GB2252168A

GB2252168A - Magnetic field correction device for nmr magnet coil.

Info

Publication number: GB2252168A
Application number: GB9123941A
Authority: GB
Inventors: Shimada Uji; Oue Tatuya
Original assignee: Mitsubishi Electric Corp
Current assignee: Mitsubishi Electric Corp
Priority date: 1990-11-09
Filing date: 1991-11-11
Publication date: 1992-07-29
Anticipated expiration: 2011-11-11
Also published as: DE4136834C2; GB9123941D0; JPH0816695B2; JPH04177187A; GB2252168B; DE4136834A1

Description

2'16 2 5 2 1

MAGNETIC FIELD CORRECTION DEVICE

BACKGROUND OF THE INVENTION

This invention relates to magnetic field correction devices utilized, for example, in electromagnets for generating a uniform field for nuclear magnetic resonance.

Fig. 8 is a schematic perspective view of a conventional magnetic field correction device, which is disclosed, for example, in Japanese Laid-Open Patent (Kokai) No. 52-193230. Within a coil 3 is disposed an interior cylinder 10 made of a non-magnetic material, on which rod-shaped magnetic members 2 are adhered. The magnetic field generated by the coil 3 is not sufficiently uniform as required within the uniform field region 4. Thus, the magnetic members 2 are attached on the interior cylinder 10 to modify the spatial distribution of the magnetic field and to enhance the uniformity of magnetic field within the uniform field region 4.

In the case of the conventional device, the magnetic members 2 are attached to arbitrarily selected positions on the interior cylinder 10 and the variation of the magnetic field distribution within the uniform field region 4 is determined experimentally. An arrangement of magnetic members 2 is selected by those skilled in the art on the basis of their experience so as to. achieve the required uniformity within the uniform field region 4.

The above conventional magnetic field correction device thus has the following disadvantage. The dimensions, number,

2 and positions of the magnetic members 2 are determined, for the main part, by the experience of the assembling engineer. There are no fast and definite rules for determining the dimensions, number, and positions of the magnetic members 2. Thus, the arrangements of the magnetic members 2 are not necessarily optimized, and the qualities of the magnetic field vary from one device to another. Further, the magnetic members 2 are sometimes attached to positions outside of the region on which the designer of the magnetic field correction device intends to mount the magnetic members 2 for the purpose of avoiding interferences with other parts of the device.

SUMMARY OF THE INVENTION

It is therefore an object of this invention to provide a magnetic field correction device by which the magnetic members can be easily mounted at axial and circumferential positions according to the' intention of the designer of the field correction device.

The above object is accomplished in accordance with the principle of this invention by a magnetic field correction device which comprises: a plurality of non-magnetic tubes disposed on a cylinder of a predetermined radius disposed coaxially with said coil, said non-magnetic tubes each extending along a direction of axis of said coil and disposed at predetermined angles along a circumference of said cylinder; and a plurality of rod-shaped magnetic members removably inserted into said non-magnetic tubes, said magnetic members each 2 - 3 consisting of two rod-shaped components of predetermined lengths and predetermined transverse sectional area ratio, such that said magnetic members form predetermined end angles when inserted into respective non- magnetic tubes.

For the purpose of eliminating the first order errors, it is preferred that said non-magnetic tubes are disposed at circumferential angles (n/2)( 1/2+1/3+1/4), (-n/2)(.tI/2+1/3+1/4)+n, (n/2) ( 1/2+1/3+1/4)+(1/2)n, or (-,E/2)( 1/2+1/3+1/4)+(3/2)n to accommodate respective magnetic members thereat; when said magnetic members are inserted into respective non-magnetic tubes, a sum of two end angles of each of the two rod-shaped components of said magnetic members with respect to an origin at a center of a uniform field region are equal to n; and when said magnetic members are inserted into respective non-magnetic tubes, transverse cross sectional areas Al and A2 and inner end angles al and a2, with respect to said origin, of the two rod-shaped components of said magnetic members satisfy:

(A2/Al) = -P 1 4 (cosal)sin 5 M1/P 1 4(cosa2)sin 5 a2, wherein: P 1 4 is an associated Legendre polynomial; and al and a2 are two distinct angles such that g(cxl) =g(cc2), where g(a) = P 1 6 (cosa)sin 2 C(/P 1 4(cosce), P 1 6 and P 1 4 being associated Legendre polynomials.

