GB2329967A - Superconducting magnet with internal correction coils - Google Patents

Abstract

A superconducting magnet for magnetic resonance spectroscopy comprises a set of coils 12 for generating the main magnetic field, and at least one inner coil 10 which homogenizes the magnetic field within a central region of interest enabling the axial length of the magnet to be reduced. The current density of the outer set of coils 12 is of the opposite direction to that of the inner coil 10, and it has a much greater magnitude. An outer shielding coil 14 with a current density opposite to that of the coils 12 may be provided. Preferably, all the coils of a group are connected in series. All of the coils may have an elliptical cross-section.

Description

1 SUPERCONDUCTING MAGNETS 2329967

This invention relates to improved designs for compact, high field, superconducting magnets for use in magnetic resonance spectroscopy and magnetic resonance microscopy or small scale imaging. In particular, the invention is directed to magnet systems that produce a homogeneous magnetic field component over a volume and where the length of the magnet system is restricted by the design configuration. Furthermore, the field outside the compact magnet is small due to shielding windings in the magnet structure.

Magnetic resonance microscopy (MRM) is a powerful tool for probing structure and molecular dynamics on a microscopic is scale. While the resolution of MRM is poor in relation to other modalities, such as electron microscopy, it has the advantage of being nondestructive and the ability to examine the dynamics of a system, and not only its inherent structure. MRM is fundamentally magnetic resonance imaging (MRI) on a smaller scale with the system redesigned to provide high resolution images. The major requirement to perform MRM over MRI is the need for a large increase in the signal-to-noise ratio (SNR) For example, in order to translate from a typical MRI isotropic resolution of 1 MM3 to a MRM scale resolution of 5 AM3 requires an improvement in SNR per voxel of 8 x 106. The SNR is not the only 2 contributing factor to MRM resolution, however, with properties such as molecular diffusion, relaxation behavior, and sample-induced susceptibility boundary distortions affecting ultimate limits.

The method used to obtain SNR improvements is normally to decrease the size of the sample and associated hardware, namely radio frequency (rf) probes and gradient sets, and to increase the static field strength of operation. When small samples of rf coils are used, the resonant impedance of the coil usually dominates over sample impedance and the SNR is approximately proportional to B0714 where B 0 is the static flux density in Tesla. Herein lies the requirement of MRM to operate in strong magnetic fields, typically 7 T (300 MHz proton precessional frequency) or higher is used for modern

MRM.

operating at high field strength is also of great advantage to nuclear magnetic resonance (NMR) spectroscopists due again to the increase in SNR but also the increased chemical shift dispersion. The use of high field systems for molecular structural determination considerably predates MRM. All known MRM systems use magnets designed for molecular structure determinations, and these magnets are typically very long relative to their bore size, offering little access to the sample under study. This limited access is 3 is a distinct disadvantage in many MRM applications. NMR magnets for high field applications typically consist of a set of coaxial solenoidal coils connected with two or more external "correction,' coils in the fashion described some time ago by Garrett (M. W. Garrett, J. Appl. Phys. 22, 1091 (1951); M. W. Garrett, J. Appl. Phys. 38, 2563 (1967)). These layouts have formed the basis of even the most modern coil structures (T. Kamikado et al., IEEE Trans. Magn. 30, 2214 (1994); S.-T. Wang et al., IEEE Trans. Magn. 30, 2340 (1994)). The magnet designs disclosed in these publications are typically very long relative to their bore size, (usually having a total coil length to diameter of sensitive volume ratio of 20 or so) offering little access to the sample under study. This limited access can be a distinct disadvantage in many applications. A representative layout is shown in the cross-section of Figure 1, where each of the sections contains many thousands of turns of superconducting wire. The requirements of this design are that it is "homogeneous" over a diameter- sensitive -volume (dsv), where the conductors are operating with suitable factors of safety in terms of their critical current-carrying capacity and the critical field within which they reside. For simplicity, only the coil structure is detailed in this specification and not the ancillary cryogenic structures.

