Abstract:
A magnet device provided with a shield current carrying means in which two sets of magneto-static field generating sources for generating magnetic fields directed towards a first direction are disposed facing each other across a finite region and at least one set of the magneto-static field generating sources are disclosed on at least two almost concentric circles. A first plane includes a first axis, a second axis and a first point. The first point is a point of insertion between the first axis parallel to the first direction and passing almost through the center of the shield current carrying means. The second axis crosses at right angles to the first axis and is spaced almost equal distance from the two sets of the generating sources. The alternately arranged positive and negative current carrying directions of the shield current carrying means are set in the order of increasing value of θn.

Description:
FIELD OF THE INVENTION 
   The present invention relates to a magnet and leakage magnetic field shield assembly suitable for a nuclear magnetic resonance imaging (MRI) apparatus and more particularly, to a magnet device and leakage magnet field shield assembly which have a wide opening to provide a sense of openness for the test subject, a highly uniform magnetic field, and a low leakage magnetic field. 
   BACKGROUND OF THE INVENTION 
   In the field of the nuclear magnetic resonance imaging (MRI) apparatuses, those of the so-called open-type concept has being developed in recent years. These apparatuses can generally fall into the two types of the apparatuses: apparatuses using conventional cylindrical solenoid magnets with elongated axes for increasing the sense of openness, and apparatuses using open-type magnets for generating a uniform magnetic field between two opposite magnet assemblies to enable the access to the patient being imaged. The MRI apparatuses with the former magnets provide a greater sense of openness than the conventional apparatuses but the sense is still insufficient to meet the demand in the medical field. 
   The MRI apparatuses with the latter magnets can provide a remarkable sense of openness, which can make possible the so-called IVR (Interventional Radiology). International Laid-open Publication WO99/27851 “MAGNET APPARATUS AND MRI APPARATUS” discloses superconducting magnets suitable for such open-type MRI apparatuses. 
   The superconducting magnets consist of two magnet assemblies opposed across an MRI imaging area. Each magnet assembly has more than one superconducting magnets and is almost symmetric with respect to the z-axis. Main coils have alternately positive and negative pole coils and can generate a highly uniform magnetic field although they are compact. 
   The open-type magnets have, however, essentially lower efficiency of the magnetic field generation than conventional solenoid magnets and need a larger magnetomotive force of the magnets which may result in a high leakage magnetic field, as described in S. Kakugawa et al., “A Study on Optimal Coil Configurations in a Split-Type Superconducting MRI Magnet,” IEEE Trans. Appl. Supercond., Vol. 9, No. 2, pp. 366-369, 1999. 
   One of solutions to the above problem is the use of shield coils as described in the above patent, reference, and U.S. Pat. No. 5,883,558, entitled “OPEN SUPERCONDUCTIVE MAGNET HAVING SHIELDING.” Conventional solenoid magnets generally use the shield coils as lightweight and effective solutions. 
   Furthermore, as a method for shielding the leakage magnetic field, Japanese Laid-open patent Publication No. Hei 07-336023, entitled “SUPERCONDUCTING MAGNET DEVICE” discloses a superconducting magnet device consisting of a main coil for making a current in a constant direction flow, and a bucking coil for making a current in the reverse direction to the main coil flow, and correction coils for correcting the uniform degree of the magnetic field. 
   As described in the above patent and patent application, the shield coils can decrease the leakage magnetic field in the open-type magnets. However, more leakage magnetic fields may remain in the open-type magnets with the shield coils than in the conventional solenoid magnets with the shield coils, which may adversely affect the MRI apparatus installation in the hospital. More leakage magnetic fields may remain because the coils or permanent magnets for static magnetic fields may have a larger magnetomotive force, as described in the above reference, resulting in the larger magnetomotive force of the shield coils which may cause larger leakage magnetic field from the shield coil itself. 
   Therefore it is an object of the present invention to provide a magnet and shield coil assembly with a low leakage magnetic field. 