4 For the purpose of eliminating the second order errors relative to ZX and ZY, it is preferred that said non-magnetic tubes are disposed at circumferential angles (n/2)(+1/2+1/3+1/4), (n/2)(+1/2+1/3+1/4)+7, (n/2)(+ 1/2+1/3+1/4)+(1/2)n, or (n/2)(+1/2+1/3+1/4)+(3/2)n to accommodate respective magnetic members thereat; when said magnetic members are inserted into respective non-magnetic tubes, outer end angles aII of the two rod-shaped components of said magnetic members with respect to an origin at a center of a uniform field region are equal to each other; and when said magnetic members are inserted into respective non-magnetic tubes, transverse cross sectional areas Al and A2 and inner end angles al and (x2, with respect to said origin, of the two rod-shaped components of said magnetic members satisfy:

(A2/Al) = P 1 5(coscel) sin 6 al/P 1 5(cosa2) sin 6 a2, wherein: P 1 5 is an associated Legendre polynomial; and ml and a2 are two distinct angles such that g(a1)=g(a2)=g(aII), where g(a) = P 1 7(cosa) sin 2 OC/P 1 5(cosce), P 1 7 and P 1 5 being associated Legendre polynomials.

For the purpose of eliminating the second order errors 2_ 2 relative to XY and X Y, it is preferred that said non-magnetic tubes are disposed at circumferential angles (n/2)(+1/1+1/3+1/4)+(1/4)n, (-x/2)(+1/1+1/3+1/4)+(3/4)n, (n/2)(+1/1+1/3+1/4), or (n/2)(+1/1+1/3+1/4)+ (1/2)n to accommodate respective magnetic members thereat; when said magnetic members are inserted into respective non-magnetic tubes, a sum of two end angles of each of the two rod-shaped components of said magnetic members with respect to an origin at a center of a uniform field region are equal to -n; and when said magnetic members are inserted into respective non-magnetic tubes, transverse cross sectional areas Al and A2 and inner end angles al and (x2, with respect to said origin, of the two rod-shaped components of said magnetic members satisfy:

(A2/Al) = -P 2 5(cosocl)sin 6 ot 1 /P 2 5(cosa2)sin 6 cc 2, wherein: P 2 5 is an associated Legendre polynomial; and al and a2 are two distinct angles such that g(al) = g(a2), where g(a) = P 2 7(coscx)sin 2 a/P 2 5(cosa),P 2 7 and P 2 5 being associated Legendre polynomials.

BRIEF DESCRIPTION OF THE DRAWINGS

The features which are believed to be characteristi of this invention are set forth with particularity in the appended claims. The structure and method of operation of this invention itself, however, will be best understood from the following detailed description, taken in conjunction with the accompanying drawings, in which:

6 Fig. 1 shows a transverse sectional view of an electromagnet device provided with a magnetic field correction device according to this invention;

Fig. 2 shows a longitudinal sectional view of the device of Fig. 1; Fig. 3 is a diagrammatic transverse section view showing circumferential position of a magnetic shim (magnetic member); Fig. 4 is a diagrammatic longitudinal sectional view of a magnet shim (magnetic member); Fig. 5 is a perspective view of a magnetic shim consisting of two rod components.

Fig. 6 is a diagram showing the values of a function g(a) with respect to end angle a; Fig. 7 is a diagram showing an example of circumferential angular positions of the non-magnetic tubes for accommodating magnetic shims (magnetic members); and Fig. 8 is a schematic perspective view of a conventional magnetic field correction device.

In the drawings, like reference numerals represent like or corresponding parts or portions.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to the accompanying drawings, the preferred embodiments of this invention are described.

Fig. 1 be selectively inserted non-magnetic tubes 1. For the non-magnetic tubes 1 shows a transverse sectional view of an electromagnet device provided with a magnetic field correction device according to this invention, and Fig. 2 shows a longitudinal sectional view of the device of Fig. 1.

An interior cylinder 10 is coaxially inserted within a cylinder-shaped coil 3 which generates the main magnetic field therewithin. A plurality of non-magnetic tubes 1 made of a non-magnetic material are attached on the interior surface of

ZD the interior cylinder 10, such that the magnetic members 2 can into and removed from respective simplicity, Figs. 1 and 2 show only and the magnetic members 2 for correcting the positive linear X-component error field. As described below, the field within a uniform field region 4 is rendered homogeneous by means of the fields generated by the magnetic members 2.