This invention seeks to provide magnet designs suitable for 4 high f ield, high resolution spectroscopy and imaging that have a reduced length over conventional designs and still produce suitably homogeneous f ields over a central volume while simultaneously allowing only a small amount of field leakage external to the magnet.

According to the present invention there is provided a magnet for use in magnetic resonance spectroscopy, the magnet having a primary section with at least one first coil forming an inner part of the primary section of the magnet and at least one group of second coils having a larger radius than the said at least one first coil, the coils being wound such that the said at least one first coil has a current density opposite that of the second coils and the said group of second coils than the current density coil.

has a current density much larger of the said at least one f irst By convention, the current density of the group of second coils is designated as a positive current density and the current density of the or each first coil is designated as a negative current density. The group of second coils forms the outer part of the primary section of the magnet. The said at least one first coil may be part of a group of first coils comprising two or more coils. The or a first coil may be an internal correction coil or all the first coils in the group may be internal correction coils.

The magnet may included at least one third.coil wound on a larger radius than the second coils. There may be a group of such third coils. Some or all of the said third coils in this group may have a negative current density, that is a current density opposite that of the current density in the group of second coils. This group of third coils acts as a shielding section to reduce the stray field of the magnet.

The or each first coil acts to enable the overall length of the magnet to be reduced while maintaining a homogenous field over the central region. Preferably, all of the coils in any group are connected in series, therefore all carrying the same transport current.

Figure 1 shows an example of a typical prior art high field magnet system;

Figure 2 shows an embodiment of the invention having a magnet coil configuration having one first coil 10, three second coils 12 in a group and one third coil 14; Figure 3 shows an embodiment of a magnet coil configuration similar to that shown in Figure 2 except that there is a group of first coils 10, comprising four coils; Figure 4 is a cut-away perspective view of the embodiment of Figure 2; 6 Figure 5 shows an embodiment of a magnet coil configuration like that shown in Figure 2 except that there is a group of third coils 14 comprising three third coils; and Figure 6 shows a further embodiment of a magnet coil configuration.

As there are a large number of design variables in such magnet system it is necessary to design an optimisation routine for these systems. A brief discussion of the methodology follows.

In Magnetic Resonance (MR), the f ield component of usual interest may be described by the Laplacian is Z 2 B,=0 which may be expanded in spherical harmonics over a sphere of radius r in the usual way B, r" (a,, cos mo + b,,, sin ino) P,,, (COSO) where a,m and b,, are the amplitudes of the harmonics and P,, (coso) are the associated Legendre polynomials of order n and degree m. In the case of systems possessing total cylindrical symmetry, as in the structures discussed here, 7 only zonal spherical harmonics (m = o) need to be considered in the design process. In order for the magnet to be deemed homogeneous over its diameter sensitive volume (dsv), the sum of all zonal harmonics should be less than a prescribed amount of the zero order harmonic; the BZ f ield, usually termed the BO field in NMR. The harmonic terms of interest are further restricted to even order zonal terms as the current density distribution in these magnets is even and axisymmetric. For a theoretical design the homogeneity requirements should be less than 5 parts per million.

A bare magnet homogeneity requirement of 20 ppm or less over the dsv is common for MRI systems.

It is also important that the spatial distribution of the field inhomogeneity in the field be characterized by low order terms after construction, so that they may be removed by passive or active (superconducting) shimming, a process where the purity of the field is improved using additional (shim) coils. The theoretical design process, therefore, must place special emphasis on reducing the higher order terms. The problem then, is to generate a coil structure to satisfy the harmonic purity requirements while restricting the total length of the magnet. In addition it must be specified to reduce the field outside the magnet.

