Multi-axis magnetic field vector generation

Abstract

A method, a system, and a computer program product are disclosed. The method includes obtaining a configuration of a dipole line (DL) magnet and selecting a magnetic field vector to be generated. The method also includes determining an orientation of the DL magnet to generate the magnetic field vector based on the configuration.

Description

Technical Field

[0001] The present disclosure relates to magnetic field vector generation, and more particularly to magnetic field vector generation using a rotary parallel dipole line magnet.

Background Art

[0002] The generation of magnetic field vectors (e.g., multi-axis magnetic field vectors) in one to three spatial dimensions has applications in a wide range of scientific and engineering fields. For example, modern technological uses of multi-axis magnetic field vectors can include magnetic resonance imaging (MRI), magnetic particle imaging (MPI), vibrating sample magnetometry, and analytical techniques such as measurements based on the magnetoresistive effect, Hall effect, Faraday rotation, magneto-optical Kerr effect, ferromagnetic resonance, etc. These applications typically require a strong direct current or alternating current (DC or AC) magnetic field.

Summary of the Invention

[0003] Various embodiments relate to a method including obtaining a configuration of a dipole line (DL) magnet and selecting a magnetic field vector to be generated. The method also includes determining an orientation of the DL magnet to generate the magnetic field vector based on the configuration. One advantage of the disclosed method can include enabling the generation of one to three dimensional magnetic field vectors depending on the configuration. For example, there can be at least one pair of independent / dependent DL magnets, at least two parallel independent DL magnets, three mutually orthogonal independent DL magnets, three independent DL magnets positioned at the vertices of a triangle, etc. It is also possible to determine the maximum torque for generating the magnetic field. In some embodiments, the orientation of the DL magnet can be adjusted based on the magnetic field detected by a Hall sensor. This can advantageously be used to obtain an accurate orientation of the DL magnet.

[0004] Yet another embodiment relates to a system comprising a memory and a processor communicatively coupled to the memory, wherein the processor is configured to execute the method. Yet another embodiment relates to a computer program product comprising a computer-readable storage medium having program instructions embodied thereon, the program instructions being executable by a processor to cause a device to execute the method.

[0005] The above summary is not intended to describe every illustrated embodiment or every implementation of the present disclosure.

[0006] The drawings included in this application are incorporated herein and form a part hereof. The drawings illustrate embodiments of the present disclosure and, together with the specification, serve to explain the principles of the present disclosure. The drawings are merely exemplary of particular embodiments and do not limit the present disclosure.

Brief Description of the Drawings

[0007]

Figure 1A

Figure 1B

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6A

Figure 6B

Figure 7A

Figure 7B

Figure 8

Figure 9

[0008] While the present invention is susceptible to various modifications and alternative forms, specific ones thereof have been shown by way of example in the drawings and will be described in detail. It should be understood, however, that the intention is not to limit the present invention to the specific embodiments described. Rather, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present invention.

[0009] Embodiments of the present invention generally relate to magnetic field vector generation, and more particularly to magnetic field vector generation using a rotary parallel dipole line magnet. While the present disclosure is not necessarily limited to such applications, various aspects of the present disclosure can be understood by considering examples using this context.

[0010] Various embodiments of the present disclosure are described herein with reference to the accompanying drawings, in which like numbers refer to like components. Alternative embodiments may be devised without departing from the scope of the present disclosure. It is noted that various connections and positional relationships (e.g., above, below, adjacent, etc.) are described between elements in the following description and the drawings. These connections or positional relationships or both can be direct or indirect, and the present disclosure is not intended to be limited in this regard. Thus, the coupling of entities can refer to either direct or indirect coupling, and the positional relationship between entities can be direct or indirect. As an example of an indirect positional relationship, a reference herein to forming layer "A" above layer "B" includes a situation where one or more intermediate layers (e.g., layer "C") are between layer "A" and layer "B" as long as the relevant characteristics and functionality of layer "A" and layer "B" are not substantially changed by the intermediate layer(s).

[0011] The following definitions and abbreviations are used for the interpretation of the claims and the specification. As used herein, the terms "comprises", "comprising", "includes", "including", "has", "having", "contains" or "containing" or any other variation thereof are intended to cover non-exclusive inclusion. For example, a composition, mixture, process, method, article, or apparatus that includes a listing of elements is not necessarily limited to only those elements, and can include other elements not expressly listed or inherent to such composition, mixture, process, method, article, or apparatus.

