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WO2007120057A1 - Appareil generateur de champ magnetique - Google Patents

Appareil generateur de champ magnetique Download PDF

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Publication number
WO2007120057A1
WO2007120057A1 PCT/NZ2007/000082 NZ2007000082W WO2007120057A1 WO 2007120057 A1 WO2007120057 A1 WO 2007120057A1 NZ 2007000082 W NZ2007000082 W NZ 2007000082W WO 2007120057 A1 WO2007120057 A1 WO 2007120057A1
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WIPO (PCT)
Prior art keywords
sub
arrays
assembly
array
magnetic field
Prior art date
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PCT/NZ2007/000082
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English (en)
Inventor
Benjamin John Parkinson
Paul Terence Callaghan
Mark Warwick Hunter
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Victoria Link Ltd
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Victoria Link Ltd
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Priority to NZ571863A priority Critical patent/NZ571863A/en
Publication of WO2007120057A1 publication Critical patent/WO2007120057A1/fr
Anticipated expiration legal-status Critical
Ceased legal-status Critical Current

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Classifications

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

Definitions

  • the present invention relates to a method and apparatus for generating a homogenous magnetic field.
  • the present invention relates to a method and apparatus for generating a homogenous magnetic field for use in Nuclear Magnetic Resonance (NMR) systems.
  • NMR Nuclear Magnetic Resonance
  • NMR spectroscopy is an analytical and diagnostic technique that can be used for structural and quantitative analysis of a compound in a mixture.
  • An NMR spectrometer generally comprises one or more magnets producing a strong magnetic field within a test region.
  • Halbach arrays are a means of creating multiple magnetic fields from a ring of magnetised rare-earth material. The number and location of the magnetic dipoles can be varied by manipulating the orientation of the magnetisation around the ring. If a homogeneous magnetic field is requited, Halbach (1979) has shown a successive magnetisation angle may be chosen such that a dipolar magnetic field is produced by the array.
  • Figure 1 shows that, when the criterion for a dipolar Halbach array is met, the magnetic field produced by the array is transverse to the longitudinal axis of the array. The direction of the lines of magnetic flux under this condition will hereafter be known as the principal component of magnetic field.
  • NMR experiments require magnetic fields that are as strong and as homogenous as possible.
  • a dipolar Halbach array constructed from discrete magnets, the strength of the field is well understood, and is readily calculable.
  • little research has been done on characterising and improving the homogeneity of the field produced by such an array.
  • homogeneity is a desired characteristic in NMR applications.
  • US Patent No. 6,885,267 to Kuriyama et al. which describes a Halbach array-type magnetic field generating apparatus.
  • the magnets in Kuriyama et al. ate arranged such that the magnetic field generated in the Halbach array has improved magnetic field parallelness.
  • the improved parallelness is beneficial in that the apparatus can accurately magnetise the orientation of magnetic films and like devices.
  • the term 'homogeneous magnetic field' as used in this specification means a sufficiently homogeneous magnetic field so as to enable NMR excitation of a sufficient volume of sample and to provide an analysable NMR signal in that region.
  • the present invention broadly comprises an apparatus for generating a homogenous magnetic field, comprising an assembly having a plurality of sub-arrays, each sub-array comprising a plurality of permanent magnets disposed in an annular array about an axis (hereafter "longitudinal axis"), wherein a separation is provided between two of the sub-arrays that are disposed at or toward the centre of the assembly along the longitudinal axis such that second order derivatives of the principal component of the magnetic field in an area within the assembly are substantially zero in three orthogonal directions.
  • the assembly may have only two sub-arrays. Alternatively, the assembly may have more than two sub-arrays.
  • the assembly comprises an even number of sub-arrays, such as two, four, six, eight, ten, or more sub-arrays for example.
  • the separation is provided between the two central sub-arrays.
  • the assembly may comprise an odd number of sub-arrays, such as five, seven, nine, or more sub-arrays for example.
  • the separation is provided between two of the sub-arrays that are generally centrally disposed within the assembly.
  • the separation is suitably provided between the third and fourth sub-arrays.
  • at least some of the sub-arrays may have different sizes such that the separation is positioned generally centrally within the assembly.
  • satisfactory results can be achieved with sub-arrays having a substantially consistent size.
  • separations are provided between at least some of the sub-arrays, with the separations disposed in such a way as to minimise fourth order derivatives of the principal component of magnetic field.
  • each of the sub-arrays disposed in the assembly is arranged so as to minimise fourth order derivatives terms of the principal component of magnetic field.
  • the separation ⁇ ) may be occupied by air, another gas, or a vacuum.
  • the separation ⁇ ) is/are occupied by a substantially non-magnetic material.
  • the size(s) of the separation(s) is/are less than the radius of the annular array of the permanent magnets.
  • each sub-array has at least four permanent magnets.
  • the number of permanent magnets in each sub-array may be a multiple of four, such as four, eight, twelve, sixteen, or more permanent magnets.
