Transverse tubular passive shims

Abstract

Apparatus and methods for adjusting the magnetic field distribution in magnets, particularly magnets with fields transverse to the access geometry into the magnet. The passive shim apparatus magnetically soft and isotropic materials in a generally tubular shape, positioned in the magnetic field so that the axis of the tube is perpendicular to the field direction. The method for designing the passive shim utilizes an association between basis patterns of shim material and the fields the patterns create.

Description

[0001] TRANSVERSE TUBULAR PASSIVE SHIMS

[0002] FIELD OF THE INVENTION

[0003] The invention relates to the shimming of magnetic fields, particularly to passive shims for magnets in which the field is perpendicular to the geometry of the access to the working volume.

[0004] BACKGROUND TO THE INVENTION

[0005] Some scientific, medical, or industrial devices require magnetic fields for their operation. Such devices may contain resistive electromagnets, superconducting electromagnets, or permanent magnets to provide the required magnetic field in a working volume of the device.

[0006] In cases where the device is intended to investigate samples that are placed into the magnetic field, access to the working volume may be provided. For example, this access may be in the form of a cylindrical or rectangular passage or hole, or the access may be planar in general shape. In many cases, the magnetic field in the working volume may be considered to be orientated transverse to the sample access geometry. For example, it may be perpendicular to the long axis of the cylindrical or rectangular access hole, or parallel to a vector normal to the plane of a magnet assembly with planar access.

[0007] A sample to be placed into a device may have a generally cylindrical shape. An example is a sample in a tube, such as a fluid sample in a nuclear magnetic resonance tube. Another example is a human body which may be considered to have an overall cylindrical shape. A further example is a human appendage, such as an arm, or leg, or head. In some cases, the generally cylindrical sample will extend out of the interior of the magnet. The generally cylindrical shape of the sample may have one dimension in which it is longer than the orthogonal dimensions and this long dimension defines its axis. Due to the passage provided for access into the working volume, the sample axis may be perpendicular to the direction of the magnetic field in the working volume. In such a case, the magnetic field may be considered to be transverse to the sample access geometry.

[0008] Magnetic field generation using permanent magnet technology may be preferred for compact and portable devices. For such devices, a magnet assembly consisting of multiple blocks of permanent magnet material together with structures made from non-permanently magnetic or non-magnetic material may be employed. The typical permanent magnet assembly produces a transverse field and may fall into two general categories, the first being iron-core dipole magnets in which the working volume is between two magnetically soft pole pieces and the magnetic field is orientated from one pole to the other, and the second being Halbach ring magnets, also called cylindrical Halbach arrays, in which multiple blocks of permanent magnetic material are arrayed at positions surrounding the working volume. Other forms of permanent magnet assemblies may be employed and these assemblies may produce a magnetic field in their working volume that is transverse to the access geometry.

[0009] The magnetic field in the working volume may vary in strength and direction as a function of location in the working volume. The field may be said to have a spatial dependence throughout the working volume. The spatial dependence may be characterized by determining the field strength at a collection of locations in the working volume. This data is often called a field map.

[0010] In most devices that rely on magnetic fields, the field distribution is generally uniform, with variations in the field strength and direction 5% of less throughout the working volume. Hence the magnetic field in the working volume may be said to have a well-defined direction. Many devices that rely on magnetic fields for their operation benefit from improvements in the uniformity of the magnetic field in their working volume. The benefit may be in the speed or accuracy of the measurement the device makes, or a reduction in the size, weight, and cost of the device, or a different benefit. Improvements in the uniformity of the magnetic field are typically achieved by the alteration of the structure of the magnetic field source itself or via the introduction of additional sources of magnetic field that can be selected or adjusted to affect the improvement. These additional sources of magnetic field are referred to in the art as shims. When the additional sources of magnetic field do not require electrical current for the production of magnetic fields, the sources are referred to as passive shims.

[0011] It may also be the case that the magnetic field in a device is designed to have a particular degree and shape of non-uniformity. One example of this is a device that requires that the field strength vary linearly as a function of distance along a particular direction in space. For devices requiring a field with a particular non-uniformity, the use of shims can improve fidelity of the actual field with respect to the desired field non-uniformity.

[0012] Passive shims may be made from magnetically hard materials (for example, permanent magnetic materials) or magnetically soft materials. Magnetically soft materials are magnetized only when subject to a magnetic field. A piece or region of magnetically hard material may be described as having a magnetic moment which is fixed (or nearly fixed) in strength and orientation with respect to that piece of hard material. The magnetic moment may be considered to give rise to a magnetic field in the vicinity of the piece of magnetically hard material.

[0013] Once it is magnetized, a piece or region of magnetically soft material may similarly be described as having a magnetic moment that creates a field in its vicinity. In the case of the soft material, the strength of the magnet moment and field it produces depend on the strength of the magnetic field in which the piece is placed. Also, the orientation of the magnetic moment (and the resulting magnetic field) depends on the orientation of the magnetic field in which the piece is placed. The magnetic field due to the magnetic moment of the magnetized piece of magnetically soft material adds to the field in which the piece is placed, giving rise to a total magnetic field in the vicinity of the piece of magnetically soft material.

