Permanent magnet arrangement for generating a homogeneous field (“3D Halbach”)

Abstract

A magnet arrangement (1) in a magnetic resonance apparatus having a permanent magnet system for generating a homogeneous magnetic field in a direction perpendicular to a z-axis in a measurement volume. The magnet system has at least two ring-shaped magnet elements (2) in a ring plane, which are arranged coaxially around the z-axis and are constructed from individual magnet segments (3) arranged next to one another in a Halbach configuration. The magnetization direction of at least two ring-shaped magnet elements deviates from the ring plane such that the component perpendicular to the ring plane varies cosinusoidally with the azimuthal angle of the respective ring-shaped magnet element. The magnetization of in each case two ring-shaped magnet elements is mirror-symmetrical with respect to one another, wherein the mirror plane is the central x-y-plane perpendicular to the z-axis. The disclosed arrangement provides a compact and lightweight permanent magnet arrangement for an MR apparatus.

Claims

1. Method for producing a magnet arrangement, comprising: a) predefining a target magnetic field B0 and a required number of ring-shaped magnet elements composed of known magnet material and a desired internal diameter of a central hole of the magnet arrangement; b) determining a desired homogeneity and leakage field properties by equating to zero at least one field order of a central or far field expansion; c) determining free design parameters, including geometry parameters of the ring-shaped magnet elements and 3D angles α of the ring-shaped magnet elements, by optimizing a volume of the magnet arrangement in accordance with said steps a) and b); d) determining a desired weight of the magnet arrangement as a function of the design parameters determined in accordance with said step c); and e) producing individual magnet segments with defined magnetization directions in a manner complying with the 3D angles α and an associated Halbach angle before the magnet segments are assembled.

2. Method according to claim 1, wherein in said step c), calculating the field orders and the magnet volume directly from the design parameters by way of analytical formulae.

3. Method according to claim 1, further comprising assembling the individual magnet segments to form the ring-shaped magnet elements.

4. Magnet arrangement in a magnetic resonance apparatus comprising: a permanent magnet system configured to generate a homogeneous magnetic field in a direction perpendicular to a z-axis in a measurement volume (0), wherein the permanent magnet system comprises at least two ring-shaped magnet elements containing magnetic material in a ring plane, which are arranged coaxially around the z-axis and which are constructed from individual magnet segments composed of magnetic material and arranged next to one another in a Halbach configuration, wherein magnetization directions of the at least two ring-shaped magnet elements deviate from the ring plane such that respective magnetization vector components perpendicular to the ring plane vary with azimuthal angle of the respective ring-shaped magnet elements, wherein a three-dimensional (3D) angle α determines deviations of the magnetization directions from analogous magnetization directions of a planar Halbach ring, and wherein the respective magnetization directions of each of the at least two ring-shaped magnet elements are mirror-symmetrical with respect to one another in relation to a mirror plane, wherein the mirror plane is a central x-y-plane perpendicular to the z-axis, and wherein magnetization directions of the magnet segments with respect to their outer surfaces parallel to the ring plane differ respectively from those of two adjacent ones of the magnet segments in the ring-shaped magnet element.

5. Magnet arrangement according to claim 4, wherein the magnet segments are constructed such that the magnetization directions of the individual magnet segments are defined by:
Mr=M Cos[α]Cos[ϕ0],Mϕ=M Sin[ϕ0],Mz=M Cos[ϕ0] Sin[α], wherein the respective magnetization vector components are given in cylindrical coordinates r, ϕ, z and denote: M a remanence of the magnet material used in the respective ring-shaped magnet element, ϕ(0) an azimuthal angle of a segment midpoint in the measurement volume (0), and α a parameter fixed for the ring-shaped magnet element in its entirety, namely the 3D angle that determines the deviations of the magnetization directions from the analogous magnetization directions of a planar Halbach ring.

6. Magnet arrangement according to claim 4, wherein the magnet segments are produced from a hard-magnetic material having a high remanence M, wherein 1.5 T >M >0.7 T, and having a low permeability μ in the range of 1.0<μ<1.5.

7. Magnet arrangement according to claim 6, wherein the magnet segments are produced from NdFeB.

8. Magnet arrangement according to claim 4, wherein the magnet segments arranged in a region of high field strengths are produced from a high-coercivity material having a coercivity HcJ in the range of 2800 kA/m >HcJ >1500 kA/m.

9. Magnet arrangement according to claim 4, wherein the magnet segments are produced from a temperature-compensated permanent magnet material having a temperature coefficient Tk in the range of 0%/K >Tk >−0.05%/K.