According to. this invention, parameters (the number, circumferential and axial positions, the transverse sectional areas, etc) of the magnetic members 2 are determined in accordance with this invention to satisfy definite predetermined S relationships. Fig. 3 is a diagrammatic transverse section view showing circumferential position of a magnetic shim (magnetic member), and Fig. 4 is a diagrammatic longitudinal sectional view of a magnetic shim (magnetic member). In Figs. 3 and 4, a rod-shaped magnetic shim 2 having a positioned at a radius a respect to the X-axis. forms a larger angle aI and a smaller angle aII transverse area A is from the Z-axis and at an angle ?p with The two ends of the magnetic shim 2 (referred to as the "outer end angle") (referred to as the "inner end angle") with the Z-axis, which coincides with the central axis of the coil 3. The X-Y plane intersects the coil 3 at the middle, such that the origin (0, 0, 0) coincides with the center of the uniform field region 4. The position of an arbitrary point P within the uniform field region 4 is represented by the polar coordinates (r, 0, 95).

Thus, the Z-component Bz of the magnetic field generated by a magnetic shim 2 at point P is represented by:

0 Bz = -K. (l/a2 wherein K is a zonstant determined by the magnetic characteristics of the magnetic shim; am is the Neumann coefficient, which is equal to 1 A.=cc) f - - (n-m+l)! [Pmn + 1 (cosa) sinn + 2 a V II n m=0 (n+m)! aI (r/a)n. Pmn (cos 69). cos m(0 -0) (1) 9 = 1) where m = 0, and equal to 2 (6 m = 2) otherwise; and Pon represents the associated Legendre polynomial of degree n and order m.

The correspondence between the terms in polar coordinates expression (1) and those by Cartesian coordinates is given in TABLE 1 below, up to n = 2:

1 TABLE 1 n m terms in Cartesian coordinates ZX or ZY X2 - y2 or XY In the above TABLE 1, the integers n and m corresponds to those of equation (1) above.

On the other hand, the Z-component Bcz of the main magnetic field generated by the coil 3 in the uniform field region 4 is expressed, up to the second order terms, as:

Bc z = Bo + A1 X + A2 Y + A3 ZX + A4 ZY + A5 XY + A6 (X2 -y2) ----- (2) where Bo represents the magnetic field at the origin (0,0,0), and the term AlX, for example, represents the linear or first order error component along the X-axis.

According to an embodiment of this invention, the error terms up to the second order as expressed in equation (2) are compensated for and eliminated by means of the magnetic members 11 members 2, such that the magnetic field within the uniform field region 4 is rendered substantially uniform. Thus, the terms AlX, A2Yv A3= etc., are to be compensated for by means of the magnetic field generated by the magnetic members 2. In the following, the arrangement (positions and

2 for compensating for described as an example.

As seen from equation (1), the number of magnetic field components generated by a magnetic shim 2 is infinite. However, since mounting radius a of the magnetic shim 2 is greater than r (a > r), the factor: (r/a) n appearing in equation (1) is is sufficiently great. Thus, only the for small values of negligibly small if n terms of equation (1) n and m are practically important. Here, only the radial components of Bz (namely the terms for which m # 0) are considered. Thus, taken into consideration are the following terms Bno corresponding to those of the equation (1)): B11s B219 B229 B31 V B3 2 9 B3 3, B4 1, B4 2, B4 3, B4 4, BS 1 1 BS 2 y BS 3, BS 4.

As shown in TABLE 1 above, the B11 component corresponds to X-component in Cartesian coordinates. Our object here is to compensate for the error term A1X. Thus the above terms Bna must vanish except for B11. To accomplish this, the positions and dimensions of the magnetic members 2 are determined in accordance with the. principle of this invention as follows. First, as shown in Fig. 1, eight magnetic members 2 are arranged along the circumference such that the circumferential angles 0 thereof with respect to the X-axis are at:

dimensions) of the magnetic the X-comnonent error AiX is (n and m i 2(7r/2) ( (l/2) (l/3 1/4 (3) such that, for m = 2, 3, and 4, 2 cos M( 95 -0) = 0 wherein the summation extends over the eight values of 0 specified by equation (3) above.

