JP2727877B2 - Method for configuring coil of magnet for nuclear magnetic resonance apparatus - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for constructing a coil of a magnet for a nuclear magnetic resonance apparatus suitable for generating a uniform magnetic field with a small leakage magnetic field to the outside, and an apparatus using the same.

[0002]

2. Description of the Related Art As an example of a conventional superconducting magnet for nuclear magnetic resonance, as described in Japanese Patent Application Laid-Open No.
In a magnet in which a first group of superconducting coils constituting a main coil and a second group of superconducting coils constituting a cancel coil are arranged, a uniform magnetic field is generated in a measurement space, and a high-order magnetic field in a region outside the magnet is generated. Those that suppress the magnetic moment are known.

[0003]

In the above prior art, since the main coil and the cancel coil are respectively arranged on the substantially spherical surfaces, the structure of the magnet becomes complicated and large. The coils are configured such that the main coil and the cancel coil independently suppress higher-order magnetic moments in the outer region, and the magnet as a whole suppresses higher-order magnetic moments in the outer region. For this reason, there has been a problem that the wire material of the coil must be used more than necessary and sufficient.

SUMMARY OF THE INVENTION The present invention has been made in view of the above problems, and it is an object of the present invention to suppress a magnetic moment in a region outside a magnet in a total of magnetic fields generated by a main coil and a cancel coil. Specifically, in a magnet composed of a first group of coils constituting a main coil and a second group of coils constituting a cancel coil,
Disclosed is a method of determining a coil configuration for setting a development coefficient by a spherical harmonic function of a magnetic field of an inner region and an outer region represented as a sum of magnetic fields by respective coils to a desired target value for a desired order, and using this method. Thus, it is possible to provide a small and low-cost magnet for a highly uniform magnetic field generating nuclear magnetic resonance apparatus, which has a sufficiently small leakage magnetic field and is obtained.

[0005]

SUMMARY OF THE INVENTION An object of the present invention is to determine an optimal current density distribution that matches the expansion coefficient of a magnetic field based on a spherical harmonic function in the inner and outer regions of a magnet with a desired target value for a desired order. Then, the initial position of the coil is determined from the obtained current density distribution, and the coil position is optimized so that the expansion coefficient of the desired order matches the desired target value.

A procedure for calculating the optimization of the coil configuration according to the present invention will be described with reference to FIG. First, the steps of optimizing the current density distribution using the linear programming will be described.

FIG. 5 shows a calculation model for optimization using linear programming (coil arrangement is symmetrical with respect to the center plane). First, in the boxes 21 and 22, the location (coil area) where the coil is arranged is divided into elements as shown in FIG. 5, and the current density of each coil element is set as an unknown in the linear programming. In the linear programming, it is possible to set a constraint condition that can be expressed in a linear form for unknowns, and to maximize or minimize an objective function that can be expressed in a linear form for unknowns. Therefore, assuming that the current density of the k-th coil element is jk, the following constraints are applied. (1) In box 23, for the coil element corresponding to the main coil, 0 <jk <jmax jmax: the maximum value of the current density (2 ) In box 24, for the coil element corresponding to the cancellation coil: -jmax <jk <0 (3) In box 25, for the nth order expansion coefficient of the internal region magnetic field by all coil elements:

[0008]

(Equation 8)

(4) In box 26, regarding the nth order expansion coefficient of the external region magnetic field by all coil elements,

[0010]

(Equation 9)

Is set.

Next, in box 27, as an objective function F of the linear programming,

[0013]

(Equation 10)

V _k : Volume of k-th coil element F: Total volume of coil (corresponding to wire length) is set.

Next, in box 28, the objective function F is minimized using the linear programming under the constraints set in boxes 23 to 26, and the current density distribution is optimized.