   DISCLOSURE OF THE INVENTION 
   The present invention provides a magnet device comprising two magnetostatic field-generating sources opposed across a finite region for generating a magnetic field in a first direction in said finite region, at least one of said generating sources including at least two shield current carrying means in almost concentric relation, said magnet device defining: a first axis being parallel to said first direction and passing through the almost center of said shield current carrying means; a second axis intersecting at right angles with said first axis and being spaced at an almost equal distance from said two magnetostatic field-generating sources; a first point where said first axis and second axis intersect, a first plane including said first axis, second axis, and first point; and an angle θn for the n-th shield current carrying means, said angle θn being in said first plane between said first axis and a half line extending from said first point to the cross section geometric center of said n-th shield current carrying means, wherein said shield current carrying means in one or two of said magnetostatic field-generating sources have alternately positive and negative current carrying directions with increasing value of said θn. 
   The present invention provides a magnet device comprising two magnetostatic field-generating sources opposed across a finite region for generating a magnetic field in a first direction in said finite region, each of said generating sources including at least one of magnetic field generation current carrying means for generating said magnetic field, at least one of said generating sources including at least two shield current carrying means in almost concentric relation, said magnet device defining: a first axis being parallel to said first direction and passing through the almost center of said shield current carrying means; a second axis intersecting at right angles with said first axis and being spaced at an almost equal distance from said two magnetostatic field-generating sources; a first point where said first axis and second axis intersect, a first plane including said first axis, second axis, and first point; and an angle θn for the n-th shield current carrying means, said angle θn being in said first plane between said first axis and a half line extending from said first point to the cross section geometric center of said n-th shield current carrying means, wherein said shield current carrying means in one or two of said magnetostatic field-generating sources have alternately positive and negative current carrying directions with increasing value of said θn. 
   The present invention provides a magnet device comprising two magnetostatic field-generating sources opposed across a finite region for generating a magnetic field in a first direction in said finite region, each of said generating sources including at least one of magnetic field generation current carrying means for generating said magnetic field, a ferromagnet for making the magnetic field uniform in said finite area, and at least one of correction current carrying means for making the magnetic field uniform, at least one of said generating sources including at least two shield current carrying means in almost concentric relation, said magnet device defining: a first axis being parallel to said first direction and passing through the almost center of said shield current carrying means; a second axis intersecting at right angles with said first axis and being spaced at an almost equal distance from said two magnetostatic field-generating sources; a first point where said first axis and second axis intersect; a first plane including said first axis, second axis, and first point; and an angle θn for the n-th shield current carrying means, said angle θn being in said first plane between said first axis and a half line extending from said first point to the cross section geometric center of said n-th shield current carrying means, wherein said shield current carrying means in one or two of said magnetostatic field-generating sources have alternately positive and negative current carrying directions with increasing value of said θn. 
   The present invention provides a magnet device comprising two magnetostatic field-generating sources opposed across a finite region for generating a magnetic field in a first direction in said finite region, each of said generating sources including a permanent magnet, at least one of said generating sources including at least two shield current carrying means in almost concentric relation, said magnet device defining: a first axis being parallel to said first direction and passing through the almost center of said shield current carrying means; a second axis intersecting at right angles with said first axis and being spaced at an almost equal distance from said two magnetostatic field-generating sources; a first point where said first axis and second axis intersect, a first plane including said first axis, second axis, and first point; and an angle θn for the n-th shield current carrying means, said angle θn being in said first plane between said first axis and a half line extending from said first point to the cross section geometric center of said n-th shield current carrying means, wherein said shield current carrying means in one or two of said magnetostatic field-generating sources have alternately positive and negative current carrying directions with increasing value of said θn. 
   The present invention provides a magnet device comprising two magnetostatic field-generating sources opposed across a finite region for generating a magnetic field in a first direction in said finite region, at least one of said generating sources including at least two groups of shield current carrying means, each group consisting of at least one shield current carrying means, at least one group of said shield current carrying means including at least two shield current carrying means, said shield current carrying means making up each group of said shield current carrying means having the same shield current carrying direction and being in almost concentric relation, said magnet device defining: a first axis being parallel to said first direction and passing through the almost center of said shield current carrying means; a second axis intersecting at right angles with said first axis and being spaced at an almost equal distance from said two magnetostatic field-generating sources; a first point where said first axis and second axis intersect; a first plane including said first axis, second axis, and first point; and an angle θn for the n-th group of said shield current carrying means, said angle θn being in said first plane between said first axis and a half line extending from said first point to the cross section geometric center of all the shield current carrying means making up said n-th group of said shield current carrying means, wherein said groups of said shield current carrying means in one or two of said magnetostatic field-generating sources have alternately positive and negative current carrying directions with increasing value of said θn. 