[0014] The orientation of the magnetic moment induced in a piece of magnetically soft material may be in the direction of the magnetic field in which it is placed. If this is true no matter the angular disposition of the piece in the magnetic field, the magnetically soft material is said to be isotropic. A piece of magnetically soft material may be anisotropic, in which case the orientation of the induced magnetization may not be in the direction of the magnetic field in which it is placed. One source of anisotropy can be the overall shape of the piece of magnetically soft material. A piece of such material may be preferentially magnetized in the direction of the longest dimension of the piece. For example , in the case of a sheet or thin foil of magnetically soft material, the strongly preferred direction for magnetization is in the plane of the sheet or foil. This is the basis for the use of sheets or foils of magnetically soft material as magnetic shields, as is known in the art.

[0015] One example of a magnetically isotropic material is a compound material consisting of a nonmagnetic matrix containing a powder of a magnetically soft material dispersed within it. The powder particles may be dispersed in a random way, including with random orientations, so that a small but finite piece of the composite materials is magnetized isotropically when exposed to a magnetic field. The particles may be small enough that any piece of the composite material useful for passive shimming is effectively isotropic.

[0016] Any magnetized piece of material may be said to have a magnetic moment density throughout its volume. The concept of density is particularly useful for distributions of magnet moment that are continuous in space. A uniformly magnetized piece has the same value of magnetic moment density throughout its volume. The magnetic moment density of a non-uniformly magnetized piece may have a value that varies as a function of location in the piece. The total magnetic moment of a region with a magnetic moment density may be calculated by summing or integrating the magnetic moment density as a function of location throughout that region using methods known in the art. A region of non-zero magnetic moment density can be said to create a magnetic field in its vicinity.

[0017] The design of a passive shim may be specified by stating its magnetic moment density as a function of location within the shim structure. The locations may be specified by establishing a mathematical coordinate system for the shim structure and writing the magnetic moment density as a function of those coordinates. The coordinates for the shim structure may be fully three dimensional. The coordinates may instead be two dimensional and specify the locations on a surface of the shim structure. Specifications of the shim structure that are expressed as mathematical functions of coordinates may be considered to be continuousvalued.

[0018] Another way to specify the design of a passive shim structure is to divide the shim structure into separate finite regions and specify the total magnetic moment that should be present in each region. In this case, the shim design may be expressed as a list of named or numbered regions together with the total magnetic moment to be placed in each region. Such a shim structure specification would be considered to be piece-wise continuous.

[0019] The invention disclosed herein and distinguished from known art is aimed at the use of magnetically soft materials to shim magnets. The invention may be applied to magnets with transverse fields. The quintessential example of such a magnet is a permanent magnet assembly of the Halbach ring magnet design, although other permanent magnet designs and electromagnets may also benefit from the invention. In the description below, the focus will be on Halbach ring magnets; however, the term magnet should be interpreted in the disclosure and claims to apply to any magnetic field generator.

[0020] The Halbach ring magnet design is popular due to its efficient use of magnet material, leading to compact and light magnets with relatively strong magnetic fields. Ideal Halbach ring magnets would also have very high homogeneity. However, practical considerations such as magnetic material variability, reasonable structural tolerances, finite length designs, and others, result in a field uniformity lower than desired. Field homogeneity can be improved by adjusting the physical position of the magnetic material blocks used to construct the magnet. These adjustments can make large corrections to the magnetic field. However, these adjustments must be provided for in the magnet mechanical design, leading to increased magnet production costs. The adjustments are often laborious and may require very fine control over the positions of the magnet blocks. Thus, while effective for improving the magnetic field, the adjustment of the physical positions of the magnet blocks may render the resulting magnet too expensive to be practical.

[0021] A further method for improving the magnet field homogeneity in a Halbach ring magnet is by passive shimming via the placement of magnetic material in or around the ring magnet structure. Typically, the additional magnetic material is attached to a carrier structure that is then placed into the cylindrical interior space of the ring magnet. Most commonly, the additional magnetic material is in the form of small permanent magnets that are inserted into holes or pockets in a cylindrical carrier that is placed so that it lies just inside the inner surface of the ring magnet. The placement of the small permanent magnets effectively creates a magnetic moment distribution in the carrier. There are typically hundreds of pockets or holes, each of which (or each small subset of which) may be referred to as a location in the passive shim structure.

[0022] The assembly of this passive shim is labor intensive and adds to the cost of the final magnet structure. The calculation of the shim design is typically performed via the linear programming method, in which the impact of occupying each individual location the carrier structure must be included. The calculation proceeds by determining the amount of material (the total magnetic moment) that should be placed at each location that improves the uniformity of the total magnetic field. In a typical linear programming calculation, there are hundreds of locations, each of which may need to be fractionally occupied. The practically achievable level of field homogeneity may be limited by the complexity of the shim structure that can be constructed reliably.

[0023] The same challenges are faced when shimming permanent magnet assemblies of designs other than the Halbach ring magnet design. It may be difficult and time consuming to adjust the positions of the magnet assembly components. The practically achievable improvements by passive shimming via the placement of additional magnetic field sources may be limited.

[0024] Additive manufacturing enables the production of intricate solid objects using a variety of materials. Plastic filaments containing magnetizable materials are commercially available. These filaments can be printed using simple, readily available Fused Filament Fabrication (also known as Fused Deposition Modeling) 3D printers. Although not required for the practice of the invention, additive manufacturing is preferred for constructing the passive shim because it overcomes the limitations associated with shim design complexity, enabling shim design methodologies that result in shim designs that heretofore would have been considered unbuildable.