[0012] For the purposes of the following description, the terms "upper", "lower", "right", "left", "vertical", "horizontal", "top", "bottom", and derivatives thereof are to relate to the structures and methods described as oriented in the drawings. The terms "above", "on top of", "over", "upwardly", "positioned above" or "positioned on top of" mean that a first element such as a first structure is present over a second element such as a second structure, and intervening elements such as interface structures may be present between the first and second elements. The term "in direct contact" means that a first element such as a first structure and a second element such as a second structure are connected without an intervening conductive, insulating, or semiconductor layer at the interface of the two elements.

[0013] As used herein, the articles "a" and "an" that precede an element or component are intended to be non-limiting with respect to the number of instances (i.e., occurrences) of the element or component. Thus, "a" or "an" should be read to include one or at least one, and the singular form of an element or component includes the plural unless the number is clearly singular.

[0014] As used herein, the terms "invention" or "the invention" are non-limiting terms and are not intended to refer to any single embodiment of a particular invention, but rather to encompass all possible embodiments or combinations of embodiments described in this specification and the claims or both.

[0015] Unless otherwise indicated, the ranges (e.g., of time, concentration, temperature, etc.) set forth herein include both endpoints and all numbers between the endpoints. Unless otherwise specified, the use of the terms tilde (~) or "about," "substantially," "approximately," "slightly less than," and the like, and variations thereof, are intended to include the degree of error associated with the measurement of a particular quantity based on the equipment available at the time of filing of this application. For example, "about" can include ±8% or 5%, or a range of 2% of a given value, a range of values, or the endpoints of one or more ranges of values. Unless otherwise indicated, the use of such terms in connection with ranges applies to both endpoints of the range (e.g., "about 1 g to 5 g" should be construed as "about 1 g to about 5 g") and, in connection with a list of ranges, to each range in the list (e.g., "about 1 g to 5 g, 5 g to 10 g, etc." should be construed as "about 1 g to about 5 g, about 5 g to about 10 g, etc.").

[0016] Next, referring to an overview of the technologies related to aspects of the present disclosure, the generation of a magnetic field vector has a wide range of applications that can include analytical techniques such as magnetic resonance imaging (MRI), magnetic particle imaging (MPI), vibrating sample magnetometry, and measurements based on the magnetoresistance effect, Hall effect, Faraday rotation, magneto-optical Kerr effect, ferromagnetic resonance, etc. For example, techniques such as Hall effect measurements can be used for semiconductor evaluation. In general, applications involving a magnetic field vector require the generation of a strong direct current or alternating current (DC or AC) magnetic field.

[0017] Conventional techniques for generating a strong magnetic field vector can include using one or more electromagnetic coils such as a Helmholtz coil configuration of a pair of coils. However, coil-based embodiments can require cumbersome setups, cooling systems for large field operation, and expensive power systems. Additionally, electromagnetic coil systems are inherently large inductors, making it difficult to obtain a large magnetic field at high frequencies due to large impedance.

[0018] Embodiments of the present disclosure can eliminate the disadvantages of electromagnetic coil systems by generating a magnetic field vector with a permanent magnet. A permanent magnet, such as a rare earth permanent magnet, can be used, for example, to generate a large magnetic field on the order of approximately 1 tesla or more, and has been used in configurations such as Halbach arrays, double rings, magnetic disks, and parallel dipole line magnets. The use of permanent magnets can provide greater flexibility in the architecture of magnetic field vector generator systems.

[0019] The disclosed technology may include using a dipole line (DL) magnetic configuration to generate a magnetic field vector in one to three spatial dimensions. A DL magnet, also known as an antipole magnet, is a cylindrical permanent magnet having magnetization oriented along its diameter (or transverse magnetization). This magnet can be modeled as a linear distribution of transverse dipoles. A pair of DL magnets having cylindrical axes oriented in the same direction is called a PDL magnet. The PDF magnet pair can act as a diamagnetic trap system that exhibits a camelback confinement potential along the longitudinal axis. In semiconductor measurements, a rotating PDL magnet, also known as a commercial Hall measurement system called a PDL Hall system, can be used to generate a one-dimensional (1D) AC magnetic field.

