range of other polyhedral shapes. It will also be understood that in embodiments or parts of embodiments a single magnet may be a unitary magnet or may be a composite magnet.
• v is preferably oriented along a body diagonal, parallel to a face diagonal, or perpendicular to a face.
• the field direction v is oriented along a body diagonal of the magnet array and in particular embodiments is oriented perpendicular to a face of the magnet array.
• the magnets are included in the assembly so that all members of a class are included.
• the class [1,0,0] includes six magnet sites, namely [1 ,0,0], [0, 1 ,0], [0,0, 1], [-1 ,0,0], [0,-1 ,0], and [0,0,-1].
• the class [2 oJ includes 24 magnets corresponding to permutations of the numbers and changes of sign.
• first magnets 103 are larger first magnets 103 and others are smaller second magnets 106.
• the smaller second magnets form composite magnets 104 at particular points in the array.
• the use of such smaller second magnets 106 is exploited to provide a sample channel 107, in this case oriented along a body diagonal.
• a magnet array 102 of the embodiment may be formed by forming and positioning individual layers of individual magnets 101.
• a central layer is designated Layer 0 and comprises a vacant space 110 at its center, forming the testing volume.
• FIG. 6 shows a plan view of Layer 0 of the magnet array of a first example of the first embodiment. It will be seen that these magnets are primary magnets and are "first magnets" as explained in the definitions section of the disclosure.
• Layer 0 is assembled in a support frame 150 having faces 151 , 152 and ends 153, 154, shown schematically in cross section in FIG. 6B. As will be seen the frame comprises a thinner central portion 155 and thicker periphery 156 and is generally octagonal. Holes 57 are included in the frame to allow the insertion of bolts screws or other supporting or securing structures. It will be appreciated that additional openings will be incorporated as required by a user to provide for wiring and other structures.
• Layer 0 is bounded on a first side by a Layer 1 , followed by a Layer 2, and finally a Layer 3.
• Layer 0 On the opposite side of Layer 0 the same arrangement extends in the opposite direction, with Layer - , Layer -2, and Layer -3. It will be understood that the array of this example of the embodiment is generally symmetrical. Each layer is assembled in a frame and the frames will be secured together to form an assembled array 102.
• Layer 1 is shown in FIG. 7, and it will be seen that inner layers 1 and -1 align with central Layer 0 but lack the central cavity, and thus the central or testing volume is bounded on all sides and is generally cubic.
• Individual magnets 101 are formed into an ordered arrangement, and the arrangement includes shimming magnets 120, which are distinguished by stippling, and composite magnets 104 comprising smaller second magnets 106.
• the shimming magnets 120 are slightly smaller than the other primary magnets 103, etc., permitting them to be moved as desired by a user, in order to effectively adjust the magnetic field in the testing volume.
• these magnets are connected in pairs and can be moved in the plane of the frame along paths designated by arrows, 125.
• the magnets are mounted in frame 160 having edges 163, 164, top and bottom surfaces 161 , 162, a thickened central portion 165 and thinner periphery 166.
• Channels 168 are sized to accommodate shimming magnets 120 and to allow them to be moved as described herein, to shim the primary magnetic field of the assembled array. It will be appreciated that holes 67 are comprised in the frame to allow adjacent frames to be mutually secured, and that additional openings will be introduced by a user to
• Layers 2 The structure of Layers 2 is shown in FIG. 8. It will be seen that the arrangement of this layer is generally a square having five primary magnets 101 along each side. It will be seen that Layer 2 also comprises, at four positions, shimming magnets 120. These shimming magnets are slightly smaller than the other primary magnets 0 , permitting them to be moved as desired by a user, in order to effectively adjust the magnetic field in the testing volume. These four magnets are connected in pairs to corresponding magnets in layer 3 of FIG 9, and the pairs together move into and out of the plane of the figure. It will be appreciated that the seven layers of an assembled array together comprise 24 pairs of magnets that are used for shimming.
• the 24 pairs of moveable magnets in this first embodiment illustrate the potential for "coarse” shimming the magnetic field within the testing volume.
• a representative procedure for said shimming would proceed in steps as follows:
• a suitable functional representation might take the form ⁇ , ⁇ , ⁇ , ⁇ ), where x, y, and z denote the position coordinates within the testing volume where the field is to be estimated, a nd where ⁇ represents a coordinate variable along which shim magnet / is permitted to move controllably.
• This functional representation can be obtained variously by magnetostatic simulations or by mapping the magnetic field changes that occur, for example with a gaussmeter probe, when magnet / ' is moved along the coordinate ⁇ ⁇ .