[0025] 3D printing has previously been used to shim a permanent magnet assembly (Jafarzadeh et al., Adv. Eng. Mater., volume 25, 2201790 (2023)). In that work, a filament containing particles of a magnetically hard material was created. Four pieces of the shim were printed and each was separately magnetized in a magnetizing apparatus external to and separate from the magnet assembly. The now permanently magnetized blocks of the passive shim were installed into the magnet assembly. By contrast, to take full advantage of the 3D printing method, the invention disclosed here uses magnetically soft materials, which eliminates the separate external magnetization step. As a further advantage, the passive shim device according to the invention may be produced as a single piece, whereas the use of magnetically hard materials requires separate pieces which can be separately externally magnetized. The use of magnetically soft materials may be expected to allow more precise adjustment of the spatial dependence of a magnetic field.

[0026] Magnetically soft materials have been used to shim magnets in the past. For example, US 10739428 to McDowell teaches the use of magnetic ink to shim magnet assemblies by placing ink on planar surfaces perpendicular to the magnetic field in the working volume. That shim design does not adopt the form of a tubular shell. US5045794 to Dorri teaches the design methodology for shimming a superconducting MRI magnet by placing small pieces magnetically soft materials at locations in a cylindrical arrangement surrounding the working volume. In that case, the material is magnetized by the superconducting magnet in the direction parallel to the long axis of the cylinder.

[0027] US6897750 to Neuberth teaches the use of a hole-containing metal foil or sheet in a generally cylindrical arrangement for adjusting a magnetic field of a magnet assembly. Neuberth teaches the use of such a patterned cylinder for use in a superconducting magnet wherein the magnetic field is parallel to the axis of the cylinder. The field adjustment device of Neuberth would fail when the placed so that its cylindrical axis was perpendicular to the magnetic field in the working volume due to the impact of the shape of the foils on the orientation of the induced magnetic moment. A foil or sheet of metal is not magnetically isotropic. A metal sheet or foil is preferentially magnetized in a direction of the plane of the sheet or foil. A tubular structure of a sheet or foil, when placed in a magnetic field with its axis perpendicular to the field (as disclosed hereinbelow), would serve to reduce or even eliminate the magnetic field in the interior of the tube. As is known in the art, a tube made from a sheet or tube can be used in this orientation to shield the region inside the tube from a magnetic field.

[0028] Patent Application Publication No. US 2014 / 0125342 to Boliver teaches tubular structures with symmetric patterns of holes or recesses that can correct for particular mathematical field errors in a magnetic field produced by a superconducting solenoid. They teach that the cylinder is oriented with its axis parallel to the magnetic field.

[0029] US 9778334 to Mallet teaches the use of pairs of nonmagnetic tubes carrying annularly symmetric regions of magnetically soft material to provide an adjustable correction to the magnetic field interior to the tubes. They teach the use of metal sheet stock in the construction of the pairs. The tubes are oriented with their axis parallel to the magnetic field and their position is adjusted along the axis to supply the required strength of the correction field. As discussed above, these tubes carrying patterns of sheet stock would not be magnetized isotropically if the tubes were oriented with their axis perpendicular to the field.

[0030] The prior art concerning tubular passive shims containing soft magnetic materials does not recognize the need for isotropic materials. This limits their use to situations where the shim tube axis is oriented parallel to the magnetic field of the magnet assembly. This orientation is impractical for typical permanent magnet assemblies since a tubular shim oriented along the magnetic field would block the access passage into the working volume of the magnet. It is the object of the present invention to overcome drawbacks in the known art by providing a shim structure that is practical for use with typical permanent magnet assemblies.

[0031] SUMMARY OF THE INVENTION

[0032] The invention disclosed herein includes an apparatus for altering the spatial dependence of the magnetic field in the working volume of a magnet assembly, the apparatus having the form of a generally tubular shell, there being magnetically soft and isotropic material distributed non-uniformly in or on the shell, the shell being placed into the magnetic assembly so that it is oriented with its axis perpendicular to the direction of the magnetic field in the working volume, whereby the magnetically soft material becomes magnetized in the direction of the magnetic field and alters the total magnetic field in the working volume.

[0033] BRIEF DESCRIPTION OF THE DRAWINGS

[0034] FIG. 1 A shows a Halbach ring magnet design in isometric view;

[0035] FIG. IB shows a Halbach ring magnet design in a cross sectional view;

[0036] FIG. 1C shows an H-magnet design in isometric view;

[0037] FIG. ID shows an H-magnet design in a cross sectional view;

[0038] FIG. IE shows a C-magnet design in isometric view;

[0039] FIG. IF shows a C-magnet design in a cross sectional view;

[0040] FIG. 2A depicts a tubular shell with a cylindrical cross section;

[0041] FIG. 2B depicts a tubular shell with an elliptical cross section;

[0042] FIG. 2C depicts a tubular shell with a rectangular cross section;

[0043] FIG. 2D depicts a tubular shell with a cross section that is non-uniform along its length;

[0044] FIG. 2E depicts a tubular shell with a non-uniform wall thickness;

[0045] FIG. 2F depicts a solid cylinder inscribed by a tubular shell;

[0046] FIG. 3 A shows a tubular shell modified by the removal of material, leaving holes;

[0047] FIG. 3B shows a tubular shell modified by the addition and removal of material;

[0048] FIG. 3C shows a tubular shell design calling for regions positive and negative magnetic moment density;

[0049] FIG. 3D shows a tubular shell design calling for isolated regions of positive and negative magnetic moment density;