  • all of the permanent magnets in a sub-array have substantially the same length and width. More preferably, all of the permanent magnets in the assembly have substantially the same length and width.
  • each sub-array comprises an annular plate having disposed thereon or therein the plurality of permanent magnets.
  • the invention comprises an NMR apparatus comprising an apparatus as outlined in relation to the first aspect above arranged to create a zone of homogeneous magnetic field at some location within the assembly, and into a sample when provided.
  • the invention comprises a method of generating a homogenous magnetic field using an assembly comprising a plurality of sub-arrays, each sub-array comprising a plurality of permanent magnets disposed in an annular array about an axis (hereafter longitudinal axis'), the method comprising the steps of: arranging two sub-arrays that are disposed at or toward the centre of die assembly adjacent one another and along the longitudinal axis; and providing a separation between the two sub-arrays that are disposed at or toward the centre of the assembly, such that second order derivatives of the principal component of the magnetic field in an area in the assembly are substantially zero in three orthogonal directions.
  • the assembly may comprise only two sub-arrays. Alternatively, the assembly may comprise more than two sub-arrays.
  • the assembly may comprise any one or more features outlined in respect of the first aspect above.
  • the method may comprise arranging one or more further sub-arrays adjacent each of said two sub-arrays that are disposed at or toward the centre of the assembly such that the magnetic assembly has more than two sub-arrays.
  • the method further comprises: determining an optimal separation for the two sub-arrays that are disposed at or toward the centre of the assembly using some optimisation technique, for example root-finding.
  • the method further comprises: determining an optimal radius for the two sub- arrays that are disposed at or toward the centre of the assembly using some optimisation technique, for example root finding.
  • some optimisation technique for example root finding.
  • a Newton-Rhapson root-finding algorithm is used.
  • the method further comprises: determining an optimal separation between each of the sub-arrays other than the two sub-arrays that are disposed at or toward the centre of the assembly using some optimisation technique, for example, minimisation of a figure of merit that describes the performance of the assembly.
  • the method further comprises: determining an optimal longitudinal dimension for each of the sub-arrays using some optimisation technique, for example minimising a figure of merit that describes the performance of the assembly.
  • some optimisation technique for example minimising a figure of merit that describes the performance of the assembly.
  • a Nelder- Mead minimisation algorithm is used.
  • the optimisation technique(s) is/are carried out on a computer programmed with optimisation algorithm(s).
  • the invention consists in the foregoing and also envisages constructions of which the following gives examples only.
  • Figure 1 shows a diagrammatic illustration of magnetic flux lines produced by a dipolar Halbach array
  • Figures 2a and 2b show schematic views of a part of a Halbach array
  • Figure 3 shows a perspective view of a Halbach array with one sub-array
  • Figure 4 shows contour lines representing homogeneity of the magnetic field produced by the Halbach array of Figure 3;
  • Figure 5 shows a perspective view of a first preferred form Halbach array with two sub-arrays
  • Figure 6 shows contour lines representing homogeneity of the magnetic field produced by the Halbach array of Figure 5;
  • Figure 7 shows a perspective view of second preferred form Halbach array with a plurality of sub-arrays
  • Figure 8 shows contour lines representing homogeneity of the magnetic field produced by the Halbach array of Figure 7;
  • Figures 9a to 9d show graphs of Halbach array geometry and parameter changes in response to a change in separation between two centre sub-arrays, in accordance with possible preferred forms of the present invention
  • Figure 10 shows the standard deviation of second order derivatives for a 10,000- trial Monte-Carlo simulation
  • Figures 1 Ia to 1 If show graphs of Halbach array geometry and parameter changes in response to a change in separation between two centre sub-arrays for arrays with two, four, six, eight, ten and twelve sub-arrays, in accordance with possible preferred forms of the present invention
  • Figure 12 shows a perspective view of a third preferred form Halbach array
  • Figure 13 shows contour lines representing homogeneity of the magnetic field produced by the preferred form Halbach array of Figure 12 respectively
  • Figure 14a shows a sub-array former design
  • Figure 14b shows an assembled sub-array
  • Figures 15 to 19 show various stages of assembly of the preferred form array.
  • the applicants have invented modified arrangements of a dipolar Halbach array, which offer improved homogeneity.
  • the preferred form arrays are designed such that the homogeneity of their magnetic fields can be enhanced through a process of setting to zero the second derivatives of the principal component of the magnetic field in each direction.
  • the principal component of magnetic field is arbitrarily chosen to lie in the ⁇ -direction; thus die principal component of magnetic field is denoted B ⁇ and the total magnetic field denoted B.
  • the longitudinal axis is similarly chosen to lie in thejy-direction.
  • the three orthogonal directions along which the derivatives of the principal component of magnetic are evaluated are arbitrarily chosen to be the Cartesian axes, xy and ⁇ .
  • the current density distribution is that of a current sheet at the surface of the material.
  • a homogeneously magnetised piece of rare-earth material may be modelled simply as a current sheet with the same shape as the piece of rare-earth metal.