FIG. 6 shows an example of execution of the linear programming model described above. The constraints on the expansion coefficient are as follows: D0 = 1.5T, D2 = D4 =... D10 = 0 for the inner area, and H1 = H3 = 0 for the outer area. The upper limit Jmax of the current density was set to 141.2 A / mm ² . In the optimal solution in FIG. 6, coil elements having a current density equal to the maximum value Jmax appear adjacent to each other, and the coil elements between them have a property that the optimized current density becomes zero. This property suggests that the optimal coil arrangement is mathematically determined.

Next, the step of deciding the initial arrangement of the coils from the current density distribution optimized by the linear programming method and optimizing the position of each small coil using the Davidon method which is a kind of the gradient method will be described. I do. First, in box 29, from the optimal current density distribution obtained by the linear programming method, taking into account the actual conductor cross-sectional shape and winding method,
Determine the initial placement of the coil.

Next, in box 30, an evaluation function for the internal region magnetic field in consideration of the spatial distribution (Equation 1) of the magnetic field of each order.

[0019]

[Equation 11]

Is minimized by optimizing the coil position using the Davidon method. This evaluation function represents the sum of squares of the higher-order irregular magnetic field, and △ B _i can be considered as a measure of the irregular magnetic field generated by the entire coil. Similarly, in box 31, the evaluation function for the external region magnetic field

[0021]

(Equation 12)

Is minimized by optimizing the coil position using the Davidon method. Here, it is desirable that the order and the target value of the expansion coefficient specified in the boxes 30 and 31 match the values specified in the boxes 25 and 26 in order to match the optimization step by the linear programming method.

Next, in a decision box 32, it is decided whether or not the evaluation functions relating to the magnetic fields of the inner region and the outer region have converged to predetermined tolerances εi and εe, respectively. If the convergence does not occur, the boxes 30 and 31 are repeated until the evaluation function becomes equal to or smaller than a predetermined allowable value.

[0024]

The magnetic field generated by the linear circular current i shown in FIG. 2 is defined as follows. Since the magnetic field is symmetric with respect to the z axis, it can be represented only by the z component and the ρ component in the cylindrical coordinates. These are called the Legendre function P _n and the associated Legendre function P _n
When expressed using m, in the internal region of the circular current (r <c),

[0025]

(Equation 13)

[0026]

[Equation 14]

[0027]

(Equation 15)

In the external region of the circular current (r> c),

[0029]

(Equation 16)

[0030]

[Equation 17]

[0031]

(Equation 18)

## EQU1 ##

Next, a magnetic field generated by a coil (solenoid) having a rectangular cross section shown in FIG. 3 will be defined. The magnetic fields in the inner and outer regions can be expressed as the sum of spherical harmonics of the same form as above. That is, focusing on the magnetic field in the z-axis direction, the internal magnetic field

[0034]

[Equation 19]

Regarding the external magnetic field,

[0036]

(Equation 20)

Can be expressed as Where D _n , H _n
Is referred to as the expansion coefficient of the magnetic field. When the current density of the solenoid and j, the expansion coefficients D _n, H _n of the magnetic field of the inner and outer regions of Figure 3 with a d _n, h _n number 10 and number 13

[0038]

(Equation 21)

[0039]

(Equation 22)

Is given by Here, D ₀ is the intensity of the uniform magnetic field, higher order expansion coefficient D _n (n> 0) is the intensity of the irregular magnetic field that degrades the magnetic field uniformity, and H ₁ is the leakage magnetic field due to the magnetic dipole moment. The strength, higher order expansion coefficient H _n (n> 0), is the strength of the stray magnetic field due to the higher order magnetic moment. If the coil has symmetry with respect to the center plane (z = 0) of the magnet and the same solenoid is located at a position symmetrical with the center plane, in Equation 1, n is an odd expansion coefficient of zero and n is an even expansion coefficient. Is twice (Equation 1), and
, The expansion coefficient with n being an even number is zero, and the expansion coefficient with n being an odd number is twice as large as (Equation 2).