[0050] FIG. 4 is a graph showing an example of field map data;

[0051] FIG. 5 A is a diagram showing coordinate systems and methods for specifying passive shims and basic patterns; FIG 5B shows a flattened planar version of a shim design coordinate system;

[0052] FIG. 6A diagrams an example of a basic pattern;

[0053] FIG. 6B diagrams a different example of a basic pattern;

[0054] FIG. 6C diagrams a further different example of a basic pattern;

[0055] FIG. 7 provides a schematic of the relationship between a basic pattern and an associated magnetic field;

[0056] FIG. 8A provides a schematic of the relationship between a basic pattern and an associated magnetic field;

[0057] FIG. 8B provides a schematic of the relationship between a different basic pattern and an associated magnetic field;

[0058] FIG. 8C provides a schematic of the relationship between a further different basic pattern and an associated magnetic field; and

[0059] FIG. 8D is a schematic representation of the process of using basic patterns to develop a passive shim design.

[0060] DETAILED DESCRIPTION

[0061] FIGS. 1 A-1F present three examples of magnet designs together with which the invention may be advantageously practiced. A Halbach ring magnet design is shown in plan 2 perspective in FIG. 1 A and in cross sectional 10 perspective in FIG. IB. The segments 3, 11 of the typical Halbach ring magnet construction are shown. The arrow 5, 13 shows the direction of the magnetic field in the working volume 4, 12. The access passage into the working volume 4, 12 is cylindrical in overall shape and is depicted with dashed lines 6, 14. The axis of the access passage is shown by the arrow 7 on the plan view and the circled dot 15 on the cross section. The circled dot symbol shows that the axis vector points out of the page. The axis of the access passage is perpendicular to the magnetic field direction for the Halbach ring magnet design.

[0062] An H-magnet design is shown in both plan 20 perspective in FIG. 1C and cross sectional 30 perspective in FIG. ID. The frame 21, 31 and pole pieces 22, 32 of the magnet are shown. The arrow 24, 34 shows the direction of the magnetic field in the working volume 23, 33. The access passage into the working volume 23, 33 is an elongated rectangular prism in overall shape and is depicted with dashed lines 25, 35. The axis of the access passage is shown by the arrow 26 on the plan view and the circled dot 36 on the cross section. The circled dot symbol shows that the axis vector points out of the page. The axis of the access passage is perpendicular to the magnetic field direction for the H-magnet design.

[0063] A C-magnet design is shown in both plan 40 perspective in FIG. IE and cross sectional 50 perspective in FIG. IF. The frame 41, 51 and pole pieces 42, 52 of the magnet are shown. The arrow 44, 54 shows the direction of the magnetic field in the working volume 43, 53. The access passage into the working volume 43, 53 is planar in overall shape and is depicted with dashed lines 45, 55. The normal vector to the planar access geometry is shown by the arrow 46, 56. The normal vector is parallel to the magnetic field direction for the C-magnet design, which means that the magnetic field is perpendicular to the planar access geometry.

[0064] FIG. 2A shows a preferred embodiment of the invention, in which the generally tubular shell may be cylindrical 60 in cross section. The shell may instead be elliptical 62 as shown in FIG. 2B, or rectangular 64 as shown in FIG. 2C, or irregular 68 in cross section as shown in FIG. 2E. The cross section may be non-uniform along the length of the tubular shell 66 as shown in FIG 2D. The wall thickness may not be uniform around the circumferential dimension of the shell 70.

[0065] The tubular shell 71 may inscribe a solid cylinder 72 as shown in FIG. 2F. The region of space enclosed by the inscribed cylinder may define the interior of the shell. The inscribed cylinder’s axis 73 may define the axis 61, 63, 65, 67, 69 of the tubular shell. The tubular shell may be longer in the direction of its axis than in either of the directions orthogonal to the axis.

[0066] As depicted in FIG. 3 A, the shell 80 may have regions that are modified by removing material thereby leaving a hole or void 81 in the shell. In FIG. 3B, the shell 85 may have regions that are modified by adding material 86 to the shell, thereby increasing its thickness in those regions. The shell 85 may have regions that are modified by removing material 87, thereby decreasing the thickness of the shell in those regions. Regardless of these or similar modifications, the structure is still considered a generally tubular shell for the purposes of the invention. The tubular shell may be made from a magnetically soft material. The tubular shell may be a non-magnetic support structure that can carry magnetically soft material. The shell may be constructed from a combination of magnetic and non-magnetic materials. The non-uniform distribution of magnetically soft material may be created by adding or subtracting magnetically soft materials at various locations on the tubular shell. The addition or subtraction of material may make the thickness of the shell wall non-uniform. The subtraction of material may create a hole through the side of the shell. The tubular shell may be initially created with the non-uniform thickness of the shell wall already present. The non- uniform distribution of the magnetically soft material may be created by using more than one material each with a distinct magnetic moment density value. One of the materials may have a magnetic moment density of zero. The non-uniform distribution may be created by depositing or affixing different amounts of magnetic material onto the tubular shell. In some cases, the deposited material may not substantially change the overall thickness of the shell wall. The non-uniform distribution of magnetically soft material may be created by constructing the tubular shell out of a non-magnetic material that contains within it a controllable concentration of a magnetically soft material. An example of such a material is a powder of magnetically soft particles dispersed in a plastic material. During construction of the shell, the concentration of the magnetically soft material may be controlled so that desired distribution is achieved.