  • Halbach (1979) has described an arrangement of magnetic elements which can lead to a uniform magnetic field distribution.
  • this array can be realised using rectangular cuboid magnets.
  • a magnet array is required to produce a field that is homogeneous.
  • B B r ]n(r mtir /r, ⁇ mr ) Where B r is the remnant magnetisation of the rare earth material.
  • the magnetic flux is contained within the ring of magnetised material in a dipolar configuration.
  • the field that is produced is therefore homogenous and additionally has no stray field outside the ring of magnetised material.
  • This type of Halbach array is therefore ideal for forming the B 0 field of an NMR system. What is more, the generation of a B 0 field that is orthogonal to the long axis of the array is particularly convenient for performing NMR experiments.
  • equation 1 The implication of equation 1 is that the magnetisation direction should be continuously varied around the circle of rare-earth material. The requirement for a continually varying magnetisation direction is presently impossible to physically realise, thus it has been proposed that the ring of material could be broken into segments which each had a magnetisation direction given by equation 1.
  • a root finding approach to optimisation requires some property of the array that can be set to zero by intelligently iterating the array parameters.
  • the design of the dipolar Halbach array means the B z component of the magnetic field of the array may, to first order, be regarded as being equal to B at any point inside the array.
  • the second derivative of the B z component of the magnetic field produced by the array has the desired effect of increasing the field homogeneity when set to zero at the geometric origin of the array.
  • a root finding method that can intelligently iterate the geometry of the array in such a way as to make the second derivative of the B z component of magnetic field equal to zero in each direction can improve the homogeneity of the array to second order.
  • What is particularly attractive about a root finding approach to improve homogeneity is that the stun of second derivatives of the B z component of magnetic field is zero. This may be understood from consideration of Maxwell's equations:
  • V.B 0 3
  • Vx B ⁇ j + ⁇ o ⁇ o — ⁇ 4 ot dE
  • J represents the current density where VxB is evaluated, the rate of change of dt electric field with time at the same point and S 0 the permittivity of free space.
  • each component of the vector VxB must equal zero.
  • the third direction will additionally have a second derivative equal to zero.
  • the minimisation process should set the higher order derivatives of B z to zero; however, by so doing other features of the array, particularly the strength of the magnetic field, may be compromised. A minimisation process is therefore preferable, since there are significant improvements in homogeneity to be made by simply reducing the value of the higher order derivatives compared to a solution that only sets the second order derivatives of B n to zero.
  • Halbach array geometries that have the desired second order homogeneity.
  • the solution that emerges at the end of a root finding or minimisation optimisation is not guaranteed to be the globally optimum solution.
  • factors such as field strength, homogeneity and practicality of the design are considered.
  • An array produced using a minimisation technique tends to have a lower field strength and greater homogeneity.
  • an array that is produced using a pure root finding exercise has higher field strength, but lower homogeneity.
  • Magnetised rare-earth material can be modelled by a current sheet at the surface of the material with linear current density B r /ju o .
  • a current sheet at the surface of the material with linear current density B r /ju o .
  • cuboid magnets have been considered. Persons skilled in the art will appreciate that other magnet forms may be used instead, such as appropriately magnetised cylindrical bar magnets for example.
  • the field from a magnet may be calculated from the Biot-Savart law for a magnetic field produced by a current carrying wire, where the wire represents one edge of the piece of rare-earth magnet.
  • a current carrying wire where the wire represents one edge of the piece of rare-earth magnet.
  • Equation 1 shows how the relative orientation of the magnets is to be varied. Additionally, any Halbach array requires that the magnet centres are positioned at the same radius, EL, from the geometric origin of the array.
  • Figure 2a shows a front view of one quadrant of a Halbach array.
  • Figure 2b shows a plan view of a number of sub-arrays 20 in the Halbach array. Each sub-array comprises a number of permanent magnets 21 arranged in an annular array about a longitudinal axis L, as will be described in detail later.
  • the B x , E I and B components of the magnetic field at the rotated point P' are then calculated using the method outlined previously.
  • the B x , B and B z components of magnetic field are then rotated back into the original frame of reference using the inverse rotation.
  • the calculated values are then stored. This procedure is repeated for each of the magnets in the array, with the magnetic field from each successive magnet being added to the value already stored.
  • the fields may be calculated using finite element methods.
  • the fields may be calculated using finite element methods.
  • FIG. 2 shows how the array can be parameterised for the purposes of this calculation.
  • Each magnet 21 is specified in terms of its length /, width n>, height h and strength. It can be seen that the height of each magnet corresponds in direction to the longitudinal axis L of the assembly.
  • the orientation and location of the magnets 21 are given by the radial distance R and the angles ⁇ and ⁇ , where ⁇ is the angle between magnet centres and ⁇ is the angle through which the magnet is rotated about its centte.