   The present invention provides a magnet device comprising two magnetostatic field-generating sources opposed across a finite region for generating a magnetic field in a first direction in said finite region, each of said generating sources including at least one of magnetic field generation current carrying means for generating said magnetic field, at least one of said generating sources including at least two groups of shield current carrying means, each group consisting of at least one shield current carrying means, at least one group of said shield current carrying means including at least two shield current carrying means, said shield current carrying means making up each group of said shield current carrying means having the same shield current carrying direction and being in almost concentric relation, said magnet device defining: a first axis being parallel to said first direction and passing through the almost center of said shield current carrying means; a second axis intersecting at right angles with said first axis and being spaced at an almost equal distance from said two magnetostatic field-generating sources; a first point where said first axis and second axis intersect; a first plane including said first axis, second axis, and first point; and an angle θn for the n-th group of said shield current carrying means, said angle θn being in said first plane between said first axis and a half line extending from said first point to the cross section geometric center of all the shield current carrying means making up said n-th group of said shield current carrying means, wherein said groups of said shield current carrying means in one or two of said magnetostatic field-generating sources have alternately positive and negative current carrying directions with increasing value of said θn. 
   The present invention provides a magnet device comprising two magnetostatic field-generating sources opposed across a finite region for generating a magnetic field in a first direction in said finite region, each of said generating sources including at least one of magnetic field generation current carrying means for generating said magnetic field and a ferromagnet for making the magnetic field uniform in said finite area, at least one of said generating sources including at least two groups of shield current carrying means, each group consisting of at least one shield current carrying means, at least one group of said shield current carrying means including at least two shield current carrying means, said shield current carrying means making up each group of said shield current carrying means having the same shield current carrying direction and being in almost concentric relation, said magnet device defining: a first axis being parallel to said first direction and passing through the almost center of said shield current carrying means; a second axis intersecting at right angles with said first axis and being spaced at an almost equal distance from said two magnetostatic field-generating sources; a first point where said first axis and second axis intersect; a first plane including said first axis, second axis, and first point; and an angle θn for the n-th group of said shield current carrying means, said angle θn being in said first plane between said first axis and a half line extending from said first point to the cross section geometric center of all the shield current carrying means making up said n-th group of said shield current carrying means, wherein said groups of said shield current carrying means in one or two of said magnetostatic field-generating sources have alternately positive and negative current carrying directions with increasing value of said θn. 
   The present invention provides a magnet device comprising two magnetostatic field-generating sources opposed across a finite region for generating a magnetic field in a first direction in said finite region, each of said generating sources including at least one of magnetic field generation current carrying means for generating said magnetic field, a ferromagnet for making the magnetic field uniform in said finite area, and at least one of correction current carrying means for making the magnetic field uniform, at least one of said generating sources including at least two groups of shield current carrying means, each group consisting of at least one shield current carrying means, at least one group of said shield current carrying means including at least two shield current carrying means, said shield current carrying means making up each group of said shield current carrying means having the same shield current carrying direction and being in almost concentric relation, said magnet device defining: a first axis being parallel to said first direction and passing through the almost center of said shield current carrying means; a second axis intersecting at right angles with said first axis and being spaced at an almost equal distance from said two magnetostatic field-generating sources; a first point where said first axis and second axis intersect; a first plane including said first axis, second axis, and first point; and an angle θn for the n-th group of said shield current carrying means, said angle θn being in said first plane between said first axis and a half line extending from said first point to the cross section geometric center of all the shield current carrying means making up said n-th group of said shield current carrying means, wherein said groups of said shield current carrying means in one or two of said magnetostatic field-generating sources have alternately positive and negative current carrying directions with increasing value of said θn. 