8 The Simulated Annealing method (SA) (S. Kirkpatrick, D. C. Gelatt and M. P. Vechhi, Science 220, 671 (1983)) is an effective large scale optimization method and may be applied to high field magnet design. By imposing length constraints, the SA routine effectively attempts to find the,best" solution possible within these limits. Here "best" refers to the minimization of an error function which, in this case, contains terms representing the homogeneity of the diameter sensitive volume and the stray field outside the magnet. It is possible to include other terms in the function as the designer requires. The error function for the designs presented here was simply:

9 1 1 E = k. 1 k,,A 2n + kb B.d (z.) + B niod (y.) n=l is m=l m=l where k,, and kb are the weighting factors for the homogeneity and shielding terms respectively, kn are the weighting factors for the zonal harmonics and A2, are the amplitudes of the even order zonal harmonics of B,. The two summations of the shielding terms are the modulus field additions longitudinally and vertically at the chosen shielding distances respectively and for each iteration ten points per direction were summed (ie. I=10)

9 The homogeneity term is the most difficult to minimize and so may be weighted 5:1 when compared to the shielding term.

Even order zonal harmonics may be weighted 1:10:100:1000:5000:8000:10000:12000:15000 up to 18 th order.

The parameters for perturbation in the design process for each iteration were; the axial and radial dimensions of each coil, the number of turns per coil and the radial and axial position of each coil. In order to introduce sufficient degrees of freedom in these constrained problems, the design began with relatively large numbers of coils (ten) and allowed the SA process to redistribute them. Adaptive step sizing (A. Corona, M. Marchesi, C. Martini and S. Ridella, ACM Trans. Math. Soft 13, 262 (1987)) was implemented and initial step sizes and temperatures selected by testing each coil for parametric sensitivity prior to the SA run.

Table 1 Compact Shielded Magnet Homogeneity Transport current for 7.05T (Amps) 427.5 Length of conductor (km) 17.12 Homogeneity (35 mm dsv) (ppm) peak-to-peak 0.6 Rms 0.3 Shielding (axial 5 g contour) 1.7m Shielding (radial 5 9 contour) 2.Om Field Harmonics (ppm)

Z2 5.1e-3 Z4 4.1e-2 Z6 -3.9e-1 Z8 -1.1e-1 Z10 -1.1e-3 Z12 1.8e-4 Z14 -1.3e-6 Z16 3.2e-8 Z18 3.3e-8 In an exemplary embodiment, the process was used to design a 7 Tesla magnet system with an inner coil radius restricted to 55 mm so that the free bore diameter may approximate 89 mm (a standard commercial figure). The invention is not limited to the precise form or dimensions disclosed in this example. Figure 2 shows the schematic of the resultant 11 compact design in cross-section. Figure 4 shows a perspective view of the optimized structure. The bore of the resultant design may be oriented in either a vertical or horizontal sense as shown in this figure. In a further embodiment of the invention, all coils are arranged to have elliptical cross-sectional areas rather than the circular cross-sections indicated in the figures.

is The performance of the magnet is detailed in Table 1 and indicates the high homogeneity and small fringe fields of the magnet. The total length of the magnet coils in the z axial direction is 200 mm giving a coil length to homogeneous region diameter ratio of 5.7, indicating the compactness of the system. The harmonics of the field were calculated to 18th order and the peak-to-peak and rms field deviations were calculated over 800 points on the surface of the dsv in 20 planes, the distribution of these planes being chosen to be the zeros of the 20th order Legendre polynomial so that Gaussian integration may be readily implemented, and to ensure that Nyquist sampling requirements were met for 18 th order harmonic analyses. Note that the homogeneity figures are bare homogeneity values, that is, that no additional superconducting or room temperature coils were added to further improve the field purity.

Figure 6 shows a cut away view of a couplet magnet coil is 12 configuration. In this embodiment the shielding section 14 in the previously described embodiment has been omitted. Coil 20 is counter wound to the winding direction adopted for coils 21. Additional coils 22 and 23 are shown present between adjacent coils 21. Table 3 gives performance characteristics for the magnet coil of Figure 6.

Table 3

Transport current for 7.OST (Amps) 390 Length of conductor (km) 10.0 Homogeneity (40 mm dsv) (ppm) peak-to-peak 0.74 Rms 0.4 Field harmonics (ppm)

Z2 4.1e-2 Z4 -2.0e2 Z6 2.0e-1 Z8 -4.4e-1 zio 2.0e-3 Z12 8.7e-4 Z14 -1.4e-5 Z16 -1.8e-8 Z18 3.1e-7 Table 4 provides details of magnet coil layouts where ta is the turns density in each coil of the embodiment of Figure 13 6.