  • the number of sub-arrays 20 that make up the final array may be specified, as is the separation s between each of these sub-arrays.
  • the number of magnets in a sub-array can also be chosen, although for reasons of symmetry this variable is preferably restricted to integer multiples of four.
  • a Newton-Rhapson algorithm is used to perform the root finding.
  • This particular implementation of the algorithm is capable of calculating the /2 th derivative in any number of directions, provided that the program had an equal number of array parameters to adjust.
  • the input to the Newton-Rhapson program must be the value of the second derivative of the field in that direction.
  • the output from the program is the perturbation to the chosen array parameter that will force the second derivative to be closer to zero.
  • the field from the array is then calculated with the new array parameter and the second derivative of that field in the appropriate direction is fed back into the program. Once a value of the array parameter has been obtained that yields a magnetic field from the array whose second derivative is sufficiently close to zero, the program terminates.
  • a Nelder-Mead minimisation algorithm is used to perform the optimisation.
  • Halbach array geometry is parameterised, and then fed into the mitiimisation algorithm.
  • the minimisation algorithm then calculates a figure of merit for this array geometry based on appropriately weighted values of the second and fourth order derivatives. It then makes a perturbation to the initial Halbach array geometry in an attempt to minimise the figure of merit. After many iterations, when the figure of merit is sufficiently small, the algorithm terminates and returns the optimised array geometry.
  • a conventional f ⁇ tm of a Halbach array is shown in Figure 3.
  • the array comprises one sub-array 30 having sixteen permanent magnets 31 arranged in an annular arrangement about a longitudinal axis, L.
  • an array performance parameter f w (r) may be used (Raich 2004):
  • B (r) is the average magnetic field inside a circle of radius r
  • AB (r) is the variation in magnetic field strength over the same area
  • A is the total area occupied by all of the magnets in the sub-array. The presence of A in the denominator tends to optimise for the lowest mass array design.
  • the array shown in Figure 3 it is possible to find a one sub-array geometry that produces a second derivative of the magnetic field equal to zero in the ⁇ -direction alone.
  • the second derivative is set to zero by using the root finding algorithm described earlier to iterate the radius of the array. It is possible that the algorithm results in non-realisable geometries since the radius at which the second derivative is at zero may be infinite as a result of non-convergence of the optimisation algorithm, or may specify an array geometry that results in overlap of adjacent magnets, which is clearly unrealisable.
  • the geometry will have a close packed configuration, such as shown in Figure 3, where the component magnets will almost be touching one another as this will generate the strongest possible magnetic field.
  • Both the preferred method optimisation algorithms discussed previously work by making perturbations to some initial Halbach array geometry.
  • the success of the algorithm in producing a desirable and realisable array geometry following the optimisation process is consequently dependent on the quality of the initial array geometry.
  • the solution that emerges following the optimisation process may, for example, have so small a magnetic field strength as to be unusable for NMR experiments.
  • Figure 4 shows a good quality magnetic field profile from a Halbach array such as that shown in Figure 3.
  • This example array has had only the second derivative of B in the ⁇ direction set to zero.
  • the profile shows contour lines indicative of the variation in magnetic field strength at distances along the x and % — axes within the Halbach array.
  • the 0.01% contour line delineates the area in which the magnetic field strength varies by 0.01% at most.
  • the effect of having set the second derivative equal to zero in the ⁇ -direction is that the dimension of the 0.01% contour line is larger in the ⁇ -direction than in the x-direction where no optimisation has taken place.
  • modified Halbach arrays that offer significantly improved homogeneity. That is achieved by arranging the sub-arrays within the array with particular spacings. Generally, the magnets within the sub-arrays will be arranged so as to produce a dipolar magnetic field according to equation 1. It will be appreciated that if desired for particular applications, the principle of the present invention could be used to create higher order magnetic fields; for example, a quadrapokr magnetic field may be envisioned. This higher order field may be achieved by varying the arrangement of the magnets in the sub- arrays according to equation 1.
  • improved homogeneity is achieved by separating the sub-arrays that are disposed at or toward the centre of the magnetic assembly. Correct selection of that separation results in second order derivatives of the principal component of the magnetic field in an area within the assembly being substantially zero in each of the three orthogonal directions.
  • the sub- arrays that are disposed at or toward the centre of the assembly are again provided with a separation such that second order derivatives of the principal component of the magnetic field in an area within the assembly are substantially zero in each of the three orthogonal directions.
  • separations are provided between other sub-arrays in the assembly, with those separations disposed in such a way as to minimise fourth order derivatives of the principal component of magnetic field.
  • a modified Halbach array in accordance with the first preferred form of the present invention is shown in Figure 5.
  • the Halbach array indicated generally as 50, has two sub- arrays 51.