   The present invention provides a magnet device comprising two magnetostatic field-generating sources opposed across a finite region for generating a magnetic field in a first direction in said finite region, each of said generating sources including a permanent magnet, at least one of said generating sources including at least two groups of shield current carrying means, each group consisting of at least one shield current carrying means, at least one group of said shield current carrying means including at least two shield current carrying means, said shield current carrying means making up each group of said shield current carrying means having the same shield current carrying direction being in almost concentric relation, said magnet device defining: a first axis being parallel to said first direction and passing through the almost center of said shield current carrying means; a second axis intersecting at right angles with said first axis and being spaced at an almost equal distance from said two magnetostatic field-generating sources; a first point where said first axis and second axis intersect; a first plane including said first axis, second axis, and first point; and an angle θn for the n-th group of said shield current carrying means, said angle θn being in said first plane between said first axis and a half line extending from said first point to the cross section geometric center of all the shield current carrying means making up said n-th group of said shield current carrying means, wherein said groups of said shield current carrying means in one or two of said magnetostatic field-generating sources have alternately positive and negative current carrying directions with increasing value of said θn. 
   The present invention provides a magnet device and shield current carrying means assembly comprising: a magnet device for generating a magnetic field in a first direction in a finite region; and at least two shield current carrying means almost concentric with a first axis being almost parallel to said first direction and passing through the almost center of said magnet device, said magnet device and shield current carrying means assembly defining: a first point on said first axis at said almost center of said magnet device; a first plane including said first axis and first point; a second plane including said first point and intersecting at almost right angles with said first axis; and an angle θn for the n-th shield current carrying means, said angle θn being in said first plane between said first axis and a half line extending from said first point to the cross section geometric center of said n-th shield current carrying means, wherein said shield current carrying means in at least one of the two spaces separated by said second plane has alternately positive and negative current carrying directions with increasing value of said θn. 
   The present invention provides a magnet device and shield current carrying means group assembly comprising: a magnet device for generating a magnetic field in a first direction in a finite region; and at least two groups of shield current carrying means almost concentric with a first axis being almost parallel to said first direction and passing through the almost center of said magnet device, each group consisting of at least one shield current carrying means, at least one group of said shield current carrying means including at least two shield current carrying means, said shield current carrying means making up each group of said shield current carrying means having the same shield current carrying direction, said assembly including: a first point on said first axis at said almost center of said magnet device; a first plane including said first axis; a second plane including said first point and intersecting at almost right angles with said first axis; and an angle θn for the n-th group of said shield current carrying means, said angle θn being in said first plane between said first axis and a half line extending from said first point to the cross section geometric center of all the shield current carrying means making up said n-th group of said shield current carrying means, wherein said groups of said shield current carrying means in at least one of the two spaces separated by said second plane has alternately positive and negative current carrying directions with increasing value of said θn. 
   The present invention provides a shield current carrying means group assembly for controlling or reducing the magnetic field leakage of a magnet device for generating a magnetic field in a first direction in a finite region, comprising at least two groups of shield current carrying means almost concentric with a first axis being almost parallel to said first direction and passing through the almost center of said magnet device, each group consisting of at least one shield current carrying means, at least one group of said shield current carrying means including at least two shield current carrying means, said shield current carrying means making up each group of said shield current carrying means having the same shield current carrying direction, said assembly including: a first point on said first axis at said almost center of said magnet device; a first plane including said first axis and first point; a second plane including said first point and intersecting at almost right angles with said first axis; and an angle θn for the n-th group of said shield current carrying means, said angle θn being in said first plane between said first axis and a half line extending from said first point to the cross section geometric center of all the shield current carrying means making up said n-th group of said shield current carrying means, wherein said groups of said shield current carrying means in at least one of the two spaces separated by said second plane has alternately positive and negative current carrying directions with increasing value of said θn. 