10. Magnet arrangement according to claim 8, wherein the magnet segments are produced from SmCo.

11. Magnet arrangement according to claim 4, further comprising at least one further ring-shaped magnet element as a planar Halbach ring, where α=0, arranged coaxially with respect to the at least two ring-shaped magnet elements, which are arranged coaxially around the z-axis.

12. Magnet arrangement according to claim 4, further comprising at least one further ring-shaped magnet element as a laterally homogeneously magnetized ring, where α=π, arranged coaxially with respect to the at least two ring-shaped magnet elements, which are arranged coaxially around the z-axis.

13. Magnet arrangement according to claim 4, wherein the ring-shaped magnet elements are constructed such that far field coefficients of low order n≤6 vanish.

14. Magnet arrangement according to claim 13, wherein the ring-shaped magnet elements are constructed such that a dipole moment of the permanent magnet system vanishes.

15. Magnet arrangement according to claim 4, wherein the ring-shaped magnet elements are arranged concentrically around the z-axis, and a radially inner one of the ring-shaped magnet elements has a higher coercive field strength than do radially outer ones of the ring-shaped magnet elements.

16. Magnet arrangement according to claim 4, wherein the magnet segments of each ring-shaped magnet element have one same outer shape.

17. Magnet arrangement according to claim 4, wherein the magnet segments of each ring-shaped magnet element have a trapezoidal prism shape.

18. Magnet arrangement according to claim 4, wherein the magnet segments of each ring-shaped magnetic element are arranged directly adjacent to each other in an assembled state of the magnet arrangement.

19. Magnet arrangement in a magnetic resonance apparatus comprising: a permanent magnet system configured to generate a homogeneous magnetic field in a direction perpendicular to a z-axis in a measurement volume (0), wherein the permanent magnet system comprises at least two ring-shaped magnet elements containing magnetic material in a ring plane, which are arranged coaxially around the z-axis and which are constructed from individual magnet segments composed of magnetic material and arranged next to one another in a Halbach configuration, wherein magnetization directions of the at least two ring-shaped magnet elements deviate from the ring plane such that respective magnetization vector components perpendicular to the ring plane vary with azimuthal angle of the respective ring-shaped magnet elements, wherein a three-dimensional (3D) angle α determines deviations of the magnetization directions from analogous magnetization directions of a planar Halbach ring, and wherein respective magnetization directions of each of the at least two ring-shaped magnet elements are mirror-symmetrical in a mirror plane with respect to one another in relation to a mirror plane, wherein the mirror plane is a central x-y-plane perpendicular to the z-axis, wherein magnetization directions of the magnet segments with respect to their outer surfaces parallel to the ring plane differ respectively from those of two adjacent ones of the magnet segments in the ring-shaped magnet element, and wherein the magnet segments of each of the at least two ring-shaped magnetic elements are arranged directly adjacent to each other in an assembled state and the magnet segments are constructed such that the magnetization directions of the individual magnet segments are defined by
Mr=M Cos[α]Cos[ϕ0],Mϕ=M Sin[ϕ0],Mz=M Cos[ϕ0] Sin[α], wherein the respective magnetization vector components are given in cylindrical coordinates r, ϕ, z, and denote: M a remanence of the magnet material used in the respective ring-shaped magnet element, ϕ(0) an azimuthal angle of a segment midpoint in a measurement volume (0), and α a parameter fixed for the ring-shaped magnet element in its entirety, namely the 3D angle that determines the deviations of the magnetization directions from the analogous magnetization directions of a planar Halbach ring.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention is illustrated in the figures and diagrams of the drawings section and is explained in greater detail on the basis of exemplary embodiments.

(2) In the figures:

(3) FIG. 1A shows a schematic spatial vertical sectional half-illustration of a simple embodiment of the magnet arrangement according to the invention having two ring-shaped magnet elements arranged mirror-symmetrically with respect to the xy-plane, and having 3D Halbach magnetization of the individual magnet segments that is indicated by arrows in each case;

(4) FIG. 1B shows a schematic spatial illustration of a complete ring-shaped magnet element according to the invention with depicted azimuthal angle ϕ and 3D angle α;

(5) FIG. 2A shows a schematic spatial illustration of the spatial 3D Halbach configuration according to the invention, visualized with arrows for the respective magnetization direction;

(6) FIG. 2B shows the spatial illustration of FIG. 2A, but with a flat 2D Halbach configuration in a ring plane according to the prior art;

(7) FIG. 3A shows a schematic sectional illustration through a ring plane of a magnet arrangement having a flat 2D Halbach configuration of the local magnetization directions according to the prior art;

(8) FIG. 3B shows the magnet arrangement according to the prior art from FIG. 3A in a schematic vertical sectional view;