  • Each sub-array 51 comprises a number of permanent magnets 52 arranged in an annular array about a longitudinal axis, L 1 .
  • sixteen permanent magnets 52 are preferably provided in each sub-array 51.
  • the Halbach amy in the preferred form is provided with a separation 53 between the two sub-arrays 51. With this design, the second derivative of the principal component of magnetic field generated by the array is substantially zero in each of the three orthogonal directions.
  • a root finding or minimisation algorithm as previously described may be used.
  • the second derivatives in the % andj/ — directions may be set to zero.
  • an optimal separation for the two sub-arrays that are disposed at or toward the centre of the assembly is determined using an optimisation technique, and preferably a root finding technique.
  • an optimal radius for the two sub-arrays that are disposed at or toward the centre of the assembly is determined using an optimisation technique, and preferably a root finding technique such as by using a Newton-Rhapson root-finding algorithm.
  • an optimal separation between each of the sub-arrays other than said two sub-arrays that are disposed at or toward the centre of the assembly is determined using an optimisation technique, and preferably by minimising a figure of merit that describes the performance of the assembly.
  • an optimal longitudinal dimension for each of the sub-arrays is determined using an optimisation technique, and preferably by minimising a figure of merit that describes the performance of the assembly such as by using a Nelder-Mead minimisation algorithm.
  • the optimisation techniques are preferably carried out on a computer programmed with optimisation algorithms.
  • the longitudinal dimension of each of the sub- arrays, the separations between each of the coupled sub-arrays and the radius are iterated such that the second derivatives in the % andj/ - directions may be set to zero, whilst the fourth derivatives in the x, j and ⁇ -directions are additionally minimised.
  • the length and width of the magnets are preferably identical to ensure the optimisation algorithm converges on a realisable Halbach array geometry.
  • the required separation to set the second derivative of the magnetic field equal to zero along thej/- axis of the array is less than the radius of the array.
  • the separation may be smaller than 1 mm for certain geometries.
  • Figure 6 shows the magnetic field profile of the array of Figure 5.
  • the contour lines shown in Figure 6 show a substantial increase in the size of the area that has better than 0.01% variation in the magnetic field strength.
  • the main increase in the dimension of the 0.01 % contour line has been in the .v-direction.
  • a similar increase in the size of the homogeneous region can be seen in the % -y plane when compared to the field produced by a one sub-array design.
  • FIGS 9a and 9b show how the parameters of length of magnet and radius of the array vary as the separation is varied.
  • Figures 9c and 9d show how the array quality factors of magnetic field strength B z and the area of the homogenous region of the array vary as the separation is varied. Referring to Figure 9d, there are clear improvements in the size of the homogeneous region to be obtained from a solution tiiat has a larger separation. This gain is traded against slightly reduced magnetic field strength, as shown in Figure 9c, and a physically larger, and consequently heavier, array.
  • Halbach array In addition to the design characteristics of the preferred form Halbach array, it is also important for the expected magnetic field to be robust, given the manufacturing errors associated with each of the design parameters. Since the homogeneity of the field depends on the value of the second derivative along each axis, the value of die second derivative forms an appropriate measure of the robustness of any proposed design for the present invention.
  • the Monte-Carlo simulation tfierefore perturbs each of the defining parameters of one particular Halbach array geometry by some random, normally weighted amount, and calculates the resulting sum of die second derivatives of the magnetic field in the x,j and indirections. This process is repeated for 10,000 trials. The mean and standard deviation of die calculated second derivatives from all of the trials is subsequendy calculated.
  • the manufacturers of the magnets again specify that the dimensional tolerances of d ⁇ eir magnets as being ⁇ 0.1mm. Again, assuming that this represents approximately the 95% confidence interval for the magnet dimensions, it can be presumed that the standard deviation of a particular magnet dimension is 0.05 mm.
  • the errors associated with the positioning of die magnets were estimated from standard engineering tolerances for machining. Using the same assumptions about the means of obtaining the errors, the standard deviation of the radius of the array and separation of each of the sub-arrays was set to be 0.1 mm. Finally, the standard deviation of the error in the angles ⁇ and ⁇ was estimated to be 1°.
  • FIG. 7 A modified Halbach array in accordance with a second preferred form of the present invention is shown in Figure 7.
  • the Halbach array 150 has eight sub-arrays 151a-151h. Again each sub-array 151a-151h comprises a number of permanent magnets 152 arranged in an annular array about a longitudinal axis. As before, sixteen permanent magnets 152 are preferably provided in each sub-array 15Ia-151 h.
  • spacings are provided between at least some of, and preferably all of, the other sub-arrays in the apparatus.
  • the spacings can be chosen to minimise, fourth order derivatives of the principal component of the magnetic field.
  • the lengths of the magnets in the j-dimension vary along the array.
  • the Halbach array is provided with ten sub-arrays and a centre separation of 7 mm.
  • the size of the homogeneous region, the robustness and the strength of the magnetic field of the array has been found to be reasonably well improved in diis preferred form.