   The present invention provides a magnet device comprising one or more magnetostatic field-generating sources almost concentric with a center axis, said magnet device defining: a sphere centered at the center of said one or more magnetostatic field-generating sources and circumscribed about said magnet device; and a semicircle centered at said center with both ends of said semicircle on said center axis and with a radius from 1.1 to 2.0 times the radius of said sphere, wherein a magnetic field vector on said semicircle has a radial component having alternately opposite directions along the arc from one end to another of said semicircle and having more than five adjacent regions with different direction, and/or a tangential component having alternately opposite directions along the arc from one end to another of said semicircle and having more than four adjacent regions with different directions. 
   The principle and operation of the solution described above will be described below. The magnetic field can fall into two fields: a magnetic field in the internal area  234  of a sphere inscribed in the magnetic field-generating source, for example, a current  236  such as a coil or a magnetic material, and a magnetic field in the external area  235  of a sphere circumscribed about the magnetic field-generating source, as shown in FIG.  17 . If the field point P is in either the internal area  234  or the external area  235 , the magnetic field at the point P satisfies the Laplace equation (1),
 
Δ{right arrow over (B)}=0  (equation 1)
 
   The general solution of the equation (1) in the internal area  234  is the well-known spherical harmonics as given in the equation (2), 
               B   z     =       ∑     n   =   0     ∞     ⁢       D   n     ⁢     r   n     ⁢       P   n     ⁡     (     cos   ⁢           ⁢   θ     )                   (     equation   ⁢           ⁢   2     )             
 
   The general solution of the equation (1) in the external area  235  is the spherical surface harmonics including an inverse power of r to be holomorphic at infinity as given in the equation (3), 
                     B   z     =       ∑     n   =   1     ∞     ⁢       H   n     ⁢     1     r     n   +   2         ⁢       P     n   +   1       ⁡     (     cos   ⁢           ⁢   θ     )                         B   p     =     -       ∑     n   =   1     ∞     ⁢       H   n     ⁢     1       (     n   +   1     )     ⁢     r     n   +   2           ⁢       P     n   +   1     1     ⁡     (     cos   ⁢           ⁢   θ     )                           (     equation   ⁢           ⁢   3     )             
 
   Where P n  and P n   m  are the Legendre function and associated Legendre function, respectively, r and θ are the polar coordinates of the field point P, and D n  and H n  are expansion coefficients in the internal and external areas, respectively. The equation (3) shows that higher order in the magnetic field in the external area  235 , i.e., the leakage magnetic field, will decrease more rapidly. If the magnets are symmetric with respect to the central plane at z=0, the magnetic fields of even order vanish due to the symmetry. 
     FIGS. 18  to  21  show the magnetic field distributions for order n=1, 3, 5, 7. The magnetic fields of the first, third, fifth, and seventh order decrease in inverse proportion to the third, fifth, seventh, and ninth power of r from the origin. Thus, the sequential elimination from the lower order magnetic field can decrease rapidly the leakage magnetic field. The magnetic field strength of each order can be adjusted to control the leakage magnetic field distribution. The first order component of the leakage magnetic field is proportional to the magnetic moment of the magnet. 
   The leakage magnetic field expanded in the spherical surface harmonics will have components that need to be controlled with more than one shield coil, of which the arrangement can be calculated by the equation (3). The embodiments of the present invention will disclose the calculation examples on the shield coils.  FIGS. 18 ,  19 ,  20 , and  21  show the characteristics requirements for the shield coils. It is supposed here that the magnets are symmetric with respect to the central plane at z=0. The discussion below will demonstrate, however, that the shield coils will require the same characteristics even if the magnets are not symmetric. In figures below, there are general symbols near the coils for representing the coils&#39; electric current directions. 
   To suppress or control the first order component of the leakage magnetic field  238  shown in  FIG. 18 , a pair of shield coils, in others word, one shield coil for each of the two magnetostatic field-generating sources may be provided. The references described above disclose such a shield coil arrangement. As mentioned above, however, a pair of shield coils cannot decrease sufficiently the leakage magnetic field for the open-type magnets in which the two magnetostatic field-generating sources are opposed across a uniform magnetic field area. 