[0067] The magnetically soft material that is non-uniformly distributed may be an isotropic material so that it is magnetized in the direction of the magnetic field to which it is exposed. The magnetically soft material may be free of shape anisotropy effects so that the shape of the magnetically soft material does not influence the direction in which it may become magnetized.

[0068] The non-uniform distribution of magnetically soft material may be a piece-wise constant distribution. The distribution may be a continuously varying function of location in or on the tubular structure. The distribution may be piece-wise constant in some regions and continuously varying in other regions. The distribution may be such that regions of the tubular structure have no magnetically soft material. The distribution may be derived from mathematical distributions that have a well-defined symmetry with respect to the center of the working volume. The distribution may be derived from a set of mathematical distributions that overlap. The tubular shell with a non-uniform distribution of magnetically soft materials may be placed into the magnet assembly’s magnetic field so that it becomes magnetized. The modified tube may be positioned so that its axis is perpendicular to the magnetic field in the working volume. In the magnetic field, the different regions of the tubular shell may carry different strengths of magnetic moment. The magnetic moments of the magnetically soft material create a field in the working volume, thereby contributing to the spatial dependence of the total field in the working volume. If the pattern of magnetic moment strength throughout the tube is appropriate, then the total field in the working volume is adjusted in an advantageous way.

[0069] The tubular shell may be placed into the magnet assembly as a single cohesive or integral part. The tubular shell may surround the working volume in a general way. The working volume may be fully inside the volume of space defined by a solid cylinder inscribed by the tubular shell. The tubular shell may have holes and voids so that it only partially surrounds the working volume. The tubular shell may be installed into the magnet assembly in such a way that it never enters into the working volume. Nevertheless, when a shell is placed into the magnetic assembly, the magnetically soft and isotropic material becomes magnetized and thereby alters the total magnetic field in the working volume.

[0070] In a preferred embodiment, the modified tube is produced using an additive manufacturing technique. For one example, a filament containing magnetically soft particles may be used in a standard fused filament fabrication 3D printer. In this case, the entire volume of the tubular structure may be magnetizable, and the distribution of magnetically soft material in the tubular shell may be created by varying the wall thickness of the shell. Some regions of the shell may have a thicker wall and some may have a thinner wall.

[0071] The passive shim may be produced by printing with magnetic ink. Aversion of this approach is to start with a non-magnetic tubular shell. The non-uniform distribution of magnetically soft material on the tubular shell may be created by depositing magnetic ink directly on the shell in a pattern such that some regions of the shell receive more ink and some less ink. An inkjet printing head may be used to print the magnetic ink directly onto the tube. The magnetic ink may be printed onto a flexible substrate that is then affixed to the tube. Standard paper may be used as a flexible substrate. Magnetic ink may also be printed or affixed onto a magnetic tubular shell, for example, a passive shim produced using three dimensional printing. Other magnetically soft and isotropic materials may be employed. These may be formed into a passive shim utilizing any method appropriate to the material.

[0072] The invention disclosed herein includes a method for adjusting the spatial dependence of the magnetic field in the working volume of a magnet assembly, the method consisting of measuring the magnetic field as a function of location in the working volume, choosing a generally tubular shell structure, choosing a set of basis patterns that each specify a distribution of magnetic moment in or on the chosen tubular shell, associating each of the basis patterns with an associated magnetic field, decomposing the measured magnetic field spatial dependence into a linear combination of the associated magnetic fields, forming a corresponding linear combination of the basis patterns to form a shim design, constructing a tubular passive shim by realizing the design, and positioning the tubular shell in the magnet assembly so that the axis of the tube is perpendicular to the direction of the magnetic field in the working volume.

[0073] A specification for the distribution of magnetically soft material in the tubular passive shim may be called the design of the passive shim. The design may be realized as a physical passive shim by any means capable of creating the distribution specified by the design. The design may take the form of a list of regions of the tubular shell and the amount of material to be located in each region. The design may take the form of a mathematical function of three- dimensional spatial coordinates that specifies the magnetic moment density throughout the volume of the passive shim. Alternatively, the design may take the form of a mathematical function of two spatial coordinates that define a location on the surface of the tube. The function may specify a two-dimensional magnetic moment density at each location on the surface of the tube. Other methods and forms may be adopted for expressing the design of the passive shim.

[0074] Finding an appropriate design for a passive shim is a central problem for the task of improving the quality of magnetic fields. In a preferred implementation of the invention disclosed herein, the spatial dependence of the magnetic field in the working volume of a magnetic assembly is characterized. The characterization may be done by field mapping. The field map data may be acquired using a point sensor that is moved from location to location in the working volume with a field measurement acquired at each location. The point sensor may be a Hall Probe. The point sensor may be a small nuclear magnetic resonance probe. The field measurements may be acquired by gradient methods or by magnetic resonance imaging methods, as are known in the art. A visualization of a field map is given in FIG. 4. The map data are shown as points 172 plotted with respect to two axes, the field values 171 versus the map data point number 170.

[0075] The physical structure of the passive shim may be determined by choosing a generally tubular shell structure for the passive shim. The shell may have a cylindrical cross section. It may have a rectangular, square, or triangular cross section. The cross section may be of any shape, including a general shape. The cross section may not be uniform along the length of the shell. The shell may be hollow. The shell may be such that it inscribes a solid cylinder. The inscribed cylinder’s axis of symmetry may define the axis of the chosen tubular shell structure.