Thus, the components Bno for which m = 2, 3, 4, namely, B22 B32 1 B33, B42, B43, B44, B52, B53, B54, vanish. Only the terms Wm where m = 1: B111 B21, B31, B41, and B51, remain, which are still to be vanished except for the first term B11.

The terms B21 and B41 are vanished by selecting the end angles of the magnetic members 2 appropriately. Namely, if the sum of the inner angle a I and outer end angle a II of the magnetic shim 2 is equal to 7r:

al = 7r - aII ---- (4) then, B2 1 CC [ P' 3 (COS a) s in4 a] aII 2r - a II B41 CC [P1s (cosa) sin4 a f 7r K aII Thus, B21 and B41 vanish..

Finally, the terms B31 and B51 are to be vanished. Thus, the magnetic members 2 are each composed of two rods as shown in 1 --:2) Fig. 5, and the transverse sectional areas A1 and A2 thereof and the inner end angles ai and a2 are selected to satisfy the relationships as specified below, the outer end angles being determined by the equation (4) above. The lengths L1 and L2 Of the two rod-shaped components of the magnetic members 2 are determined by the inner and outer end angles and the mounting radius a of the magnetic members 2 (see Fig. 4).

The terms B31 and B51 for the magnetic shim 2 of Fig. satisfy the following proportionalities:

B31 cc A1 [P' 4 (COSa 1)sins a 11 + A2 [ P' i (COSCt2)sins a 2 1 ---- (5) BS 1 cc Ai [P' 6 (cosai)sin7 a l] + A2 [P' 6 (COSa2)sin7 a 2 1 (6) Let a function g(a) of a be defined by:

g(a P16 (cosa)sin7a/P14 (cosa)sins a = P' 6 (cos a)sin2 a /P' 4 (cos a) Then, the proportionality equation (6) becomes:

B5 1 cc Ai g( a l) [P' 4 (cosa 1)sins a 1 1 + A2g(.a2) [jP14 (COSa2)sin.' a2 7a) Fig. 6 shows the values of g(a) with respect to the angle a. It is apparent from Fig. 6 that, for a given R, there 1.14 exist al and a2 such that R = 9(a 1) = 9(a2) l a 1 # a 2 - - - - (8) Substituting R of equation (8) into equation ('a), we obtain:

B51 cc R{Ai[P14(C0 sal)sinsal 1 + Az [P14 (cosa2)sinsa2 1} ---- (7b) The expression within the braces {} of equation (7b) is identical to the right hand side of equation (5). As noted above, it is seen from Fig. 6 that if a certain value of R is selected, then two distinct angles al and az satisfying the above equation (8) for that value of R can be determined. For such a pair a l and a 2, the terms B31 and Bs 1 are proportional to each other, since:

B31 cc Al [P' 4 (C0Sa 1)sins a l] + A2 [P14 (COSa2)sins a 2 1 Bs l cc R {Ai [P' 4 (COsc l)sins a l 1 + A2 [ Pl 4 (COS a 2)S ills a2 1} Thus, both terms B31 and B51 vanish if the transverse sectional areas Al and A2 satisfy:

Al[P14(cosal)sin-sall f A2 [P14 (cosa2)sins a21 = 0 ----- (9) or i -5 A2/A1 = - P14 (cosal)sins al/P14 (cosa2)sins a2 (9a) The equation (9a) specifies the cross-sectional area ratio of the two rod components of each one of the magnetic members 2.

Next, a specific numeric example is given. It is assumed that the designer of the magnetic field correction device intends to limit the range for the end angles of the magnetic members 2 to within 140 degrees. If the value of R = g(a) is selected at R = - 0.5 as shown in Fig. 6, the inner end angles of the respective rod components of a magnetic shim 2 satisfying the equation (8) above are: a 1 = 4 0. 1' and a 2 = 66.5. Then, the outer end angles corresponding thereto are: 7C - 40.1 = 139.9 and 7t - 66.5 = 113.5, which are within 140intended by the designer of the magnetic field correction device. Further, the cross-sectional area ratio of the two rod components as shown in Fig. 5 is determined by equation (9a) above as: A2/A1 = 0.1336, such that both terms B31 and BSI vanish. Since the value of R can freely selected, the freedom of design of the magnetic field correction device is ensured.