   It is because, as shown in  FIG. 22 , the arrangement of the magnetostatic field-generating sources such as main coils  242 ,  243  and, a pair of shield coils  244 ,  245  almost corresponds to the magnetic field generation arrangement which may increase the third order component of the leakage magnetic field  239 . Such a shield coil arrangement disclosed in the references described above may cause the shield coils themselves to significantly increase the third order component of the leakage magnetic field  239  so that the leakage magnetic field cannot decrease sufficiently. Thus, more shield coils are needed to decrease the third order component of the leakage magnetic field  239 . 
     FIG. 23  shows an arrangement of two pairs of the shield coils. The arrangement of the main coils  246 ,  247  for the magnetostatic field-generating sources and the shield coils  248 ,  249 ,  250 , and  251  almost corresponds to the magnetic field generation which may produce the fifth order component of the leakage magnetic field  240 . As the coil arrangement in  FIG. 23  is symmetric with respect to the central plane at z=0, the area of the z&gt;0 will only be discussed below. 
   In  FIG. 23 , the shield coils are arranged as follows: if half lines  254 ,  256  are defined as lines extending from the origin  253  to the cross section geometric center of each of the shield coils  248  and  250 , respectively, and θ1, θ2 are defined as angles  255 ,  257  between the z-axis  252  and the half lines  254 ,  256 , respectively, then the shield coil  248  corresponding to the θ1 has a positive current direction (the same direction as that of the main coils), and the shield coil  250  corresponding to the θ2 has a negative current direction (the opposite direction to that of the main coils). This can be generalized in that if the θn is defined as the angle for the n-th shield coil, the shield coils will have alternately positive and negative current directions with increasing value of the θn. Thus, to control the fifth order component of the leakage magnetic field, the shield coils with the positive current direction (the same direction as that of the main coils) are necessary. 
     FIG. 24  shows three pairs of the shield coils to control the seventh order component of the leakage magnetic field. The arrangement of the main coils  258 ,  259  for the magnetostatic field-generating sources and the three pairs of the shield coils  260 ,  261 ,  262 ,  263 ,  264 , and  265  almost corresponds to the magnetic field generation which may produce the seventh order component of the leakage magnetic field  241 . As the coil arrangement in  FIG. 24  is also symmetric with respect to the central plane at z=0, the area of the z&gt;0 will only be discussed below. 
   In  FIG. 24 , the shield coils are arranged as follows: if half lines  268 ,  270 , and  272  are defined as lines extending from the origin  267  to the cross section geometric center of each of the shield coils  260 ,  262 , and  264 , respectively, and θ1, θ2, and θ3 are defined as angles  269 ,  271 , and  273  between the z-axis  266  and the half lines  268 ,  270 , and  272 , respectively, then the shield coil  260  corresponding to the θ1 will have a negative current direction (the opposite direction to that of the main coils), the shield coil  262  corresponding to the θ2 will have a positive current direction (the same direction as that of the main coils), and the shield coil  264  corresponding to the θ3 will have a negative current direction (the opposite direction to that of the main coils). This can be generalized in that if the θn is defined as the angle for the n-th shield coil, the shield coils will have alternately positive and negative current directions with increasing value of the θn. 
   As described above, to reduce the leakage magnetic field in the open-type magnet, the higher order components of the leakage magnetic fields need to be controlled. To do so, the shield coils with the negative current direction (the opposite direction to that of the main coils) and the shield coils with the positive current direction (the same direction as that of the main coils) are both necessary. 
   The arrangement of this more than one shield coil follows the magnetic field generation that corresponds to the space distribution of the higher components of the leakage magnetic field as shown in  FIGS. 19  to  21 . The arrangement can be generalized in that, if the following is defined: two magneto-static field-generating sources are opposed; each magneto-static field-generating source includes more than one shield coil in almost concentric relation; the center axis is the z-axis; θ is an angle between the z-axis and a half line extending from the origin to the cross section geometric and the n-th shield coil corresponds to the θn, then the shield coils in one or two of the two magneto-static field-generating sources have alternately positive and negative current directions with increasing value of the θn. The inventors have provided the shield coils arrangement disclosed in the present invention for the first time, by determining the general solution in spherical harmonics (equation (3)) for the Laplace equation for the magnetic field in the external area  235  in  FIG. 17 , and by figuring out the magnetic field generation arrangement which may provide the space distribution of the higher order components of the leakage magnetic field as shown in  FIGS. 19  to  21 . 