  • the layout of the permanent magnets and sub-arrays in the third preferred form is shown in Figure 12, and the profile of the magnetic field generated by the third preferred form is shown in Figure 13.
  • Figure 11a shows the length of component magnets and Figure lib shows the radius of the array required to achieve homogeneity to second order for different separations.
  • Figure lie shows the magnetic field strength at centre of array, while Figures 1 Id and lie show the area of the magnetic field with a variation of less than 0.01%.
  • Figure Hf shows the standard deviation of second order derivatives for 10,000 sample Monte-Carlo simulation. This figure indicates that there are gains to be made in robustness by using more than two sub-arrays, as indicated by the drop in standard deviation with an increasing number of sub-arrays.
  • Figure lie shows that the gain in robustness does not significantly reduce the magnetic field strength of the array.
  • Figures Hd and lie show that the homogeneity of the magnetic field is not affected by increasing the robustness.
  • the separation is provided between two of the sub-arrays that are generally centrally disposed within the assembly.
  • the separation is suitably provided between the third and fourth arrays.
  • satisfactory results can be achieved with even sized sub-arrays.
  • Construction of a Halbach array represents a number of engineering challenges. The crux of these challenges is to ensure that the array is safe to use, while ensuring the manufacturing errors are similar to, or ideally less than, those used in the Monte-Carlo simulation.
  • the amount of force exerted by the component magnets in a Halbach array is substantial.
  • the orientation of the magnets inside a sub-array is such that the magnets will be urged to twist around to reduce the magnetic force being exerted on them by neighbouring magnets. This sets up large forces internal to the sub-array. What is more, once manufactured, a sub-array has a net magnetisation that extends along its longitudinal axis. Thus, when putting the array itself together, the sub-arrays are trying to repel one another.
  • a sub-array housing or former 130 is preferably used to house the magnets in the y-direction of the array, while leaving the ends of magnets exposed.
  • the former 130 comprises a ring within which apertures 131 are located such that the placement of the permanent magnets in the apertures 131 results in an arrangement of permanent magnets in an annular array about a longitudinal axis.
  • a former housing permanent magnets in accordance with the preferred form of the invention is shown in Figure 14b.
  • a generous amount of former material is provided both on the inside and outside of the sub-array former to provide necessary strength.
  • the sub-arrays are open-ended. In this form, it is possible to use laser cutting to produce the formers.
  • a laser cutter is capable of a positional accuracy of ⁇ 0.02 mm compared with +0.2 mm for more conventional machining techniques.
  • the amount of time it takes to produce one former using a laser cutter is approximately one hour, compared with approximately five hours for conventional machining techniques.
  • the ability to use laser cutters therefore gready reduces the machining time required to produce the formers to build the array, while increasing the precision to which the sub-arrays can be constructed.
  • polymethyl methacrylate is chosen for manufacturing the sub-array formers.
  • This material is cost-effective, readily available, sufficiently strong and easily cut with a laser cutter.
  • acrylic is non-limiting and any other suitable material may be used instead.
  • the acrylic formers may be reinforced and coupled by running polyoxymethylene (acetyl) rods through the lengdi of the array. These will contribute to the strength of the array by acting as strain relief within the sub-array formers by assisting in resisting the torque force exerted by the magnets.
  • the rods can be threaded at either end and then used to hold the array itself together.
  • the rods can be formed from any suitable material.
  • the preferred form configuration of the improved Halbach array is based on a preferred manufacturing technique. Since it is relatively easy to make sub-arrays that are 24 mm thick due to the ready availability of 8mm acrylic sheet, the component magnets were chosen to have this longitudinal dimension.
  • Figure 15 shows an assembly apparatus being used to bring together a new sub-array 140 onto the stack of sub-arrays 141.
  • the figure also shows aluminium spacers 143 that are used to retain the magnets in the sub-arrays while the new sub-array is being lowered down.
  • Acetyl rods 144 as described earlier are provided in the array to afford alignment and strength to the assembly.
  • the rods 144 extend through holes provided on a top plate 145 and a bottom plate 146.
  • Figure 16 shows in further detail the top plate 150 and the wing nuts 151 that are used to push the new sub-array onto the stack of sub-arrays.
  • Figure 17 shows the first half of the array 160 having five sub-arrays.
  • the first half 160 includes a cover 161 on one side and a spacer 162 on the other side to retain the permanent magnets in the array while the other half of the array is constructed.
  • the other half of the array is also built using the assembly apparatus.
  • the placement of the permanent magnets in the sub-array may be modified.
  • separating material may be provided instead, as long as the material is at least substantially non-magnetic.
  • a preferred form apparatus is preferably suitable for use in NMR applications, including bench top testing of magnetic materials using magnetic fields.
  • Field cycling NMR is an example of such an application.
  • a preferred form NMR apparatus will typically include other items as well as the magnetic assembly, such as a radio frequency transceiver coil, a radio frequency amplifier, a spectrometer, and possibly a computer to control the spectrometer, for example.