• the magnet-coordinate variables ⁇ ⁇ can be combined linearly into new variables possibly adapted to the symmetry of the shim-magnet positioning, and the sum function expressed in terms of both the spatial variables x, y, z and the symmetry-adapted variables.
• Those skilled in the art of shimming will choose functional forms (polynomials, for example) in the spatial variables x, y, z to suit the particular application.
• This response function might be a magnetic field map or an NMR parameter, such as a resonance line width.
• Layer 2 is mounted in a frame 170, having external face 171 and internal face 172, and sloped edges 173, 174.
• Central region 175 comprises a recessed portion 178 on internal face 172, and the periphery of the frame is thickened 176.
• Recessed portion 178 fits snugly with the thickened central portion 165 of frame 160 holding adjacent layer 1. Openings 177 are provided to allow adjacent frames to be mutually secured, for example, with bolts.
• Layers 3 are shown in plan view in FIG. 9. It will be seen that Layer 3 is a square with three magnets along each side, comprising central primary magnets 101 , and four shimming magnets again designated 120, at its corner positions. Again these shimming magnets are slightly smaller than the other primary magnets and can be moved to shim the primary field.
• the layer is assembled in frame 180 having sloped edges 183, 184, an outer face 181 and an inner face 182 which will fit snugly with adjacent frame 170. Openings 187 are again provided to allow adjacent frames to be mutually secured.
• the composite magnet positions comprising composite magnets 104 comprised of secondary magnets 106 allow the formation of a sample channel 107 accessible from a corner of the array.
• FIGS. 6A, 7A, 8A, and 9A show magnets in positions constrained by the frame, which is shown in plan view.
• FIGS. 6B, 7B, 8B, and 9B respectively show cross sectional end views of the respective frames for the layers illustrated.
• the framing materials will be selected by a user from a range of suitable materials and in the exemplary embodiment are made of any suitable material.
• Openings are provided in the frames as necessary or desirable to accommodate wires, mountings, bolts, screws and the like and to permit access to the array as required by a user.
• both primary and shimming magnets are unitary magnets. In alternative embodiments it will be understood that composite magnets can also be used.
• the truncated cubic primary magnets or first magnets are about 1.250 inches face to face.
• the second magnets, which comprise composite magnets, are about 0.500 inches face to face.
• the testing volume of the array is about the same size as one of the larger first or primary magnets.
• Suitable materials in particular applications include aluminum, brass, or a strong plastic such as PEEKTM or DelrinTM, or a ceramic material such as MacorTM.
• PEEKTM or DelrinTM a strong plastic
• MacorTM a ceramic material
• the magnets themselves are made from any suitable material.
• High coercivity materials are suitable, as are strong rare-earth based magnets.
• Exemplary possibilities are neodymium-iron-boron and samarium-cobalt alloys. Those skilled in the art will readily identify and implement a range of possible alternatives.
• a field in the range of 1.0 to 2.5 Tesla is achievable, however the field strength of any particular embodiment will depend on the number of layers of lattice sites, the strength of the individual component magnets, the presence and types of pole piece and construction materials used and other variables. Those skilled in the art will understand all such variables and make suitable allowances therefore.
• Pole pieces are not illustrated being part of the general common knowledge in the art. It will be understood that those skilled in the art may wish to incorporate pole pieces into the array of the example order to further modify the field. In modifications of the example that contain pole pieces incorporated in the array to shim the magnetic field in the testing volume, it has been found that suitable materials for such pole pieces include Hiperco , soft iron materials, or other suitable materials, all of which will be readily identified and utilized by those skilled in the art.
• the primary magnets 131 of the magnet array 130 are rhombic dodecahedra which shape is illustrated in FIG 5N.
• FIG. 13A illustrates an array based on this configuration in exploded view and FIG. 3B illustrates a central layer of such an array.
• the rhombic dodecahedra are configured in layers 520, 540, 560, each of which is based on a triangular, 2-dimensional lattice of points.
• the central layer 520 is bounded by first layers 540 and 540', and then second layers 560 and 560'.
• the 2-dimensional lattices together comprise a face-centered cubic lattice.
• the central layer comprises a lattice site, centrally located, designated as the testing volume 132.
• the rhombic dodecahedra may be chamfered, or the lattice expanded, to permit access to the central testing volume.
• FIG. 14 A third alternative embodiment is shown in FIG. 14 and is generally designated 600.
• the magnet array 600 shown in FIG. 14 is based on a space-filling structure consisting solely of cubes 601 in a portion of a simple cubic lattice.
• the central cube is removed to provide the central cavity or testing volume 604.