FIG. 4 shows the magnetic field distributions of the first, third and fifth-order terms in the expansion formula (Equation 2) of the magnetic field in the outer region of the magnet. When r is the distance from the origin o, the first, third, and fifth order terms are inversely proportional to r3, r5, and r7, respectively, so that a magnetic field having a higher order has a property of rapidly attenuating at a greater distance.
Therefore, the leakage magnetic field can be reduced by sequentially erasing the low-order terms that reach far away.

Further, in order to improve the uniformity of the magnetic field in the magnet inner region, the irregular magnetic field component may be eliminated from the low-order terms, and the uniform magnetic field region is expanded by eliminating the higher-order terms.

As described above, focusing on the expansion coefficient of the magnetic field by the spherical harmonic function, the magnetomotive force distribution and position of each small coil are set so that the expansion coefficient of a desired order becomes a desired target value (zero). By performing the optimization, it is possible to achieve a desired magnetic field uniformity in the inner region, and at the same time, a desired leakage magnetic field characteristic in the outer region.

[0044]

【Example】

(Embodiment 1) An embodiment of a superconducting magnet for a nuclear magnetic resonance apparatus using the coil configuration method of the present invention will be described. In the following, for simplicity, a magnet in which the primary and tertiary components of the external magnetic field are eliminated is called a fifth-order active shield type magnet, and a magnet in which the primary, tertiary and fifth-order components are eliminated is a seventh-order active shield type magnet. Call.

FIG. 7 is a sectional view of a superconducting magnet for a fifth-order active shield type nuclear magnetic resonance apparatus having six main coils according to an embodiment of the present invention.

Six types of small superconducting coils 1, 1 ', 2, 2', 3,
3 ', 4, 4', 5, 5 'and 6, 6' are wound. FIG. 1 shows only the cylindrical portion of the bobbin. Of these small superconducting coils, small coils 1, 1 ', 2, 2' and 3, 3 'constituting a main coil and small coils 4, 4', 5, 5 'and 6, constituting a cancel coil
6 'each have a substantially equal mean winding radius and are symmetrically arranged with respect to the center plane of the magnet (z = 0). Also, the central axis of each small superconducting coil coincides with the z-axis. Of the 12 small superconducting coils, the small superconducting coils 1, 1 ', 2, 2' and 3, which constitute the main coil,
3 ′ and a small superconducting coil 4 constituting a cancel coil
4 ', 5, 5' and 6, 6 'are electrically connected in series, and the directions of currents are all the same in the small superconducting coil constituting the main coil, and the small superconducting coil constituting the cancel coil is formed. The direction of the coil is opposite to the direction of the small superconducting coil constituting the main coil.

In the above coil configuration, the central magnetic field intensity is 1.
5T, the irregular magnetic field from the second to the 10th order in the inner region is zero, the first and third order components of the outer region magnetic field are zero, the current density of each small superconducting coil is 141.2 A / mm ² , and the main coil is configured. The average winding radius of the small superconducting coil is approximately 567m
m, the result of optimization under the condition that the average winding radius of the small superconducting coil constituting the cancel coil is approximately 833 mm. Here, in the step of optimizing the current density distribution,
By limiting the axial length of the area where the coils are arranged, the axial lengths of the main coil and the cancel coil are made substantially the same. At this time, the values of the parameters of each small superconducting coil are as shown in Table 1.

Table 1 Coil number (i) r (mm) zi (mm) Magnetomotive force (kAT) 1 567.0 91.4 396.0 2 567.0 304.0 510.4 3 567.0 696.1 1393.9 4 833.0 39.2-198.6 5 833.0 331.8-171.5 6 833.0 777.5-695.5 where r is the average winding radius of each coil, and zi is This is the average distance from the center plane of each coil.