[0076] The design may be found by considering a set of fundamental patterns that act as building blocks for the design. The fundamental patterns may be called basis patterns. The set of fundamental patterns may be called the basis set. The basis patterns each specify a distribution of magnetic moment density that is expressed in the same way as the design. A linear combination of these basis patterns can be formed to give the design of the passive shim. For the first example described above, the basis patterns could each specify the tube wall thickness as a function of the two-dimensional surface coordinates and the linear combination will be the algebraic sum of the thicknesses at each position on the tube. The algebraic sum will be the design, and a 3D printer would then be programmed to produce the tubular shell with different wall thicknesses at various locations according to the design. For the second example described above, the basis patterns could each be defined by the particular pattern of ink deposition amounts across the surface of the tube or the paper, and the linear combination would be the algebraic sum of the deposition amounts at each location on the surface. The passive shim could be produced by printing total sum deposition amount at each location on the surface of the tubular shell.

[0077] FIGS. 5 A and 5B present two examples of how a shim designs and basis patterns may be specified. In FIG. 5A, a generally tubular shell 100 is shown surrounding a working volume 106. The axis of the shell 108 is perpendicular to the direction of the magnetic field 109. A Cartesian coordinate system 107 is shown with its origin at the center of the working volume 106. The Z axis of the coordinate system is parallel to the magnetic field 109. The Y axis is parallel to the axis 108 of the tubular shell, and the X axis is orthogonal to both the Y and Z axes. The coordinate values of the coordinate system 107 can be used to specify locations on or within the tubular shell 100. Alternatively, the surface of the shell 101 may be used to specify a shim design or a basis pattern. To aid in explaining one way to use the surface 101 to specify the shim, points A 102, B 103, C 104, and D 105 are labeled around the circumference of the surface.

[0078] Conceptually, the surface 101 may be cut at A 102 and rolled flat as presented as the structure 120 in FIG. 5B. The labeled points A 121, B 122, C 123, and D 124 on the flat plane 120 correspond to the equivalently labeled points on the tubular form 100. The label A 125 reappears at the top of the flat plane 120 as this is at the other side of the cut at A 102. The label Y=0 126 indicates the centerline of the plane where the value of the Y coordinate of the coordinate system 107 is zero. The labels Ymax 127 and Ymin 128 are also consistent with the coordinate system 107. The correspondence between the labels A 121, B 122, C 123, and D 124 and the coordinate value of the coordinate system 107 are indicated by the labels 129, 130, 131, and 132.

[0079] A wide variety of fundamental basis patterns may be employed, resulting in a wide variety of total shim structures, depending on the application, construction method, needs of a device, or other constraint. A basis pattern may be piece-wise constant, which means that each separate, extended region of the tube surface has a fixed magnetic moment density value. FIGS. 6A-6C presents three examples 140, 150, 160 of piecewise continuous basis patterns, each depiction labeled to correspond to the presentation 120 of such patterns in FIG.5B. The first basis pattern 140 has a region 142 of positive magnetic moment density at locations for which the Y coordinate of the coordinate system 107 has a positive value. The pattern 140 has a region 141 of negative magnetic moment density where Y is negative. The basis pattern 150 has positive 152 and negative 151 regions which correspond to the regions where the product YZ of the Y and Z coordinates 107 is positive and negative, respectively. Basis pattern 160 has a negative value in region 163, a positive value in region 162 and a zero value in regions 161. A basis pattern may be a simple as having two regions with two distinct magnetic moment density values, it may have more regions that each adopt one of two distinct magnetic moment density values, or it may have more regions that each adopt a single value from a set of values.

[0080] A basis pattern may specify that the magnetic moment density varies continuously as a function of location on the tube. An individual pattern may have regions in which it varies continuously and other regions in which it is piece-wise constant. The set of fundamental basis functions may contain members that are fully continuously, members that are fully piece-wise constant, members that are partially continuous and partially piece-wise constant, or any combination of members of these various types.

[0081] It may be advantageous for the basis patterns in the basis set to overlap, although this is not a requirement of the invention. A pair of patterns is said to overlap when they individually specify different magnetic moment values in at least one region in space or one set of coordinates. For example, the basis patterns 140, 150, and 160 depicted in FIGS. 6A-6C all overlap. The basis set may be such that the majority of its member basis patterns overlap with at least one other basis pattern in the basis set. The basis set may be such that a majority of the possible pairs of basis patterns overlap.

[0082] It may be advantageous for the fundamental basis patterns to have forms that have well- defined symmetry properties, although this is not a requirement of the invention. The patterns may be symmetric with respect to the center of the working volume. The symmetries may be defined with respect to a mathematical coordinate system. For example, a Cartesian coordinate system that has its origin at the center of the working volume. The coordinate system may have its Z axis along the direction of the magnetic field of the magnet assembly, its Y axis along the axis of the tubular structure, and the X axis orthogonal to the Z and Y axes may be used. One example of a basis pattern with a well-defined symmetry would be a pattern with a single positive value of magnetic moment density at all locations for which the Y coordinate is positive, and a negative value of equal absolute value at all locations where the Y coordinate is negative. Such a basis pattern is depicted 140 in FIG. 6A. A related example of a well-defined symmetry would be a distribution of magnetic moment density such that the density is proportional to the signed value of the Y coordinate of the position on the tube. A more complicated example of a well-defined mathematical symmetry would be a distribution of magnetic moment density that is proportional to the product XZ of the location on the surface of the tube. Any distribution of magnetic moment density that is proportional to a mathematical function of the coordinates X, Y and Z may define a basis pattern that has a well-defined mathematical symmetry. It will be recognized that the basis patterns 140, 150, and 160 depicted in FIGS. 6A-6C are all symmetric as defined for the purposes of the invention.