(9) FIG. 4A shows a spatial diagram of the relationship of the design variables “external radius”, “3D angle” and “half length” for the optimized design of a magnet arrangement according to the invention;

(10) FIG. 4B shows a spatial diagram of the function of the parameter “weight” as a function of the design variables “external radius” and “half length” for the optimized design of a magnet arrangement according to the invention;

(11) FIG. 5 shows a schematic vertical sectional view through a simple embodiment of the invention having two 3D Halbach rings in a mirror-symmetrical arrangement (=exemplary embodiment 1);

(12) FIG. 6 shows a schematic vertical sectional view through a further embodiment of the invention having three Halbach rings, wherein the central ring has a 3D angle of α=0, while the two outer rings are in a mirror-symmetrical arrangement with respect to one another (=exemplary embodiment 2); and

(13) FIG. 7 shows an even more complex embodiment of the magnet arrangement according to the invention having eight magnet rings (=exemplary embodiment 3).

DETAILED DESCRIPTION

(14) The magnet arrangement 1 according to the invention such as is illustrated in each case schematically in various embodiments in the drawing finds its main application as part of a magnetic resonance apparatus—not shown specifically in the drawing—having a permanent magnet system for generating a homogeneous magnetic field in the direction of a z-axis in a measurement volume 0 (indicated in FIG. 3B), wherein the permanent magnet system comprises at least two ring-shaped magnet elements 2, 2′ composed of magnetic material in a ring plane, which are arranged coaxially around the z-axis and are constructed from individual magnet segments 3 arranged next to one another in a Halbach configuration.

(15) A “traditional” Halbach configuration such as has also already been described in the prior art is illustrated schematically in FIGS. 3A and 3B:

(16) FIG. 3A shows a sectional view through a ring plane of such a magnet arrangement having a flat (2D) Halbach configuration of the local magnetization directions of in each case 2 ϕ at a location with azimuthal angle f.

(17) FIG. 3B shows the magnet arrangement from FIG. 3A in a schematic vertical sectional view.

(18) The present invention indeed likewise relates to a magnet ring system composed of a plurality of rings in a Halbach configuration, but the outer rings comprise, in the magnetization direction, a spatial component (3D) pointing out of the ring plane. As an essential useful effect, this arrangement makes possible a more compact design of the magnet for higher field strength and also a lower leakage field.

(19) Generally, the magnet arrangement 1 according to the present invention—as is shown illustratively in FIGS. 1A and 1B is distinguished by the fact that the magnetization direction of at least two ring-shaped magnet elements 2, 2′ deviates from the ring plane in such a way that the component perpendicular to the ring plane varies cosinusoidally with the azimuthal angle of the respective ring-shaped magnet element 2, 2′, wherein a 3D angle α determines the deviation of the magnetization directions from those of a planar (2D) Halbach ring, and that the magnetization of in each case two ring-shaped magnet elements 2, 2′ is mirror-symmetrical with respect to one another, wherein the mirror plane is the central x-y-plane perpendicular to the z-axis. In FIG. 1B, the 3D angle α is depicted as the angle between the x-axis and the magnetization direction of that segment which is positioned in the x-direction.

(20) A 3-dimensional distribution of the magnetization directions in a 3D Halbach ring, in the case of which distribution the magnetization vectors partly project from the ring plane according to the invention, is illustrated in FIG. 2A.

(21) For comparison, FIG. 2B shows the distribution of magnetization directions in a “traditional” 2D Halbach ring according to the prior art, in the case of which distribution the magnetization vectors always lie within the ring plane.

(22) Preferably, the magnet segments 3 are constructed in the magnet arrangement according to the invention such that the magnetization direction of the individual magnet segments 3 follows the formula
Mr=M Cos[α]Cos[ϕ0], Mϕ=M Sin[ϕ0], Mz=M Cos[ϕ0]Sin[α],
wherein the components of the magnetization vector in cylindrical coordinates denote:
M the remanence of the magnet material used in the respective ring-shaped magnet element 2, 2′,
ϕ0 the azimuthal angle of the segment midpoint, and
α a parameter fixed for the entire ring-shaped magnet element 2, 2′, namely the 3D angle that determines the deviation of the magnetization directions from those of a planar Halbach ring.

(23) FIG. 5 shows a first, particularly simple exemplary embodiment:

Example 1

(24) The determination of an optimized geometry of a Halbach magnet according to the invention here comprises just two ring-shaped magnet elements 2, 2′ arranged mirror-symmetrically and having mirror-symmetrical magnetization. For illustrating the design process according to the invention, the simplest possible case shall be considered: two three-dimensional Halbach rings 2 and 2′ comprising identical magnet material are situated symmetrically with respect to the origin plane. The inner hole shall be fixedly predefined.