FIG. 8 shows the calculation results of the leakage magnetic field of the fifth-order active shield type superconducting magnet. In this figure, contour lines where the magnitude of the leakage magnetic field is 10 G, 5 G and 1 G are shown on a plane including the center axis of the magnet. It can be seen that by eliminating the primary and tertiary components of the magnetic field in the external region, the magnitude of the leakage magnetic field rapidly attenuates far away, and the leakage magnetic field can be kept very small.
Further, the absolute value of the leakage magnetic field on the z-axis and the ρ-axis is 10 G,
The distances from the origin of 5G and 1G are r10,
Assuming that r5 and r1, ρ10, ρ5 and ρ1, r5 / r10 = 1.10 r1 / r10 = 1.38 ρ5 / ρ10 = 1.11 ρ1 / ρ10 = 1.43. When the leakage magnetic field is attenuated in inverse proportion to the seventh power of the distance from the origin, the above ratio is 1.10 and 1.39. It can be seen that this has been achieved.

(Embodiment 2) FIG. 9 shows another embodiment of the present invention. This embodiment is a result of optimization performed when the average winding radius of the second group of coils constituting the cancel coil is approximately 933 mm and other conditions are the same as those in FIG.
Table 2 shows parameter values of each small superconducting coil.

Table 2 Coil number (i) r (mm) zi (mm) Magnetomotive force (kAT) 1 567.0 91.7 333.2 2 567.0 304.8 439.9 3 567.0 692.3 1208.5 4 933.0 0.0 -311.9 5 933.0 760.0 -575.8 As shown in FIGS. 7 and 9, when the radius of the cancel coil is changed, the number of small coils constituting the cancel coil is changed. , Placement,
The magnetomotive force changes. As the radius of the cancel coil is larger than the radius of the main coil, the number of small coils constituting the cancel coil tends to decrease.

The leakage magnetic field in the embodiment shown in FIG. 9 has substantially the same distribution as in FIG. As described above, the fifth-order active shield type magnet can achieve a sufficiently low leakage magnetic field in any of the embodiments by making the leakage magnetic field dominant the fifth-order component that is inversely proportional to the seventh power of the distance from the center of the magnet. Recognize.

(Embodiment 3) An embodiment according to the present invention of a seventh-order active shield type superconducting magnet for nuclear magnetic resonance having six main coils will be described. FIG. 10 shows an average winding radius of the main coil of about 567 mm, an average winding radius of the cancel coil of about 833 mm, six main coils and six cancel coils, and FIG. 12 shows an average winding radius of the main coil of about 567 mm. The average winding radius of the coil is approximately 933
FIG. 3 is a cross-sectional view of a magnet having six main coils and three cancel coils. This coil configuration has a center magnetic field of 1.5T, an irregular magnetic field from the second to the tenth order in the inner region is zero, first, third and fifth order components of the outer region magnetic field are zero, and a current density is 141.2 A /. This is the result of optimization under the condition of mm ² . Figure 1 shows the values of the parameters of each small superconducting coil.
0 and FIG. 12 are shown in Tables 3 and 4, respectively.

Table 3 Coil number (i) r (mm) zi (mm) Magnetomotive force (kAT) 1 567.0 91.5 483.7 2 567.0 301.8 559.4 3 567.0 691.5 1213.3 4 833.0 86.1-420.2 5 833.0 304.9-241.0 6 833.0 980.0-384.4 Table 4 Coil number (i) r (mm) zi (mm) ) Magnetomotive force (kAT) 1 567.0 90.8 403.1 2 567.0 300.8 470.2 3 567.0 688.1 1086.2 4 933.0 0.0 -891.0 5 933. 0 1050.1 -278.3 FIG. 11 shows the distribution of the stray magnetic field of the magnet shown in FIG. The magnet shown in FIG. 12 has almost the same leakage magnetic field distribution. Assuming that the distances from the origin where the absolute values of the leakage magnetic fields are 10G, 5G and 1G on the z-axis or ρ-axis are r10, r5 and r1, ρ10, ρ5 and ρ1, respectively, r5 / r10 = 1.08 r1 / r10 = 1.29 ρ5 / ρ10 = 1.09 ρ1 / ρ10 = 1.28. When the leakage magnetic field attenuates in inverse proportion to the ninth power of the distance from the origin, the above ratios are 1.08 and 1.29. It can be seen that this has been achieved. Thus, the seventh-order active shield type magnet can achieve a very small leakage magnetic field in any of the embodiments by making the leakage magnetic field dominant the seventh-order component which is inversely proportional to the ninth power of the distance from the center of the magnet. I understand. Compared with the above-described fifth-order active shield type magnet, the leakage magnetic field is attenuated faster, and better leakage magnetic field characteristics are achieved.