[0083] Those skilled in the art of magnetic resonance may recognize that a set of symmetric basis patterns may be analogous to shim designs that produce magnetic field adjustment patterns corresponding to the real-valued spherical harmonics. The real-valued spherical harmonics have similarly well-defined mathematical symmetries.

[0084] The number of fundamental basis patterns included in the linear combination to form the design of the passive shim may be a small number like two or three. The number may be larger, for example eight, fifteen, or twenty four, or any other number sufficient to achieve the required degree of adjustment to the magnetic field of the magnet assembly.

[0085] The mathematical pattern of a basis set may call for negative magnetic moment values at some locations. FIG. 3C shows a visualization of a basis pattern 82 having both positive 83 and negative 84 magnetic moment values. Since an isotropic magnetically soft passive shim material is always magnetized in the direction of the magnetic field of the magnet assembly, the induced magnetic moment is always positive. The negative values of a basis set pattern may be realized by starting with magnetically soft material in a location and then removing it. An example is provided in FIG. 3D, wherein the passive shim 85 having a region of increased 86 wall thickness and a region of decreased 87 wall thickness corresponds to a depiction of a shim design 88 having a region of positive value 89 and a region of negative value 90 of magnetic moment density. The removal of material in the realized passive shim is conceptually equivalent to the positioning of negatively magnetized material at the location of the removal.

[0086] For example, the tubular passive shim structure may begin from a cylindrical shell of magnetically soft material of uniform wall thickness. To realize the basis pattern 82 described above with positive magnetic moments at Y>0 and negative moments at Y<0, the uniform shell can be modified by adding material at locations satisfying Y>0 by increasing the wall thickness there and also removing material at Y<0 by reducing the wall thickness for those locations. The originally unform shell of magnetically soft material forms a background for the development of the realizable passive shim. A pattern of uniformly distributed magnetically soft material may be included as one of the members of the basis set of fundamental basis patterns.

[0087] For any one of the fundamental basis patterns, there is an associated magnetic field. The associated field is the magnetic field that would be produced if the basis pattern itself was used as a shim design which was realized in an actual passive shim and was placed into the magnetic field of a magnet assembly. FIG. 7 depicts the association relationship 181 between a basis pattern 180 and the magnetic field 182 such a basis pattern might create in the working volume. The association 181 between the basis pattern 180 and the magnetic field its realization would produce 182 may be determined by realizing the fundamental basic pattern, for example, by printing it, and then measuring the field it creates in the working volume of the magnet assembly. It may also be possible to calculate the field that a realization of the basis pattern would create in the working volume and thereby establish the association via theoretical methods. Any method that can determine the expected magnetic field produced by a realization of each of the basis set member patterns may be utilized to find the associated magnetic fields. The set of associated magnetic fields corresponding to a chosen set of fundamental basis patterns may be used to design the total shim structure.

[0088] The set of associated magnetic fields may be orthogonal. For the set to be orthogonal, any pair of distinct fields selected from the set must be mathematically orthogonal, as is known in the art. When each field in the set is expressed as a mathematical function of three- dimensional space, the mathematical integral of the product of the two fields in a pair will evaluate to zero over an integration domain corresponding to the working volume. The fields may be approximately or largely orthogonal, by which is meant that the integral may evaluate to a relatively small number. The number may be small when its absolute value is 10% or less than the result of integrating one of the paired functions after squaring it. The associated magnetic fields may be largely proportional to the real-space spherical harmonics, for example.

[0089] A preferred method for determining the design of the total shim structure is to first measure the magnetic field in the working volume. It is advantageous to determine the strength of the magnetic field at a number of points throughout the working volume where the number of points is larger than the number of fundamental basis patterns in the chosen basis set. The difference between the measured field value and desired field value at each location in the working volume is the error field. The error field may be visualized as a field map, such as the data 172 plotted in FIG. 4.

[0090] The linear combination of the set of associated magnetic fields that best counteracts the error fields may be found. In FIGS. 8A-8C, three basis patterns are depicted together with their associated magnetic fields, visualized as field map plots. The first basis pattern 190 is associated 192 with magnetic field 191. The second basis pattern 193 is associated 195 with magnetic field 194. The third basis pattern 196 is associated 198 with magnetic field 197. The linear combination 200 of these three fields can be formed to give a total magnetic field 203 depicted in map form. Least squares methods may be used to find the coefficients of the linear combination that results in a total magnetic field that best compensates for the error field measured for the magnetic field to be adjusted. The coefficients may be found by an integration method in which the product of the field error and one of the associated fields is calculated. Singular-value-decomposition based methods may be used to find the coefficients. Linear programming methods may be used to find the coefficients. In general, there are many methods known in the art that may be used to find the best linear combination to correct the error fields, and any of these may be employed.

[0091] FIG. 8D depicts the coefficients of this linear combination 200 being applied to form a linear sum 199 of the corresponding fundamental basis patterns 190, 193, 196, resulting in the design of a passive shim 201. In this example, the design 201 would have regions 202 over which it would be piece-wise constant. The values of the coefficients found during the formation of the optimal linear combination 200 may be scaled as a group or individually to create the values needed to form the combination 199 of basis functions to determine the shim design.