By arranging the magnetic members 2 at circumferential angles tP = (7t/2) ( (1/2) (1/3) (1/4)) with respect to the X-axis as shown in Fig. 1, negative linear (or first order) X-component (AiX <.0) i! generated. If the angles 0 are each increased by 7r such that 0 - 0 + 7c, or 0 = (7r /2) ( ( 1/2) (1/3) (1/4)) + it then, positive linear X-component (AiX > 0) is generated.

1 G Similarly, by arranging the magnetic members 2 at circumferential angles 0 = (7r/2) ( (1/2) (1/3) (1/4))+7t/2 with respect to the X-axis, negative linear Y-component (A2Y < 0) is generated. Further, if the angles 0 are each increased by x such that (7c/2) ( (1/2) (1/3) (1/4)) + 37r/2, positive linear Y-component (AzY > 0) is generated. Thus, the linear or first order error terms in equation (2) of either polarity can be compensated for and eliminated.

As shown in TABLE 1, the second order error terms A3ZX and A4ZY in equation (2) correspond to the output term B21 of the magnetic members 2, while those AsXY and A6(X2-y2) correspond to B22. Thus, by an argument similar to the above, it is shown that the second order error components can be compensated for and eliminated by arranging the magnetic members 2 each of which consists of two rod components (of transverse sectional area Ai and A2, end angles a, and circumferential angles 0 with respect to the X-axis), such that the transverse sectional area ratio A1/A29 the end angles, and the circumferential angles ?p satisfy specific relationships.

More specifically, for the purpose of eliminating first order error terms with respect to X and Y: (1) the non-magnetic tubes are disposed at circumferential angles (7r/2)( 1/2 1/3 1/4), (ic/2)( 1/2 113 1/4)+7t, (7t/2)( 1/2 1/3 1/4)+(1/2) 7c, or (7c/2)( 1/2 1/P 1/4)+(3/2)7r to accommodate respective magnetic members thereat; (2) when said magnetic members are inserted into respective non-magnetic tubes, a sum of two end angles of each of the two rod-shaped components of said magnetic 17 members with respect to an origin at a center of a uniform field region are equal to n; and (3) when said magnetic members are inserted into respective non-magnetic tubes, transverse cross sectional areas Al and A2 and inner end angles al and a2, with respect to said origin, of the two rod-shaped components of said magnetic members satisfy:

(A2/Al) = -P 1 4 (cosal)sin 5 C(I/P 1 4(cosce2)sin 5 a 2, wherein: P 1 4 is an associated Legendre polynomial; and al and a2 are two distinct angles such that g(cel) =g (cc 2), where g(a) = P 1 6 (cosa)sin 2 Ce/P 1 4(cosa), P 1 6 and P 1 4 being associated Legendre polynomials.

For the purpose of eliminating the second order terms with respect to Zx and Zy: (1) the non-magnetic tubes are disposed at circumferential angles (n/2)(.L1/2+1/3+1/4), (n/2)(+1/2+1/3+1/4)+n, (n/2) (+1/2+1/3+1/4)+(1/2)n, or (7/2)(.L1/2+1/3+1/4)+(3/2)n to accommodate respective magnetic members 2 thereat; (2) when said magnetic members are inserted into respective non-magnetic tubes, outer end angles a(II) of the two rod-shaped components of the magnetic members with respect-to an origin at a center of a uniform field region are equal to each other; and (3) when said

18 magnetic members are inserted into respective non-magnetic tubes, transverse cross sectional areas Al and A2 and inner end angles al and a2, with respect to said origin, of the two rod-shaped components of said magnetic members satisfy: (A2/Al) = -P 1 5(cosal) sin 6 C(l/P 1 5(cosa2) sin 6 a2, wherein: P 1 5 is an associated Legendre polynomial; and al and a2 are two distinct angles such that g(a1)=g(a2)=g(aII), where g(a) = P I 7(cosa) sin 2 a/P 1 5(cosa),P 1 7 and P 1 5 being associated Legendre polynomials.