Next, an embodiment of the present invention in the case where the number of small superconducting coils constituting the main coil is 7, 8, or 9 will be described. In each case, the central magnetic field strength is 1.5 T, and the current density of the coil is 141.2 A / mm ² .

(Embodiment 4) FIGS. 13 and 14 are cross-sectional views of a nuclear magnetic resonance magnet according to an embodiment of the present invention when the number of small superconducting coils constituting the main coil is seven. FIG. 13 shows a fifth-order active shield type magnet.
The result of optimization under the condition that the number of main coils is seven and the number of cancellation coils is six, the irregular magnetic field from the second to the twelfth in the inner region is zero, and the first and third order components of the outer region magnetic field are zero. It is. FIG. 14 shows a seventh-order active shield type magnet having seven main coils and six canceling coils. The irregular magnetic field from the second to the twelfth order in the inner region is zero, and the primary and third magnetic fields in the outer region. Next and 5
This is the result of optimization under the condition that the next component is zero. The average winding radii of the main coil and the cancel coil are approximately 567 mm and 833 mm, respectively. Tables 5 and 6 show the values of the parameters of each small coil for FIGS. 13 and 14, respectively.
Shown in

Table 5 Coil number (i) r (mm) zi (mm) Magnetomotive force (kAT) 1 567.0 0.0 350.2 2 567.0 160.9 374.1 3 567.0 361.6 484.8 4 833.0 751.6 138.7 5 833.0 54.0-151.6 6 833.0 195.1-241.0 7 833.0 824.0-729.2 Table 6 Coil number (I) r (mm) zi (mm) Magnetomotive force (kAT) 1 567.0 0.0 371.4 2 567.0 162.3 417.0 3 567.0 361.8 557.6 4 567.0 744.1 1214.8 5 833.0 140.0 -288.0 6 833.0 342.9 -444.2 7 833.0 1040.4-368.4 In the above two embodiments, in the internal region, From secondary 1
Since the second-order irregular magnetic field is set to zero, there is an effect that a highly uniform magnetic field can be obtained in a range that is about 10% wider than the case where the number of main coils is six.

The leakage magnetic field distribution of the fifth-order active shield type magnet shown in FIG. 13 is substantially the same as the distribution shown in FIG. 8, and the leakage magnetic field attenuates almost in inverse proportion to the seventh power of the distance from the center of the magnet. There is an effect that good leakage magnetic field characteristics can be obtained.

The leakage magnetic field distribution of the seventh-order active shield type magnet shown in FIG. 14 is almost the same as the distribution shown in FIG. 11, and the leakage magnetic field attenuates in inverse proportion to the ninth power of the distance from the center of the magnet. There is an effect that better leakage magnetic field characteristics can be obtained than the fifth-order active shield type magnet.

(Embodiment 5) FIGS. 15 and 16 are sectional views of a nuclear magnetic resonance magnet according to an embodiment of the present invention when the number of small superconducting coils constituting the main coil is eight. FIG. 15 shows a fifth-order active shield type magnet having eight main coils and four cancellation coils, having zero random magnetic fields from the second to 14th order in the inner region, and the first and third magnetic fields in the outer region. This is the result of optimization under the condition that the next component is zero. FIG. 16 shows a seventh-order active shield type magnet having eight main coils and seven canceling coils. The irregular magnetic field from the second to the 14th order in the internal region is zero, and the primary and external magnetic fields in the outer region are three. Next and 5
This is the result of optimization under the condition that the next component is zero. The average winding radius of the main coil and the cancellation is approximately 567, respectively.
mm and 833 mm. The values of the parameters of each small superconducting coil are shown in Tables 7 and 8 for FIGS. 15 and 16, respectively.
Shown in