[0020] In some embodiments, the DL magnet generates a more cost-effective magnetic field vector than an electromagnetic coil. For example, in some embodiments, the DL magnet system does not require the expensive power supply and cooling system of an electromagnetic coil-based system. In addition, the DL magnet system can achieve a strong magnetic field (e.g., about 1 tesla or more) with a more compact setup than a coil-based system. The disclosed DL system can also be adapted to generate both DC and AC fields in one to three dimensions. These properties can enable the use of DL magnets as basic building blocks for numerous applications, including the generation of magnetic field vectors.

[0021] Next, referring to the drawings, like numbers in the drawings represent the same or similar elements, and FIG. 1A is a block diagram showing a magnetic field vector generation environment 100 according to some embodiments of the present disclosure.

[0022] The environment 100 includes a DL magnet system 105 having at least one motor-driven magnet (not shown in FIG. 1A) connected to a motor 120 via a shaft 115. In some embodiments, the motor 120 is a stepper motor. The shaft 115 of the motor 120 can have an attached gearbox (not shown) for adjusting (e.g., increasing) the torque τ in the DL system 105. The environment 100 also includes a computing system 130 (e.g., the computing system 900 shown in FIG. 9) for instrument control, data acquisition, data analysis, etc.

[0023] The components of the computing system 130 are in electrical communication with a Hall sensor 140 that can be used to determine the orientation of the magnets in the DL system 105 and a controller (not shown) for rotating the magnets of the DL system 105 and adjusting the torque via the gearbox / shaft 115. In some embodiments, such as applications including optical Hall measurements for semiconductor device testing, the environment 100 can include components (not shown) for performing Hall measurements, such as a sample stage, a measurement chamber, a light source, a photodetector, etc. The computing system 130 can be used to control an instrument (not shown) having components for source and measurement operations, a switch matrix and buffer amplifier, motor control, magnetic field sensors, temperature control, etc.

[0024] Figure 1B is a schematic diagram showing a DL magnet configuration 101 according to some embodiments of the present disclosure. Configuration 101 includes a cylindrical magnet 110 having a length L and a radius R with a transverse magnetization M. This DL magnet 110 can be an example of a single magnet from a configuration having two or more magnets shown herein. When the length of the magnet 110 is much larger than its radius (L >> R), the magnetic field lines outside the magnet 110 are circular in the xy plane. The magnetic field strength profile at a distance r from the DL magnet 110 exhibits a transition from a line dipole behavior B ~ r in the near-field regime (r < L) -2 to a point dipole behavior B ~ r in the non-near-field regime (r > L). -3 The long dipole line magnet 110 generates a magnetic field

[0025] which can be represented by the following equation

Number

Number

Number

Number

Number

Number

Number

[0026] The magnetic field B in the xy plane can be approximated by the magnetic field due to a long DL magnet (L >> R). Equation 2 gives the magnitude B0 of the magnetic field at a point P on the xy plane as

Equation

Equation

[0027] In the following example, the magnetic field vector can be generated by the DL magnet system 105 using at least two magnets identical to the magnet 110. The magnets can be motor - driven or freely rotatable. Although the motor 120 is not shown in all of the later figures, it will be understood that the motor - driven magnets can be rotated by a motor such as the motor 120 shown in FIG. 1A. In this specification, motor - driven magnets and freely rotatable magnets are also referred to as "independent" magnets and "dependent" magnets, respectively.

[0028] FIG. 2 is a schematic diagram showing a DL magnet configuration 200 that generates a one-dimensional (1D) magnetic field vector according to some embodiments of the present disclosure. The configuration 200 includes an independent magnet 210A and a dependent magnet 210B (collectively magnets 210). The magnets 210 are separated by a distance g. By using the motor 120 to rotate the independent magnet 210A, a one-dimensional (1D) oscillating magnetic field B can be generated. The dependent magnet 210B can rotate freely and reflects the orientation of the motor-driven magnet 210A. The net magnetic field B always aligns in one direction (the x-axis in FIG. 2) because each of the magnets 210 generates an opposing magnetic field in the orthogonal direction (the y-axis in FIG. 2). Rotation of the magnets 210 results in a single harmonic magnetic field B in one direction at the center of the configuration 200. The direction of this 1D oscillating magnetic field B (black block arrow) is oriented in the x-direction and has the following sinusoidal form, i.e., B(t)=B0cosωt (4) where t is time, ω is the oscillation frequency, and the magnitude B0 is given below, i.e.,