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  • Physics & Mathematics (AREA)
  • Condensed Matter Physics & Semiconductors (AREA)
  • General Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Hard Magnetic Materials (AREA)
  • Magnetic Resonance Imaging Apparatus (AREA)

Abstract

L'invention concerne un appareil générateur de champ magnétique homogène, comportant une pluralité de sous-groupes (251a-251j), incorporant chacun une pluralité d'aimants permanents formant une structure annulaire autour d'un axe. Deux (251e, 251f) des sous-groupes disposés au centre ou à proximité du centre de l'ensemble sur l'axe longitudinal sont séparés par un espace (253e) de telle sorte que les dérivées du second ordre de la composante principale du champ magnétique dans une région intérieure à l'ensemble soient sensiblement nulles dans trois directions orthogonales.
PCT/NZ2007/000082 2006-04-18 2007-04-18 Appareil generateur de champ magnetique Ceased WO2007120057A1 (fr)

Priority Applications (1)

Application Number Priority Date Filing Date Title
NZ571863A NZ571863A (en) 2006-04-18 2007-04-18 Homogenous magnetic filed generator with a gap between magnet sub-arrays at the centre of an assembly

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US79276906P 2006-04-18 2006-04-18
US60/792,769 2006-04-18

Publications (1)

Publication Number Publication Date
WO2007120057A1 true WO2007120057A1 (fr) 2007-10-25

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Country Status (2)

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NZ (1) NZ571863A (fr)
WO (1) WO2007120057A1 (fr)

Cited By (17)

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CH701267A1 (fr) * 2009-06-02 2010-12-15 Haute Ecole D'ingenierie Et De Gestion Du Canton De Vaud Heig Vd Generateur de champ magnetique et dispositif magnetocalorique comportant ledit generateur de champ magnetique.
WO2011023910A1 (fr) 2009-08-28 2011-03-03 Commissariat A L'energie Atomique Et Aux Energies Alternatives Dispositif d'aimant permanent cylindrique a champ magnetique induit d'orientation predeterminee et procede de fabrication
WO2011023913A1 (fr) 2009-08-28 2011-03-03 Commissariat A L'energie Atomique Et Aux Energies Alternatives Structure aimantee induisant en son centre un champ homogene d'orientation predeterminee
JP2013108986A (ja) * 2011-11-20 2013-06-06 Krohne Ag 核磁気流量計用の磁化装置
CN104599806A (zh) * 2015-01-23 2015-05-06 谢寰彤 一种磁聚焦和曲面矫正的高场永磁体磁共振成像磁体系统
CN105223527A (zh) * 2015-11-11 2016-01-06 中国科学院苏州生物医学工程技术研究所 一种利用元线圈阵列对霍尔巴赫磁体进行匀场的方法
RU2580841C2 (ru) * 2011-11-21 2016-04-10 Кроне Аг Магнитный конструктивный узел для ядерно-магнитного расходомера
US9395222B2 (en) 2011-11-20 2016-07-19 Krohne Ag Magnetization device for a nuclear magnetic flow meter
GB2529785B (en) * 2013-06-03 2018-02-14 Nanalysis Corp Magnet Assemblies
CN107917926A (zh) * 2016-10-10 2018-04-17 中国石油化工股份有限公司 便携式核磁共振分析传感器及便携式磁共振分析仪
US10527565B2 (en) 2015-07-29 2020-01-07 Chevron U.S.A. Inc. NMR sensor for analyzing core or fluid samples from a subsurface formation
US10679781B1 (en) 2018-11-29 2020-06-09 Epsitau Ltd. Lightweight asymmetric magnet arrays with theta magnet rings
US10690738B1 (en) 2018-11-29 2020-06-23 Epsitau Ltd. Lightweight asymmetric magnet arrays
US10732240B2 (en) 2015-10-26 2020-08-04 Antonello Sotgiu Magnet assembly for MRI comprising cylindrical rings of halbach type
US10867733B2 (en) 2018-11-29 2020-12-15 Epsitau Ltd. Lightweight asymmetric magnet arrays with mixed-phase magnet rings
CN112912748A (zh) * 2018-09-03 2021-06-04 新加坡科技设计大学 永磁体系统及其形成方法
DE102022202399A1 (de) 2022-03-10 2023-09-14 Bruker Biospin Gmbh NMR Permanentmagnet in Halbach-Anordnung basierend auf Segmenten mit regulärer Polyedergeometrie sowie Herstellungsverfahren