For the purpose of eliminating the second order errors with respect to XY and X 2_y2: (1) the non-magnetic tubes are disposed at circumferential angles (7/2)(+1/1+1/3+1/4)+(1/4)n, (n/2)(+1/1+1/3+1/4)+(3/4)7, (n/2)(+1/1+ 1/3+1/4), or (r/2)(+1/1+1/3+1/4)+(1/2)n to accommodate respective magnetic members thereat; (2) when said magnetic members are inserted into respective non-magnetic tubes, a sum of two end angles of each of the two rod-shaped components of said magnetic members with respect to an origin at a center of a uniform field region are equal to n; and (3) when said magnetic members are inserted into respective non-magnetic tubes, transverse cross sectional areas Al and A2 and inner end

19 angles ccl and cc2, with respect to said origin, of the two rod-shaped components of said magnetic members satisfy:

(A2/A1) = -P 2 5(cosccl)sin 6 cc 1 /P 2 5(cosa2)sin 6 ez 2, wherein: P 2 5 is an associated Legendre polynomial; and al and a2 are two distinct angles such that g(cel) = g(cc2), where g(a) = P 2 7(cosa)sin 2 a/P 2 5(cosoc), P 2 7 and P 2 5 being associated Legendre polynomials.

TABLE 2 below shows an example of the numeric values of the arrangement of the magnetic members 2:

2-o TABLE 2 sect. area end angles a term ratio (A2/A1) (inner) (outer circumferential angles 0 (rad) X 0.1336 40. 1 139.9 (Ai) (7r /2) ( 1/2 1/3 1/4), 66. 5 113.5 (A2) (7c /2) ( 1/2 1/3 1/4) +7r, y 0.1336 40. 1 139.9 (A1) (7r /2) 1/2 1/3 1/4)+ ( 1/2)7r 66. 5 113.5 (A2) (7r/2) 1/2 1/3 1/4)+(3/2)7t 0.673 36. 06 82.34 (A1 7r /2 1/2 1/3 1/4), 97. 66 143.94 (A1 7c /2 1/2 1/3 1/4)+7r 36. 06 82. 34' (A2 118. 58 143.84 (A2 ZY 0.673 36. 06 82.34 (A1) ( 7r /2 1/2 1/3 1/4) + ( 1/2 7r 97. 66 143.94 (A1) ( 7r /2) 1/2 1/3 1/4)+ (3/2 7c 36. 06 82.34 (A2) 118. 58 143.84 (A2) XY 0.1694 45. 71 134.29 (A1) ( 7r/2 1/1 1/3 1/4)+( 1/4)x 69. 55 110.45 (Az ( 7r /2 1/1 1/3 1/4)+ ( 3/4) 7r X2 -Y2 0.1694 45. 71 134.29 (A1 (7r /2 1/1 1/3 1/4), 69. 55 110.45 (A2 (7c/2)( 1/1 1/3 1/4)+(112)7r ' I In TABLE 2, alternative values of the pairs of the end angles for the components ZX and ZY are given.

Thus, by making each one of the magnetic members 2 out of two rod components and setting to predetermined values: (1) the transverse sectional area ratio Ai/A2 of the two rod components of each one of the magnetic members 2; (2) the end angles a of the two rod components of each one of the magnetic members 2; and (3) the circumferential attachment angles 0 of the magnetic members 2, all the error terms up to second order in equation (2) can be compensated for and eliminated by means of the magnetic field generated by magnetic members 2. Thus, according to this invention, the non-magnetic tubes 1 are disposed at predetermined locations with respect to the coil 3, such that the magnetic members 2 are selectively inserted thereinto to compensate for and eliminate the error terms in equation (2).

Fig. 7 is a diagram showing an example of circumferential angular positions of the non-magnetic tubes for accommodating magnetic shims (magnetic members), wherein: reference numerals 1A designate the nonmagnetic tubes for compensating for the X and Y components; 1B, the nonmagnetic tubes for the ZX and ZY components; and 1C, the non-magnetic tubes for the XY and X2 - y2 components. The non-magnetic tubes 1 have lengths correspQnding to the lengths of the magnetic members 2 that are to be inserted thereinto.

As can be seen from equation (1) above, the absolute output value of the correction terms Bnm (for example, B11 for If 2-2- AlX) can be adjusted by selecting the overall transverse sectional area of the magnetic members 2 while maintaining the area ratio A2/A1 of the two rod components at the specific predetermined value. Thus, a number of magnetic members 2 having different overall transverse sectional areas (the lengths determined by the end angles and the mounting radius a as above and the cross sectional area ratios are as described above) are provided, and those which balance and compensate for the error terms are selected and inserted into the non-magnetic tubes 1. The non-magnetic tubes 1 thus have inner diameters sufficient to accommodate the magnetic members 2 of largest cross-sectional area that are provided to be inserted therein.

are specif ied determined 1 2-3

Claims

What is claimed is:

1. A magnetic field correction device for generating a uniform field within a hollow cylinder-shaped coil, comprising:

a plurality of non-magnetic tubes disposed on a cylinder of a predetermined radius disposed coaxially with said coil, said non-magnetic tubes each extending along a direction of axis of said coil and disposed at predetermined angles along a circumference of said cylinder; and a plurality of rod-shaped magnetic members removably inserted into said non-magnetic tubes, said magnetic members each consisting of two rodshaped componenfs of predetermined lengths and predetermined transverse sectional area ratio, such that said magnetic members form predetermined end angles when inserted into respective non-magnetic tubes.