Number

[0029] FIG. 3 is a schematic diagram showing a magnet configuration 300 that generates a two-dimensional (2D) magnetic field vector by two independent DL magnets 310A and 310B (collectively magnets 310) according to some embodiments of the present disclosure. The magnets 310 can generate a 2D vector at the center of the configuration 300. The motor-driven magnets 310 are rotated independently at angles θ1 and θ2 to generate a magnetic field vector having an overall field amplitude B within the circle 315 defined by B max <B T having. In the configuration 300, the maximum magnetic field B max at the limit of a long magnet (L>>R) is max is

Number

[0030] In a 1D alternating current (AC) field, β2 = ωt corresponds to the phase of the oscillation. For configuration 300, β2 is

Number

[0031] In configuration 300, the overall magnetic field vector B T = B T The orientations of magnets 310A and 310B (angles θ1 and θ2 respectively) to generate B∠α are given by the following equations 8 and 9 θ1 = -α - β2 (8) θ2 = -2α - θ1 = -α + β2 (9) where α is the polar angle of vector B T with respect to the +x axis.

[0032] To calculate the maximum torque required to rotate the magnet, the unit torque τ0 is given by the following equation 10

Number

[0033] The maximum torque τ max required to generate the magnetic field vector in configuration 300 is given by equation 11

Number

[0034] Figure 4 is a schematic diagram showing a magnet configuration 400 that generates a 2D magnetic field vector by three independent DL magnets 410A, 410B, and 410C (collectively 410) according to some embodiments of the present disclosure. In the example illustrated in this figure, the magnets 410 are positioned at the vertices of an equilateral triangle at a distance r from the center. However, this configuration 400 can be generalized to other triangular configurations (e.g., the magnets 410 are positioned at the vertices of an isosceles triangle). To generate a 2D vector at the center of the configuration 400, the motor-driven magnets 410 can be independently rotated at angles θ1, θ2, and θ3. In configuration 400, a magnetic field can be generated within a circle 415 defined by B max = 3B0. The maximum magnetic field B max generated there can be expressed as

Number

[0035] In configuration 400, when determining the method of generating the magnetic field vector B T = B T ∠α, β3 can be defined as

Number

[0036] The angles of the magnets 410A, 410B, and 410C that generate the magnetic field vector B T = B T ∠α can be found using the following equation θ1 = β3 - α (14)

Number

Number

[0037] The first magnet 410A can be set to rotate simply (linearly with respect to β3). Thereby, the rotation of the other two magnets 410B and 410C, which are important functions of β3, can be suppressed. The maximum torque τ required in the configuration 400 max is

Number

[0038] FIG. 5 is a schematic diagram showing a magnet configuration 500 that generates a 2D magnetic field vector by four independent DL magnets 510A, 510B, 510C, and 510D (collectively 510) according to some embodiments of the present disclosure. In the configuration 500, a magnetic field can be generated within a circle 515 defined by B max = 4B0. To generate a 2D vector at the center of the configuration 500, the motor-driven magnets 510 can be independently rotated at angles θ X1 , θ X2 , θ Y1 , and θ Y2 . The maximum magnetic field B max in the configuration 500 is

Number

[0039] In the configuration 500, β4 can be defined as follows, i.e.,

Number

[0040] In the configuration 500, the angles of the magnets 510 that generate the magnetic field vector B T = B T ∠α are given by the following equations θ X1 = θ X2 = α - β4(20) θ Y1 = θ Y2 = α + β4(21) can be found using

[0041] The maximum torque τ required in configuration 500 max is

Number

[0042] In principle, configuration 500 can be extended to more than four magnets to generate a larger magnetic field because, in the 2D case, B max scales linearly with the number N of magnets (B max = NB0). However, such a configuration requires an additional motor driver.

[0043] FIG. 6A is a schematic diagram showing a magnet configuration 600 that generates a 3D magnetic field by three independent magnets 610A, 610B, and 610C (collectively 610) according to some embodiments of the present disclosure. To generate a 3D magnetic field vector at the center of configuration 600, the motor-driven magnets 610 can be independently rotated at angles θ1, θ2, and θ3. The orientations of the magnets in configuration 600 are orthogonal to each other. Accordingly, the magnetic field vector profile of configuration 600 is due to the superposition of three vectors (B1, B2, and B3) of equal length located on three orthogonal circular planes. The circular planes are not shown in FIG. 6A. This configuration 600 results in an important anisotropic profile (see, for example, FIG. 6B).