Table 4 coil Lef t Right Number Inner Outer td (MM) -2 No. end end of radius radius (mm) (MM) turns (MM) (MM) 1 0 9.0 733 100.089 283.523 0.444 2 28.7 40.7 67 92.705 105.280 0.444 3 40.7 88.7 3399 97.887 257.374 0.444 4 0.0 73.5 -619 54.835 73.803 0.444 The harmonics of the field were calculated to 18th order and the peak-to- peak and rms field deviations were calculated over 800 points on the surface of the dsv in 20 planes, the distribution of these planes being chosen to be the zeros of 2 Oth order Legendre polynominal so that Gaussian integration may be readily implemented, and to ensure that Nyquist sampling requirements were met for 18t' order harmonic analyses. The accuracy of the field and harmonic calculations have been verified by comparison with commercial electromagnetics software (Vector Fields, oxford); the results were within 0.01-01; of each other. Note that the homogeneity figures are bare homogeneity values, that is, that no additional superconducting or room temperature coils were added to further improve the field purity. with the addition of such shims, the magnet

14 described in Tables 3 and 4 would be appropriate for chemical applications as well as MRM.

An important consideration in superconducting magnets is to ensure that the conductors are operating within acceptable limits of current density and submersed field strengths. The maximum field in any conductor was calculated to be 12.1 T. Using a Nb3Sn conductor, with a turns density of 0.444 MM-2 (see Table 4) and a superconductor-to-matrix filling ratio of approximately 0.6 - quite a reasonable operating safety margin. While Nb3Sn is a more expensive conductor than NbTi, its ability to carry higher current density, and the compact design mean that a relatively small amount of conductor is needed when compared to conventional designs.

Table 2 provides details of magnet coil layouts where t. is the turns density in each coil of the embodiment of Figures 2 and 4.

Table 2 Magnet Coil layouts Coil A Width #Turns Inner -2 Zed (mm) radius t d (MM) (mm) (mm) 1 4.5 9.0 870 100.566 0.444 2 63.98 57.0 3852 98.281 0.444 3 37.5 75.0 -641 54.884 0.444 4 50.25 100.5 -12 350.065 0.444 is where "Zed" indicates the longitudinal position of the middle of each coil, "Width" indicates the axial extent of each coil and td is the turns density.

16

Claims (10)

1. A magnet tor use in magnetic resonance spectroscopy, the magnet having a primary section with at least one first coil forming an inner part of the primary section of the magnet and at least one group of second coils having a larger radius than the said at least one first coil, the coils being so wound that the said at least one first coil has a current density opposite that of the said group of second coils which in turn has a current density much larger than the current density of the said at least one first coil.

2. A magnet as claimed in Claim 1, wherein the said at least one first coil forms part of a group comprising two or more coils.

3. A magnet as claimed in Claim 1 or Claim 2, in which the or a said first coil is an internal correction coil.

4. A magnet as claimed in Claim 2 and Claim 3, in which all the coils in the group of first coils are internal correction coils.

5. A magnet as claimed in any of Claims 1 to 4 including at least one third coil wound on a larger 17 radius than the said first and second coils, which acts as a shielding section for reducing stray fields, the said at least one third coil being wound so as to have a current density opposite that of the said second coils.

6. A magnet as claimed in any preceding claim, wherein the coils of a group thereof are connected in series.

7. A magnet as claimed in any preceding claim, having a magnetic field strength of about 7 Tesla and in which the radius of the innermost coil is about 55mm with a free bore diameter of about 89mm.

8. A magnet as claimed in any preceding claim, wherein the said group of second coils comprises three said second coils.

9. A magnet as claimed in any preceding claim, wherein all said coils have an elliptical cross-section.

10. A magnet substantially as hereinbefore described with a reference to, and as shown in, the accompanying drawings.