Table 7 Coil number (i) r (mm) zi (mm) Magnetomotive force (kAT) 1 567.0 69.4 301.9 2 567.0 218.5 363.9 3 567.0 411.3 490.4 4 567.0 798.1 1362.3 5 833.0 233.5 -492.3 6 833.0 889.7 -674.7 Table 8 Coil number (i) r (mm) zi (mm) Magnetomotive force (kAT) 1 567.0 69.4 322.2 2 567.0 219.4 389.1 3 567.0 412.0 555.7 4 567.0 790.3 1212.9 5 833.00 0.0-148.6 6 833.0 141.4 -105.9 7 833.0 363.5 -608.8 8 833.0 1089.4-360.1 In the above two embodiments, the internal region From secondary 1
Since the fourth-order irregular magnetic field is set to zero, there is an effect that a highly uniform magnetic field can be obtained over a wider range by about 20% than in the case of six main coils.

The leakage magnetic field distribution of the fifth-order active shield type magnet shown in FIG. 15 is substantially the same as the distribution shown in FIG. 8, and the leakage magnetic field attenuates in inverse proportion to the seventh power of the distance from the center of the magnet. There is an effect that good leakage magnetic field characteristics can be obtained.

The leakage magnetic field distribution of the seventh-order active shield type magnet shown in FIG. 16 is almost the same as the distribution shown in FIG. 11, and the leakage magnetic field attenuates in inverse proportion to the ninth power of the distance from the center of the magnet. There is an effect that better leakage magnetic field characteristics can be obtained than the fifth-order active shield type magnet.

(Embodiment 6) FIGS. 17 and 18 are sectional views of a superconducting magnet for a nuclear magnetic resonance apparatus according to an embodiment of the present invention when the number of small superconducting coils constituting the main coil is nine. FIG. 17 shows a fifth-order active shield type magnet having nine main coils and eight cancellation coils. The irregular magnetic field from the second to the 16th order in the inner region is zero, and the first and third magnetic fields in the outer region. The next component is the result of optimization under the condition of zero. FIG. 18 shows a seventh-order active shield type magnet having nine main coils.
The configuration has six canceling coils, and the irregular magnetic field from the second to the 16th in the internal region is zero, and the magnetic field in the external region is 1
This is the result of optimization under the condition that the next, third and fifth order components are zero. The average winding radii of the main coil and the cancel are approximately 567 mm and 833 mm, respectively. The values of the parameters of each small superconducting coil are shown in Tables 9 and 10 for FIGS. 17 and 18, respectively.

Table 9 Coil number (i) r (mm) zi (mm) Magnetomotive force (kAT) 1 567.0 0.0 261.7 2 567.0 124.5 273.4 3 567.0 266.1 324.3 4 567.0 456.6 485.7 5 833.0 837.0 1406.6 6 833.0 59.0-20.2 7 833.0 315.8 -133.6 8 833.0 465 0.0-144.09 833.0 893.2-736.5 Table 10 Coil number (i) r (mm) zi (mm) Magnetomotive force (kAT) 1 567.0 0.0 287.3 2 567. 0 124.8 308.9 3 567.0 266.7 376.5 4 567.0 455.0 528.1 5 567.0 833.2 1214.8 6 833.0 138.7 312.7 7 833 2.0 397.3-492.5 8 833.0 110.5-388.0 2 above In the embodiment, from the secondary in the inner region 1
Since the sixth-order irregular magnetic field is set to zero, there is an effect that a highly uniform magnetic field can be obtained over a wider range by about 30% than in the case of six main coils.

The leakage magnetic field distribution of the fifth-order active shield type magnet shown in FIG. 17 is almost the same as the distribution shown in FIG. 7, and the leakage magnetic field attenuates in inverse proportion to the seventh power of the distance from the center of the magnet. There is an effect that good leakage magnetic field characteristics can be obtained.