[0044] FIG. 6B shows an exemplary magnetic field profile 601 according to configuration 600 (FIG. 6A) according to some embodiments of the present disclosure. The black dots in profile 601 indicate the cusps that are characteristic at the intersection of the profile plane and the principal axis in the 2D slice of the magnetic field generated in the xz plane. One way to characterize the maximum magnetic field in configuration 600 is the maximum field achievable

Number

[0045] Configuration 600 creates a field of magnitude only on a specific axis [Number] Note that it can cause. However, configuration 600 can create a field of magnitude in any direction [Number] of this magnitude [Number] is [Number] corresponding to the cusp feature of profile 601.

[0046] In configuration 600, to generate the magnetic field vector B T =(B x ,B y ,B z ), the following equations cos(θ1)+sin(θ2)=B x / B max (25) cos(θ2)+sin(θ3)=B y / B max (26) cos(θ3)+sin(θ1)=B z / B max (27) can be solved.

[0047] To calculate the torque for configuration 600, the magnet 610 can be considered to have a finite length. The resulting torque is determined according to the ratio L / R. Assuming that L / R = 2 in configuration 600, the maximum torque τ max is

Equation

[0048] FIG. 7A is a schematic diagram showing a magnet configuration 700 that generates a 3D magnetic field by three pairs of DL magnets according to some embodiments of the present disclosure. The six magnets in configuration 700 include three pairs of magnets 710 (X1 and X2), 711 (Y1 and Y2), and 712 (Z1 and Z2). Each pair includes an independent magnet and a dependent magnet. Each independent magnet from pairs 710, 711, and 712 is a motor-driven magnet that can be independently rotated to generate a 3D field at the center. For example, when the independent magnets are X1, Y1, and Z1, using motor 120, the magnet can be rotated at angles θ X1 θ Y1 and θ Z1 . The orientations of magnets 710-712 are as follows, i.e., θ X1 =-θ X2 =θ X (29) θ Y1 =-θ Y2 =θ Y (30) θ Z1 =-θ Z2 =θ Z (31) can be constrained as

[0049] Figure 7B shows a magnetic field profile 701 that can be obtained from configuration 700 according to some embodiments of the present disclosure. Using each pair 710, 711, and 712 of independent magnets and dependent magnets, a 1D magnetic field (respectively, B x , B y , and B z ) can be generated along the Cartesian axes (see Figure 7A). As a result, a box shape is obtained in the profile 701 shown,

Number

Number

Number

Number

Number

[0050] In configuration 700, to generate the magnetic field vector B T =(B x , B y , B z ), the orientations of magnet pairs 710, 711, and 712 are shown as

Number

Number

Number

[0051] To calculate the torque for configuration 700, magnets 710, 711, and 712 can be considered to have a finite length. If L / R = 2 in configuration 700, the required torque is as follows:

Number

[0052] Similar to configuration 600, τ max / τ0 in configuration 700 is a decreasing function of the distance r, and this decreasing function saturates at a numerical value indicating the lower limit for the required torque.

[0053] FIG. 8 is a flowchart showing a process 800 for generating a magnetic field vector according to some embodiments of the present disclosure. Process 800 can generate a one-dimensional, two-dimensional, or three-dimensional (in) magnetic field vector using the magnet configurations discussed with respect to FIGS. 1 to 7B. Therefore, process 800 will be discussed with reference to these figures.

[0054] In operation 810, the magnetic field vector to be generated can be selected. The direction, magnitude, etc. of the magnetic field can be selected based on any suitable measurement criteria known to those skilled in the art. The selected magnetic field vector can be a 1D magnetic field (e.g., configuration 200), a 2D magnetic field (e.g., configurations 300, 400, or 500), or a 3D magnetic field (e.g., configurations 600 or 700) in a given direction.

[0055] The DL magnet system 105 that generates a magnetic field vector can be selected. This is shown in operation 820. Configurations such as those illustrated herein can be obtained for the DL system 105 based on the magnetic field vector to be generated. The configuration features selected in operation 820 can include the number of dipole line magnets (e.g., 1 to 6 or more magnets), the type of rotation (e.g., all motor-driven magnets or multiple pairs of motor-driven magnets and freely rotatable magnets), the positions of the magnets relative to each other (e.g., parallel axes or perpendicular axes, Cartesian coordinates, etc.). For example, to generate a 2D magnetic field vector, configurations 300, 400, or 500 can be selected. Still other features such as the length L and radius R of the magnets, the distance r between the magnets and the center of the magnetic field to be generated (e.g., point P or the center of the configuration), the size of the gap g between pairs of independent and dependent magnets (e.g., see FIG. 2) can also be selected in operation 820.