• the lattice is expanded, and cubes on the corners of the structure (eight in number) are removed to accommodate a sample- tube, which is not illustrated.
• FIG. 15 A fourth alternative embodiment is shown in FIG. 15 and is generally designated 620.
• the design 600 of FIG.14 is supplemented with square
• FIG. 16 A fifth alternative embodiment is shown in FIG. 16 and is generally designated 71.
• the magnet block 7 1 of this embodiment is based on a spacefilling structure consisting of portions of four interpenetrating face-centered cubic (fee) lattices, but with different polyhedra. Truncated cuboctahedra occupy the corners 712 and face-centers 713 of the magnet-block 711 , and truncated cubes are placed at the edge-centers 714, with the central truncated cube removed to provide the central cavity.
• These two lattices are supplemented by two other fee lattices, each of whose sites are occupied by truncated tetrahedra 715, which are present in two different orientations.
• edge-centered truncated cubes 714 are removed and the lattices are expanded to the degree necessary, and if the interior-most truncated tetrahedra are made smaller or are chamfered, then a channel is created, which can be used as an access port to the interior of the structure.
• holes can be drilled through either the truncated cuboctahedra or the truncated cubes to accommodate the insertion of a sample tube.
• the truncated cubes are affixed to structures that permit their movement toward and away from the center of the assembly, a coarse-shimming capability can be realized.
• This coarse-shimming capability will have twelve degrees of freedom, and these twelve individual motions can be combined into concerted motions of all twelve magnets, which can facilitate assignment of the motions to particular functional components ⁇ e.g., x, yz, y 2 - z 2 , etc.) of field gradients to be shimmed based on symmetry considerations.
• FIG. 17 A further embodiment is shown in FIG. 17 and is generally designated 800.
• FIG. 17A shows an embodiment generally designated 800 for a magnet array 801 based on a space-filling structure consisting of portions of four interpenetrating face- centered cubic lattices.
• Truncated octahedra 802 occupy the corners 803 and face- centers 804 of the magnet-block shown.
• Cuboctahedra 805 are placed at the edge- centers, and then the central cuboctahedron is removed 808 in order to provide a central cavity for a sample, NMR detection coil, electronic field-shimming measures, sample spinner, or other apparatus.
• These two lattices are supplemented by two other lattices, each of whose lattice sites are occupied by truncated tetrahedra 809 (in two different orientations).
• FIG. 17B shows how a sample channel can be incorporated into the array if the edge- centered cuboctahedra 805 are removed and the lattices are expanded to the degree necessary, or if the interior-most truncated tetrahedra 810 are made smaller or are chamfered. Alternatively, holes can be drilled through the cuboctahedra to
• a coarse-shimming capability can be realized.
• This coarse-shimming capability will have twelve degrees of freedom, and these twelve individual motions can be combined into concerted motions of all twelve magnets, which can facilitate assignment of the motions to particular functional components (e.g., x, yz, y 2 - z 2 , etc.) of field gradients to be shimmed based on symmetry considerations.
• the lattice configurations can be defined by choosing from the infinite point sets defining the underlying lattices those points nearest a designated "origin" point, [0,0,0] within a neighborhood defined by a maximum radius.
• the points chosen for the lattice configuration will generally include all those generated from a given point by considerations of symmetry.
• inclusion of the lattice point [3,2,0] will induce inclusion of the symmetry-related points in the whole class [3,2,0], that is, the points [3,-2,0], [3,0,2], [3,0,-2], [2,3,0], [2,-3,0], and all others, for a total of 24 in number, obtained by permuting the numbers and changing signs. It will further be understood that some of those classes of points will be excluded from the lattice configuration in order to facilitate access to the testing volume.
• FIG. 18A shows an embodiment of a magnet array generally designated 73 comprising two interpenetrating simple cubic lattices, one with truncated cubes 731 and one with octahedra 732.
• FIG. 18B shows an embodiment of a magnet array generally designated 75 comprising four interpenetrating face-centered cubic lattices, one with rhombicuboctahedra 751 , one with cubes 752, and two with tetrahedra 753 in each of two orientations. The latter components are not shown in this illustration.
• FIG. 18C shows an embodiment of a magnet array generally designated 72 comprising five interpenetrating simple cubic lattices, one with truncated cuboctahedra 721 , one with truncated octahedra 723, and three with cubes 722 in each of three orientations.
• FIG. 18D shows an embodiment of a magnet array generally designated 74 comprising five interpenetrating simple cubic lattices, one with cuboctahedra 741 , one with rhombicuboctahedra 742, and three with cubes 743 in each of three orientations.

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