The leakage magnetic field distribution of the seventh-order active shield type magnet shown in FIG. 18 is substantially the same as the distribution shown in FIG. 10, and the leakage magnetic field is attenuated in inverse proportion to the ninth power of the distance from the center of the magnet. There is an effect that better leakage magnetic field characteristics can be obtained than the fifth-order active shield type magnet.

In the embodiment described above, in the fifth-order active shield type magnet, the axial lengths of the main coil and the cancel coil are substantially the same, and consideration is given to facilitating the manufacture of the magnet.

In all of the embodiments, the average winding radius of each of the small superconducting coils constituting the main coil and each of the small superconducting coils constituting the cancel coil are substantially the same. Each of the cancel coils can be wound around a cylindrical winding frame. Therefore, the structure and support method of the magnet can be made simple and strong. Although not shown, the winding frames 10 and 11 are cooled by separate liquid helium tanks. In this way, the small superconducting coils constituting the main coil and the cancel coil can be cooled in one liquid helium bath, respectively, so that the small superconducting coils can be connected in series. Therefore, the deviation from the initial setting of the current distribution ratio of each small coil due to the attenuation of the coil current during the operation in the permanent current mode can be minimized, and the deterioration of the magnetic field uniformity can be prevented.

In the above-described embodiment, the main coil and the cancel coil are wound on different cylindrical winding frames, respectively, and each is housed in a separate liquid helium tank for cooling. Of course, the method of cooling is not limited by the present embodiment, for example, by winding a main coil and a cancel coil on an integrated winding frame, installing in a single liquid helium tank, and cooling. Is also good. In this configuration, all the small superconducting coils can be connected in series, and the deterioration of the magnetic field uniformity due to the attenuation of the coil current can be minimized. Alternatively, the main coil and the cancel coil may be wound around different cylindrical winding frames, respectively, and placed in one liquid helium bath to cool.

[0071]

According to the present invention, it is possible to obtain an optimum coil configuration that matches the expansion coefficient of the magnetic field based on the spherical harmonics in the inner and outer regions of the magnet with a desired target value for a desired order. A coil configuration is obtained which achieves the desired properties of the regional and external region magnetic fields. Furthermore, by adopting the coil arrangement obtained by the method of the present invention, the magnetomotive force of the main coil and the cancel coil for generating the same magnitude of the central magnetic field strength is reduced, so that less superconducting wire is required, Cost can be reduced.

[Brief description of the drawings]

FIG. 1 is a calculation procedure for optimizing a coil configuration according to the present invention.

FIG. 2 is an explanatory diagram of a linear circular current.

FIG. 3 is an explanatory diagram of a coil having a rectangular cross section.

FIG. 4 is a distribution diagram of first three terms (first-order, third-order, and fifth-order) in a development formula of a magnetic field in a magnet outer region.

FIG. 5 is a calculation model for optimizing a current density distribution by a linear programming method.

FIG. 6 is a cross-sectional view of an optimized current density distribution.

FIG. 7 shows an embodiment of the present invention in which the main coil is 6
FIG. 3 is a cross-sectional view of a fifth-order active shield type superconducting magnet for nuclear magnetic resonance in the case of a single piece.

FIG. 8 is a plan view including a cross section of a fifth-order active shield type superconducting magnet according to an embodiment of the present invention.
Contour map of the leakage magnetic field.

FIG. 9 shows an embodiment of the present invention in which the main coil is 6
FIG. 5 is a cross-sectional view of a fifth-order active shield superconducting magnet in the case of a single unit.

FIG. 10 is a cross-sectional view of a seventh-order active shield type superconducting magnet in a case where there are six main coils in one embodiment of the present invention.

FIG. 11 is a contour diagram of a leakage magnetic field in a plane including a cross section of the seventh active shield type superconducting magnet in one embodiment of the present invention.

FIG. 12 is a cross-sectional view of a seventh-order active shield superconducting magnet in a case where there are six main coils in one embodiment of the present invention.

FIG. 13 is a sectional view of a fifth-order active shield type superconducting magnet in a case where the number of main coils is seven in one embodiment of the present invention.