[0056] Next, the configuration can be adjusted for the magnetic field vector (B T ) to be generated. This is shown in operation 830. To select the orientation(s) (θ) and torque (τ T ) of the magnets to generate B max in the selected configuration, the computer system 130 can use the equations described above as needed. The computer system 130 can communicate with the motor 120, the shaft / gearbox 115, and the hall sensor 140 to guide the adjustments in the DL magnet system 105 in operations 830 and 840.

[0057] Magnetic field B Tcan be detected for each motor or at a point of interest at the center (e.g., by the hall sensor 140). This is shown in operation 840. Then, based on the detected magnetic field, it is determined whether the position of the magnet is accurate. This is shown in operation 850. If the position is inaccurate, process 800 returns to operation 830, where the magnet is readjusted (e.g., by rotating the magnet, or adjusting the torque, or both). The resulting field is detected in operation 840, and operation 850 is repeated to determine whether the position is accurate. Operations 830-850 are repeated until a magnetic field B T is generated. If the position is accurate (yes in 850), process 800 can end.

[0058] As described above, the magnetic field vector can be generated for various applications and can be used to achieve various magnetic field strengths (e.g., up to about 1 T or higher). In some embodiments, the magnetic field vector is generated to provide a diamagnetic trap, a magnetic field for electron optical Hall effect measurements, or Hall mobility in a semiconductor, or a combination thereof. However, any suitable magnetic field vector application (e.g., MRI, MPI, vibrating sample magnetometry, magnetoresistance measurement, Faraday rotation measurement, magneto-optical Kerr effect measurement, ferromagnetic resonance measurement, etc.) can be performed in environment 100.

[0059] FIG. 9 is a block diagram showing a computer system 900 according to some embodiments of the present disclosure. The computer system 900 can be used to implement one or more of the methods, tools, components, and related functions described herein (e.g., using one or more processor circuits or computer processors of a computer). In some embodiments, the main components of the computer system 900 include one or more processors 902, a memory subsystem 904, a terminal interface 912, a storage interface 916, an input / output device interface 914, and a network interface 918, all of which can communicate directly or indirectly via a memory bus 903, an input / output bus 908, a bus interface unit 907, and an input / output bus interface unit 910 for component-to-component communication.

[0060] The computer system 900 includes one or more general-purpose programmable central processing units 902A, 902B, and 902-N, collectively referred to herein as CPU 902. In some embodiments, the computer system 900 includes multiple processors typical of a relatively large system, while in other embodiments, the computer system 900 can alternatively be a single CPU system. Each CPU 902 can execute instructions stored in the memory subsystem 904 and can include one or more levels of on-board cache.

[0061] Memory 904 may include a random access semiconductor memory, a storage device, or a storage medium (either volatile or non-volatile) for storing or encoding data and programs. In some embodiments, memory 904 represents the entire virtual memory of computer system 900 and may also include the virtual memory of other computer systems coupled to or connected via a network to computer system 900. Memory 904 is conceptually a single monolithic entity, but in other embodiments, memory 904 is a more complex arrangement, such as a hierarchy of caches and other memory devices. For example, the memory may exist in multiple levels of cache, and these caches may be further divided by function, so that one cache holds instructions while another cache holds non-instruction data used by one or more processors. As is known in any of various so-called non-uniform memory access (NUMA) computer architectures, the memory may be further distributed and associated with various CPUs or sets of CPUs.

[0062] The components of the computer system 130 in the environment 100 (FIG. 1A) may be included within the memory 904 in the computer system 900. However, in other embodiments, the components of the system 130 may be on various computer systems and may, for example, be remotely accessed via a network. The computer system 900 can use a virtual addressing mechanism that allows the programs of the computer system 900 to behave as if they have access only to a large single storage entity rather than access to multiple smaller storage entities. Thus, not all of the components of the memory 904 are necessarily fully contained in the same storage device at the same time. Further, although these components are shown as separate entities, in other embodiments, some of these components, some portions of these components, or all of these components may be packaged together.

[0063] In one embodiment, the computer system 130 of the environment 100 includes instructions that are executed on the processor 902 or instructions that are interpreted by instructions executed on the processor 902 to perform the functions further described in this disclosure. In another embodiment, the system 130 is implemented in hardware via semiconductor devices, chips, logic gates, circuits, circuit cards, or other physical hardware devices or combinations thereof, instead of or in addition to a processor-based system. In another embodiment, the system 130 includes data in addition to instructions.