2. A magnetic field correction device as claimed in claim 1, wherein:

said non-magnetic tubes are disposed at circumferential angles (7r /2) ( 1/2 1/3 1/4), (7r /2) 1/2 1/3 1/4)+7r, Or /2) ( 1/2 1/3 1/4)+(1/2) 7r, or (7r /2) 1/2 1/3 1/4)+ (3/2) 7r to accommodate respective magnetic members thereat; when said magnetic members are inserted into respective non-magnetic tubes, a sum of two end angles of each of the two rod-shaped components of said magnetic members with respect to an origin at a center.of 4 uniform field region are equal to 7r and when said magnetic members are inserted into respective non-magnetic tubes, transverse cross sectional areas A1 and A2 24- and inner end angles al and a2, with respect to said origin, of the two rod-shaped components of said magnetic members satisfy:

(A2/Al) = -P 1 4 (cosal)sin 5 al/P 1 4(cosa2)sin 5 a2, wherein: P 1 4 is an associated Legendre polynomial; and al and a2 are two distinct angles such that g(al)= g(a2), where g(a) = P 1 6 (cosa)sin 2 CX/P 1 Coosa), P 1 6 and P 1 4 being associated Legendre polynomials.

3. A magnetic field correction device as claimed in claim 1, wherein:

said non-magnetic tubes are disposed at circumferential angles (R/2)(+1/2+ 1/3+1/4), (7E/2)( 1/2+1/3+1/4)+n, (n/2)(+1/2+1/3+1/4)+(1/2)n, or (n/2)( 1/2+1/3+1/4)+(3/2)-x to accommodate respective magnetic members thereat; when said magnetic members are inserted into respective non-magnetic tubes, outer end angles aII of the two rod-shaped components of said magnetic members with respect to an origin at a center of a uniform field region are equal to each other; and when said magnetic members are inserted into respective non-magnetic tubes, transverse cross sectional areas Al and A2 and inner end angles al and a2, with respect to said origin, of the two rod-shaped components of said magnetic members satisfy:

(A2/Al) = -P 1 5(cosal) sin 6 al/P 1 5(cosa2) sin 6 a2, wherein: P 1 5 is an associated Legendre polynomial; and al and a2 are two distinct angles such that g(a1)=g(a2)=g(aII), where g(a) = P 1 7(cosa) sin 2 C(/P 1 5(cosc(),.p 1 7 andP 1 5 being associated Legendre polynomials.

4. A magnetic field correction device as claimed in claim 1, wherein:

said non-magnetic tubes are disposed at circumferential angles (n/2)(+1/1+ 1/3+1/4)+(1/4)Tc, (n/2)(+1/1+1/3+1/4)+(3/4)-,z, (-,,/2)(+1/1+1/3+1/4), or (n/2)(+1/1+1/3+1/4)+(1/2)n to accommodate respective magnetic members thereat; when said magnetic members are inserted into respective non-magnetic tubes, a sum of two end angles of each of the two rod-shaped components of said magnetic members with respect to an origin at a center of a uniform field region are when said magnetic members equal to Tc; and are inserted into respective non-magnetic tubes, transverse cross sectional areas A1 and A2 and inner end angles al and a2, with respect to said origin, of the two rod-shaped components of said magnetic members satisfy:

(A2/A1) = P 2 5(cosccl)sin 6 al/P 2 5(cosa2)sin 6 a.2, lX, wherein: P 2 5 is an associated Legendre polynomial; and al and a2 are two distinct angles such that g(el) = g(a2), where g(a) = P 2 7(cosa)sin 2 U/P 2 5(cosCO, P 2 7 and P 2 5 being associated Legendre polynomials.

5. A magnetic field correction device substantially as herein described with reference to Figures 1 to 7 of the accompanying drawings.