   The present invention can also be characterized by the leakage magnetic field distribution. First, discussion will be given to the leakage magnetic field distribution in the conventional active-shield type of the open-type MRI magnets shown in  FIG. 22. A  semicircle is given which is centered at the magnet center, i.e., the origin in FIG.  22  and has its both ends on the z-axis and has a radius from 1.1 to 1.5 times the radius of a semicircle circumscribed about the magnets (only the coils shown). 
   Such a radius range is selected as a range where the leakage magnetic field is practically measurable. The magnetic field vector on the semicircle can fall into radial and tangential components. As shown in  FIG. 22 , in the leakage magnetic field distribution in the conventional active-shield type of the open-type MRI magnets, the radial component on the semicircle has alternately opposite directions along the arc from one end to another of the semicircle and has four adjacent regions with different directions. The tangential component on the semicircle has alternately opposite directions along the arc from one end to another of the semicircle and has three adjacent regions with different directions. 
   In the leakage magnetic field distribution according to the embodiment of the present invention shown in  FIG. 23 , the radial component on the semicircle has alternately opposite directions along the arc from one end to another of the semicircle and has six adjacent regions with different directions. The tangential component on the semicircle has alternately opposite directions along the arc from one end to another of the semicircle and has five adjacent regions with different directions. In this way, the present invention uses the coil having a positive current direction unlike the conventional magnets shown in FIG.  22 . Thus, the present invention almost eliminates the first order component of the leakage magnetic field which is dominant in the leakage magnetic field in the conventional magnets in FIG.  22  and makes the third order component of the leakage magnetic field dominant, thus providing a different number of adjacent regions with different directions of the magnetic components on the semicircle in the leakage magnetic field as described above. 
     FIG. 23  illustrates the magnets symmetric with respect to the central plane. However, the magnets generally may not be symmetric. Including such a case, the present invention can be generalized in terms of the leakage magnetic field distribution as follows. The radial component of the magnetic field on the semicircle as described above may have alternately opposite directions along the arc from one end to another of the semicircle and has more than five adjacent regions with different directions. Alternatively, the tangential component of the magnetic field on the semicircle as described above may have alternately opposite directions along the arc from one end to another of the semicircle and has more than four adjacent regions with different directions. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  shows a cross sectional view of superconducting magnets according to an embodiment of the present invention. 
       FIG. 2  shows a cross sectional view of superconducting magnets according to an embodiment of the present invention. 
       FIG. 3  shows a cross sectional view of superconducting magnets according to an embodiment of the present invention. 
       FIG. 4  shows a cross sectional view of superconducting magnets according to an embodiment of the present invention. 
       FIG. 5  shows a cross sectional view of superconducting magnets according to an embodiment of the present invention. 
       FIG. 6  shows a cross sectional view of superconducting magnets according to an embodiment of the present invention. 
       FIG. 7  shows a cross sectional view of superconducting magnets according to an embodiment of the present invention. 
       FIG. 8  shows a cross sectional view of superconducting magnets according to an embodiment of the present invention. 
       FIG. 9  shows a cross sectional view of superconducting magnets according to an embodiment of the present invention. 
       FIG. 10  shows a cross sectional view of superconducting magnets according to an embodiment of the present invention. 
       FIG. 11  shows a cross sectional view of a conventional coil arrangement. 
       FIG. 12  shows a leakage magnetic field distribution from the conventional coil arrangement in FIG.  11 . 
       FIG. 13  shows a cross sectional view of a conventional coil arrangement. 
       FIG. 14  shows a leakage magnetic field distribution of the conventional coil arrangement in FIG.  13 . 
       FIG. 15  shows a cross sectional view of the coil arrangement according to the present invention. 
       FIG. 16  shows a leakage magnetic field distribution of the coil arrangement according to the present invention in FIG.  15 . 
       FIG. 17  shows an axial symmetric two dimensional cross section and internal and external regions of a system of coils and magnetic materials. 