[0064] The memory bus 903 is shown in FIG. 9 as a single bus structure that provides a direct communication path among the CPU 902, the memory subsystem 904, the display system 906, the bus interface 907, and the input / output bus interface 910. However, in some embodiments, the memory bus 903 can include a plurality of different buses or communication paths, which can be arranged in various forms, such as a hierarchical configuration, a star configuration, or a web configuration of point-to-point links, a plurality of hierarchical buses, parallel and redundant paths, or any other suitable form of configuration. Further, although the input / output bus interface 910 and the input / output bus 908 are shown as single respective units, on the other hand, in some embodiments, the computer system 900 can include a plurality of input / output bus interface units 910, a plurality of input / output buses 908, or both. Further, a plurality of input / output interface units are shown that separate the input / output bus 908 from various communication paths extending to various input / output devices. However, in other embodiments, some or all of the input / output devices may be directly connected to one or more system input / output buses.

[0065] Computer system 900 may include a bus interface unit 907 for handling communication between a processor 902, a memory 904, a display system 906, and an input / output bus interface unit 910. The input / output bus interface unit 910 may be connected to an input / output bus 908 to transfer data to various input / output units. The input / output bus interface unit 910 communicates via the input / output bus 908 with a plurality of input / output interface units 912, 914, 916, and 918, also known as input / output processors (IOPs) or input / output adapters (IOAs). The display system 906 may include a display controller. The display controller can provide visual data, audio data, or data in both formats to a display device 905. The display system 906 can be connected to a display device 905 such as a stand-alone display screen, a computer monitor, a television, or a tablet or handheld device display. In an alternative embodiment, one or more of the functions provided by the display system 906 may be incorporated into the integrated circuit of the processor 902. Additionally, one or more of the functions provided by the bus interface unit 907 may be incorporated into the integrated circuit of the processor 902.

[0066] In some embodiments, computer system 900 is a multi-user mainframe computer system, a single-user system, or a server computer or similar device that has little or no direct user interface but receives requests from other computer systems (clients). Further, in some embodiments, computer system 900 is implemented as a desktop computer, a portable computer, a laptop or notebook computer, a tablet computer, a pocket computer, a telephone, a smartphone, a network switch or router, or any other suitable type of electronic device.

[0067] Note that FIG. 9 is intended to show representative major components of an exemplary computer system 900. However, in some embodiments, individual components may have greater or lesser complexity than shown in FIG. 9, there may be components other than or in addition to those shown in FIG. 9, and the number, type, and configuration of such components can vary.

[0068] The present invention can be a system, method, or computer program product, or a combination thereof, at any possible technical detail integration level. The computer program product may include a computer-readable storage medium (or media) having computer-readable program instructions for causing a processor to execute aspects of the present invention.

[0069] A computer-readable storage medium can be a tangible device that holds and stores instructions for use by an instruction execution device. The computer-readable storage medium can be, for example, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing, but is not limited thereto. A non-exhaustive list of more specific examples of computer-readable storage media includes, for example, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disc (DVD), a memory stick, a floppy disk, a mechanically encoded device such as a punched card or raised structures in grooves, and any suitable combination of the foregoing. As used herein, a computer-readable medium should not be construed to be a transitory signal per se, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagating through a waveguide or other transmission medium (e.g., an optical pulse through an optical fiber cable), or an electrical signal transmitted through a wire.

[0070] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to respective computing / processing devices or to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, or a wireless network, or a combination thereof. The network can include copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computing, or edge servers, or a combination thereof. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and transfers the computer-readable program instructions for storage on a computer-readable storage medium within each respective computing / processing device.

[0071] Computer-readable program instructions for carrying out the operation of the present invention may be source code or object code written in any combination of one or more programming languages, including assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state-setting data, configuration data for integrated circuits, or object-oriented programming languages such as Smalltalk(R), C++, and procedural programming languages such as the "C" programming language or similar programming languages. The computer-readable program instructions may be executed entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer, or entirely on a remote computer or server. In a scenario where the execution is entirely on a remote computer or server, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, for example, an electronic circuit including a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA) may execute the computer-readable program instructions by using the state information of the computer-readable program instructions to customize the electronic circuit to carry out aspects of the present invention.

[0072] Aspects of the invention are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer readable program instructions.