FIG. 14 is a cross-sectional view of a seventh-order active shield superconducting magnet in a case where the number of main coils is seven in one embodiment of the present invention.

FIG. 15 is a sectional view of a fifth-order active shield type superconducting magnet in a case where the number of main coils is eight in one embodiment of the present invention.

FIG. 16 is a cross-sectional view of a seventh-order active shield superconducting magnet in a case where the number of main coils is eight in one embodiment of the present invention.

FIG. 17 is a cross-sectional view of a fifth-order active shield type superconducting magnet in a case where the number of main coils is nine in one embodiment of the present invention.

FIG. 18 is a cross-sectional view of a seventh-order active shield superconducting magnet in a case where the number of main coils is nine in one embodiment of the present invention.

[Explanation of symbols]

1,1 ', 2,2', 3,3 ', 4,4', 5,5 ',
6, 6 ', 7, 7', 8, 8 ', 9, 9' ... small superconducting coils, 10, 11 ... non-magnetic winding frames.

 ────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Toshinaka Toshinaka 4026 Kuji-cho, Hitachi City, Ibaraki Prefecture Hitachi, Ltd. Hitachi Research Laboratory (56) References -191405 (JP, A) JP-A-63-206232 (JP, A)

Claims (3)

(57) [Claims] 1. a first step of determining an optimum current density distribution for matching a development coefficient of a magnetic field based on a spherical harmonic function in an inner region and an outer region of a magnet to a desired target value with respect to a desired order; internal from the resulting current density distribution, to determine the initial placement of the coils, Ri name from the second step to optimize the coil position to match the expansion coefficient of the desired order to the desired target value, of the magnet in each region and the external region field ## EQU1 ## (Equation 2) z axis: central axis of the magnet Bz: z component of the magnetic field r, θ: polar coordinates with the center of the magnet as the origin Pn: nth-order Legendre function Dn: expansion coefficient of the internal area magnetic field Hn: expansion coefficient of the external area magnetic field in represents the first step the location and the element division to place (a) coil current to each element
(B) assigning the density jk as a variable; and (b) restricting the current density jk of each element to the following conditions (1) to (4):
And (1) for the coil element corresponding to the main coil, 0 ≦ jk ≦ jmax jmax: the maximum value of the current density (2) For the coil element corresponding to the cancel coil, −jmax ≦ jk ≦ 0 (3 ) Nth order expansion coefficient of the internal region magnetic field due to all coil elements
With respect to, [number 3] (4) Nth order expansion coefficient of the external magnetic field due to all coil elements
With respect to, [number 4] (c) evaluation function F [number 5] corresponding to the total volume of the coil Vk: setting the volume of the k-th coil element; and (d) using the linear programming method under the constraint conditions,
The step of minimizing the valence function and optimizing the current density distribution
From the result, the current density distribution obtained the second step is the step (e) (d),
Determine the initial coil layout considering the conductor cross-sectional shape.
And step, (f) evaluation function [6] relates to the magnetic field of the inner area And a step of minimizing the optimization of coil position with Davidon method, (g) the evaluation function Equation 7] about the magnetic field of the outer regions (H) alternately perform steps (f) and (g) to optimize the coil position using the Davidon method, so that the evaluation function of the internal region and the external region is reduced to a desired value or less. A method for forming a coil of a magnet for a nuclear magnetic resonance apparatus, comprising the steps of repeating until a coil is formed. 2. A mug for a nuclear magnetic resonance apparatus according to claim 1,
Net is coaxial along the central axis and symmetric about the midplane
Group of coils consisting of a plurality of small cylindrical coils arranged in
And coaxially outside the first group of coils along the central axis.
And a plurality of cylindrical small cores symmetrically arranged with respect to the center plane.
A coil configuration method for a magnet for a nuclear magnetic resonance apparatus, comprising a second group of coils made of an il . 3. The first group of coils according to claim 2,
A coil configuration method for a magnet for a nuclear magnetic resonance apparatus, wherein the second group of coils is excited in a reverse direction .