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CN119673613B (zh) * 2024-12-13 2025-11-07 天津大学 哑铃形磁体结构和磁共振成像系统

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Cited By (26)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CH701267A1 (fr) * 2009-06-02 2010-12-15 Haute Ecole D'ingenierie Et De Gestion Du Canton De Vaud Heig Vd Generateur de champ magnetique et dispositif magnetocalorique comportant ledit generateur de champ magnetique.
WO2010139083A3 (fr) * 2009-06-02 2011-02-17 Haute Ecole D'ingénierie Et De Gestion Du Canton De Vaud (Heig-Vd) Generateur de champ magnetique et dispositif magnetocalorique comportant ledit generateur de champ magnetique
US8860539B2 (en) 2009-08-28 2014-10-14 Commissariat A L'energie Atomique Et Aux Energies Alternatives Magnetised structure inducing a homogeneous field, in the centre thereof, with a pre-determined orientation
WO2011023913A1 (fr) 2009-08-28 2011-03-03 Commissariat A L'energie Atomique Et Aux Energies Alternatives Structure aimantee induisant en son centre un champ homogene d'orientation predeterminee
FR2949604A1 (fr) * 2009-08-28 2011-03-04 Commissariat Energie Atomique Structure aimantee axisymetrique induisant en son centre un champ homogene d'orientation predeterminee
WO2011023910A1 (fr) 2009-08-28 2011-03-03 Commissariat A L'energie Atomique Et Aux Energies Alternatives Dispositif d'aimant permanent cylindrique a champ magnetique induit d'orientation predeterminee et procede de fabrication
JP2013108986A (ja) * 2011-11-20 2013-06-06 Krohne Ag 核磁気流量計用の磁化装置
US9395222B2 (en) 2011-11-20 2016-07-19 Krohne Ag Magnetization device for a nuclear magnetic flow meter
EP2604983B1 (fr) * 2011-11-20 2023-01-04 Krohne AG Dispositif de magnétisation pour un appareil de mesure de débit à noyau magnétique
DE102012016402B4 (de) 2011-11-21 2025-02-06 Krohne Ag Magnetbaugruppe für ein kernmagnetisches Druchflussmessgerät
RU2580841C2 (ru) * 2011-11-21 2016-04-10 Кроне Аг Магнитный конструктивный узел для ядерно-магнитного расходомера
GB2529785B (en) * 2013-06-03 2018-02-14 Nanalysis Corp Magnet Assemblies
US9952294B2 (en) 2013-06-03 2018-04-24 Nanalysis Corp. Lattice configurations of polyhedral component magnets
CN104599806A (zh) * 2015-01-23 2015-05-06 谢寰彤 一种磁聚焦和曲面矫正的高场永磁体磁共振成像磁体系统
US10527565B2 (en) 2015-07-29 2020-01-07 Chevron U.S.A. Inc. NMR sensor for analyzing core or fluid samples from a subsurface formation
US10732240B2 (en) 2015-10-26 2020-08-04 Antonello Sotgiu Magnet assembly for MRI comprising cylindrical rings of halbach type
CN105223527A (zh) * 2015-11-11 2016-01-06 中国科学院苏州生物医学工程技术研究所 一种利用元线圈阵列对霍尔巴赫磁体进行匀场的方法
CN107917926B (zh) * 2016-10-10 2019-10-18 中国石油化工股份有限公司 便携式核磁共振分析传感器及便携式磁共振分析仪
CN107917926A (zh) * 2016-10-10 2018-04-17 中国石油化工股份有限公司 便携式核磁共振分析传感器及便携式磁共振分析仪
CN112912748A (zh) * 2018-09-03 2021-06-04 新加坡科技设计大学 永磁体系统及其形成方法
US10679781B1 (en) 2018-11-29 2020-06-09 Epsitau Ltd. Lightweight asymmetric magnet arrays with theta magnet rings
US10690738B1 (en) 2018-11-29 2020-06-23 Epsitau Ltd. Lightweight asymmetric magnet arrays
US10867733B2 (en) 2018-11-29 2020-12-15 Epsitau Ltd. Lightweight asymmetric magnet arrays with mixed-phase magnet rings
US11875937B2 (en) 2018-11-29 2024-01-16 Epsitau Ltd. Lightweight asymmetric array of magnet elements
DE102022202399A1 (de) 2022-03-10 2023-09-14 Bruker Biospin Gmbh NMR Permanentmagnet in Halbach-Anordnung basierend auf Segmenten mit regulärer Polyedergeometrie sowie Herstellungsverfahren
WO2023170030A1 (fr) 2022-03-10 2023-09-14 Bruker Biospin Gmbh Aimant permanent rmn en configuration de réseau de halbach à base de segments à géométrie polyédrique régulière et procédé de fabrication

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