[0073] These computer readable program instructions are provided to a processor of a computer or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in one or more blocks of the flowchart and / or block diagram. These computer readable programmable instructions may also be stored in a computer readable storage medium that can direct a computer, programmable data processing apparatus, or other device, or combinations thereof, to function in a particular manner, such that the storage medium comprising instructions for implementing the functions / acts specified in one or more blocks of the flowchart and / or block diagram.

[0074] The computer readable program instructions may also be loaded onto a computer, other programmable apparatus, or other device to produce a process that is executed by the computer, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions / acts specified in one or more blocks of the flowchart and / or block diagram, causing a series of operational steps to be performed on the computer, other programmable apparatus, or other device.

[0075] The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagram may represent a module, segment, or portion of instructions that include one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the blocks may occur out of the order noted in the figures. For example, two blocks shown in succession may in fact be implemented as one step, executed simultaneously, substantially simultaneously, partially or wholly in overlapping time, or the blocks may in some cases be executed in the reverse order, depending on the functionality involved. It should also be noted that each block in the block diagrams or flowchart illustrations, and combinations of blocks in the block diagrams or flowchart illustrations, can be implemented by a dedicated hardware-based system that performs the specified functions or operations, or combinations of dedicated hardware instructions and computer instructions.

[0076] The descriptions of the various embodiments of the present disclosure have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope of the described embodiments. The terms used herein were chosen to best explain the principles of the embodiments, the practical application, or improvements made to the technology found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.

[0077] Although the present disclosure has been described with respect to specific embodiments, it is expected that modifications and variations will become apparent to those of ordinary skill in the art. Accordingly, the appended claims are intended to cover all such modifications and variations that are within the scope of the present disclosure.

Claims

1. obtaining a configuration of dipole line (DL) magnets, selecting a magnetic field vector to be generated, determining the orientation of the DL magnets to generate the magnetic field vector based on the configuration A method comprising:

2. The method according to claim 1, wherein the configuration includes a pair of the DL magnets, and the pair includes an independent DL magnet and a dependent DL magnet.

3. The method according to claim 1, wherein the configuration includes two parallel independent DL magnets.

4. The method according to claim 1, wherein the configuration includes three mutually orthogonal independent DL magnets.

5. The method according to claim 1, wherein the configuration includes three DL magnets positioned at the vertices of a triangle.

6. The method according to claim 1, further comprising obtaining a maximum torque for generating the magnetic field vector.

7. The method according to claim 1, further comprising adjusting the orientation of the DL magnets based on a magnetic field detected by a Hall sensor.

8. A system comprising: a memory, and a processor communicatively connected to the memory, wherein the processor is configured to execute a method comprising: obtaining a configuration of dipole line (DL) magnets, selecting a magnetic field vector to be generated, determining the orientation of the DL magnets to generate the magnetic field vector based on the configuration

9. The system according to claim 8, wherein the configuration includes a pair of the DL magnets, and the pair includes an independent DL magnet and a dependent DL magnet.

10. The system according to claim 8, wherein the configuration includes two parallel independent DL magnets.

11. The system according to claim 8, wherein the configuration includes three mutually orthogonal independent DL magnets.

12. The system according to claim 8, wherein the configuration includes three DL magnets positioned at the vertices of a triangle.

13. The system according to claim 8, further comprising obtaining a maximum torque for generating the magnetic field vector.

14. The system according to claim 8, further comprising adjusting the orientation of the DL magnets based on a magnetic field detected by a Hall sensor.

15. A computer program product comprising a computer-readable storage medium in which program instructions are embodied, the program instructions being executable by a processor to cause a device to perform a method, the method comprising: obtaining a configuration of dipole line (DL) magnets; selecting a magnetic field vector to be generated; determining an orientation of the DL magnets to generate the magnetic field vector based on the configuration A computer program product comprising the steps of: **Claim 16** The computer program product according to claim 15, wherein the configuration includes a pair of the DL magnets, the pair including an independent DL magnet and a dependent DL magnet. **Claim 17** The computer program product according to claim 15, wherein the configuration includes two parallel independent DL magnets. **Claim 18** The computer program product according to claim 15, wherein the configuration includes three mutually orthogonal independent DL magnets. **Claim 19** The computer program product according to claim 15, wherein the configuration includes three DL magnets positioned at vertices of a triangle. **Claim 20** The computer program product according to claim 15, further comprising adjusting the orientation of the DL magnets based on a magnetic field detected by a Hall sensor.

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