[0092] The passive shim specified by the design can be realized via a construction method. The passive shim may be constructed using a magnetically soft and isotropic material. It may be constructed using an additive manufacturing method. The construction may result in a tubular shell having a variable wall thickness. The passive shim may have holes or voids. The construction may consist of a non-magnetic tubular shell to which magnetic material is added.

[0093] The constructed passive shim may be positioned into the magnet assembly so that the axis of the passive shim is perpendicular to the magnetic field in the working volume. The magnetically soft and isotropic material in the passive shim may become magnetized in the direction of the magnetic field in which it is placed. The tubular form of the passive shim may generally surround the working volume of the magnet assembly.

[0094] A specific method, with elaborations, for implementing the invention has been described in detail. The apparatus may be produced by other methods, including methods that do not utilize basis patterns. Those skilled in the art will understand how to employ these methods to any particular magnet.

Claims

CLAIMSI claim:

1. An apparatus for altering the spatial dependence of the magnetic field distribution in the working volume of a magnet assembly, comprising a generally tubular shell of magnetically soft and isotropic material wherein: a distribution of the magnetically soft and isotropic material is non-uniform in the shell; and the shell is placeable into the magnetic assembly so that the shell is oriented with its axis perpendicular to the direction of the magnetic field in the working volume; whereby when the shell is placed into the magnetic assembly the magnetically soft and isotropic material becomes magnetized and alters the total magnetic field in the working volume.

2. The apparatus of claim 1 wherein the shell has a cylindrical shape.

3. The apparatus of claim 1 wherein the distribution of magnetically soft and isotropic material is a continuous distribution.

4. The apparatus of claim 1 wherein the distribution of magnetically soft and isotropic material is a piece-wise constant distribution.

5. The apparatus of claim 1 wherein the distribution of magnetically soft and isotropic material is established by variations in the thickness of the shell as a function of position on the shell.

6. The apparatus of claim 1 wherein the distribution of magnetically soft and isotropic material is established by variations in the amount of material added to or removed from the shell as a function of position on the shell.

7. The apparatus of claim 1 wherein the magnetically soft and isotropic material comprises magnetically soft particles dispersed in a non-magnetic medium.

8. The apparatus of claim 1 wherein the shell is created using an additive manufacturing method.

9. The apparatus of claim 1 wherein the shell comprises printing on a substrate affixed onto a non-magnetic tubular shell.

10. The apparatus of claim 1 wherein the shell, when placed into the magnetic assembly, surrounds the working volume.

11. The apparatus of claim 1 wherein when the magnetically soft and isotropic material alters the total magnetic field, an alteration in the total magnetic field improves the uniformity of the field in the working volume.

12. A method for adjusting the spatial dependence of the magnetic field in the working volume of a magnet assembly, the method comprising the steps of: measuring the magnetic field as a function of location in the working volume; choosing a tubular shell structure defining a volume of space for containing a field adjusting material; choosing a set of basis patterns that each specify a distribution of magnetic moment in the chosen tubular shell structure; associating each of the basis patterns with an associated magnetic field; decomposing a measured magnetic field spatial dependence into a linear combination of the associated magnetic fields; forming a corresponding linear combination of the basis patterns to form a shim design pattern; constructing a tubular shim by locating magnetically soft and isotropic material throughout the chosen tubular shell structure as specified by the shim design pattern; and positioning the tubular shim in the magnet assembly so that the axis of the tube is perpendicular to the direction of the magnetic field in the working volume.

13. The method of claim 12 wherein choosing a tubular shell structure comprises choosing a hollow cylinder.

14. The method of claim 12, further comprising choosing a set of basis patterns in which at least one member of the set overlaps with at least one other member of the set.

15. The method of claim 12, further comprising choosing a set of basis patterns in which at least one member of the set is mathematically symmetric with respect to the center of the working volume.

16. The method of claim 12 wherein choosing a set of basis patterns further comprises choosing at least one continuous basis pattern.

17. The method of claim 12 wherein choosing a set of basis patterns further comprises choosing at least one piece-wise constant basis pattern.

18. The method of claim 12, further comprising choosing a set of basis patterns for which the associated magnetic fields form a mathematically orthogonal set.

19. The method of claim 12, further comprising providing associated fields that are proportional to real-space spherical harmonic functions.

20. The method of claim 12 wherein associating each of the basis patterns with a corresponding magnetic field comprises constructing one or more of the basic patterns into the tubular shim, positioning the tubular shim in the magnet assembly, and measuring the field produced in the working volume of the magnet assembly.

21. The method of claim 12 wherein decomposing a measured magnetic field spatial dependence comprises using a least-squares fitting method.

22. The method of claim 12 wherein decomposing a measured magnetic field spatial dependence comprises using an integration method.

23. The method of claim 12 wherein constructing the tubular shim comprises utilizing a magnetically soft and isotropic material.

24. The method of claim 12 wherein constructing the tubular shim comprises using an additive manufacturing process.

25. The method of claim 12 wherein constructing the tubular shim comprises printing onto a flexible substrate and affixing the substrate onto a non-magnetic tubular shell structure.

26. The method of claim 12 wherein constructing the tubular shim comprises adding or subtracting material from a structure made of magnetically soft and isotropic material.

27. The method of claim 12 wherein constructing the tubular shim comprises constructing a single piece.

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