(25) The (half) magnet length, the external radius and the (likewise symmetrical) 3D angle α then remain as free design variables. If a specific target field B0 (in the example, B0=Br=1.4 T was chosen given a hole having a radius of 24 mm) and homogeneity of the lowest order (vanishing second field order B2=0) are demanded, then the degrees of freedom decrease to 1.

(26) This is illustrated in the graph in FIG. 4A: the first area A shows all combinations of the design variables for which the target field B0 is attained; the second area B shows all combinations for which the second field order B2 vanishes. The external radius of the Halbach ring in [mm] is plotted on the X-axis. Y denotes the half length of the magnet in [mm]. The 3D angle is indicated in radians on the Z-axis.

(27) That curve on which both demands are met results as a line of intersection. That point on the line which minimizes the total weight of the magnet is now sought for defining the current design.

(28) The graph in FIG. 4B shows the weight of the magnet arrangement as a function of magnet length and external radius. The external radius of the Halbach ring in [mm] is plotted on the X-axis, Y once again denotes the half length of the magnet in [mm], and the resulting weight is indicated on the Z-axis. If the curve determined above is transferred to this graph, then it is evident that it rises towards the edges, while it assumes a minimum in the central region. This point corresponds to the design optimized in the sense of the invention.

(29) FIG. 6 shows a further, still relatively simple exemplary embodiment:

Example 2

(30) The permanent magnet in a Halbach configuration here comprises three rings with predefined remanence M=B0=1.4 T, wherein the central ring 2a has a 3D angle of α=0. The two outer rings 2 are once again mirror-symmetrical with respect to one another in terms of the magnetization.

(31) Essential Boundary Conditions for Exemplary Embodiment 2: B0=1.4 T (60 MHz), 48 mm hole second and fourth field orders vanish Br=1.4 T (NdFeB) weight 13 kg α=0.15 in the outer rings, planar Halbach ring in the centre

(32) FIG. 7, finally, shows a somewhat more complex exemplary embodiment:

Example 3

(33) The permanent magnet in a Halbach configuration here comprises eight rings with predefined remanence M=B0=1.9 T, wherein the central rings have a 3D angle of α=0. The laterally outer rings 2, 2′ are mirror-symmetrical with respect to one another in pairs in each case in the magnetization direction. The both radially outermost and laterally central ring 2a having a 3D angle of α=0 is adjoined radially inwardly by a further laterally central ring 2a′ having a 3D angle of likewise α=0. In this example, the flat, radially innermost ring-shaped magnet elements 2b adjoining the radially inner 3D Halbach rings 2′ from inner areas have a homogeneous magnetization with the 3D angle α=71 These rings supplement the total magnetic field and furthermore result in even greater homogeneity of the magnetic field generated.

(34) Essential Boundary Conditions for Exemplary Embodiment 3: B0=1.9 T (80 MHz), 24 mm hole second, fourth and sixth field orders vanish Br=1.4 T and 1.3 T, respectively, for radially inner rings (NdFeB) weight 14 kg α=0.62 and 0.80 in the axially outer rings 2 and 2′, respectively, laterally homogeneously magnetized in the radially innermost rings 2b, planar Halbach rings 2a, 2a′ axially in the centre

(35) It is clearly evident in Examples 2 and 3 that, with the configuration according to the invention of the magnet rings and an adapted 3D angle α in the magnetization direction, magnets having a high remanence of up to 1.9 T in conjunction with a very low weight (here: 14 kg) are producible. Comparable designs composed of “traditional” planar Halbach rings weigh 14 kg (Example 2) and 20 kg (Example 3). At the same time, the magnet in Example 3 is configured in such a way that magnetic field inhomogeneities up to the 6.sup.th order vanish, and still up to the 4.sup.th order in Example 2.

LIST OF REFERENCE SIGNS

(36) 0 Measurement volume 1 Magnet arrangement 2; 2′ Ring-shaped magnet elements having 3D Halbach magnetization 2a; 2a′ Ring-shaped magnet elements having 2D Halbach magnetization 2b Further ring-shaped magnet elements having 2D Halbach magnetization 3 Magnet segments

(37) Physical Variables x, y, z Cartesian coordinates ϕ0 Azimuthal angle of the segment midpoint α 3D angle M Remanence μ Permeability HcJ Coercivity Tk Temperature coefficients n Order of the far field coefficients B0 Target magnetic field A First area B Second area

LIST OF REFERENCES

(38) Documents taken into consideration for the assessment of patentability [1] U.S. Pat. No. 10,018,694 B2 [2] US 2010/013473 A1 [3] U.S. Pat. No. 4,837,542 [4] US 2015/0061680 A1