       FIG. 18  shows a space distribution of the first order component of the leakage magnetic field in the external region. 
       FIG. 19  shows a space distribution of the third order component of the leakage magnetic field in the external region. 
       FIG. 20  shows a space distribution of the fifth order component of the leakage magnetic field in the external region. 
       FIG. 21  shows a space distribution of the seventh order component of the leakage magnetic field in the external region. 
       FIG. 22  illustrates the principle by which the conventional shield coil arrangement may significantly increase the third order component of the leakage magnetic field. 
       FIG. 23  shows a shield coil arrangement corresponding to the fifth order component of the leakage magnetic field. 
       FIG. 24  shows a shield coil arrangement corresponding to the seventh order component of the leakage magnetic field. 
       FIG. 25  shows a cross sectional view of superconducting magnets according to an embodiment of the present invention. 
       FIG. 26  shows a cross sectional view of superconducting magnets, normal conducting shield coils, and a MRI scan room according to an embodiment of the present invention. 
       FIG. 27  shows a cross sectional view of superconducting magnets, normal conducting shield coils, and a MRI scan room according to an embodiment of the present invention. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   The embodiment of the present invention will be specifically described below referring to  FIGS. 1  to  11 . In figures below, there are general symbols near the coils for representing the coils&#39; electric current directions. 
     FIG. 1  shows a cross sectional view of superconducting magnets included in the open-type MRI apparatus. 
   The MRI apparatus in  FIG. 1  includes a pair of upper and lower superconducting magnet assemblies  17  and  18 , which may produce a uniform, magnetic field along the z-axis in the open region. The MRI imaging can be performed in the center part of the open region. The superconducting main coils  1 ,  2 ,  3 , and  4  are contained in a low-temperature enclosure  5 , which is in turn involved in a vacuum chamber  6 . Although not shown in  FIG. 1  for simplicity, the device also has a support structure for the superconducting coils and a heat shield between the vacuum chamber and low-temperature enclosure to prevent the penetration of heat radiation. The low-temperature enclosure contains liquid helium, which can cool the superconducting coils to a cryogenic temperature (4.2 K) to keep them in the superconducting state. 
   Connecting tubes  7 ,  8  between the upper and lower vacuum chambers can hold the chambers at a predetermined distance. These connecting tubes  7 ,  8  can mechanically support the upper and lower vacuum chambers. The tubes  7 ,  8  may also thermally connect the upper and lower low-temperature enclosures. This can replace the upper and lower cooling machines in the system with one cooling machine. The number of the connecting tubes  7 ,  8  does not need to be limited to two as shown in FIG.  1  and may be three or four or more, and may be one to support the vacuum chambers on one side to provide a greater sense of openness between the magnets. 
   The upper and lower magnet assemblies each include two superconducting shield coils for suppressing the leakage magnetic field. The upper magnet assembly  17  will be described below. The low-temperature enclosure  5  contains the superconducting shield coils  9 ,  10  and the liquid helium cools the coils to 4.2 K to keep them in the superconducting state. The superconducting main coils  1 ,  2 ,  3 ,  4 , and the superconducting shield coils  9 ,  10  are almost concentric with respect to the center axis  11  denoted as the z-axis in FIG.  1 . 
   The center axis (z-axis)  11  passes through the center  12  of the magnets. In the cross section of FIG.  1 , i.e., the cross section including the center axis (z-axis)  11 , θ1 is defined as an angle  14  between the center axis (z-axis)  11  and a half line  13  extending from the center  12  to the cross section geometric center of the superconducting shield coil  9 , and θ2 as an angle  16  between the center axis (z-axis)  11  and a half line  15  extending from the center  12  to the cross section geometric center of the superconducting shield coil  10 , and the θ1, θ2 are in a relation of θ1&lt;θ2. If the superconducting main coil  4  is defined to have a positive current direction, then the superconducting shield coils  9  and  10  corresponding to θ1 and θ2, respectively, will have positive and negative current directions, respectively. 
   This can be generalized in that the superconducting shield coils will have alternately positive and negative current directions with increasing value of the θn. The superconducting shield coil  10  with the largest radius of the two superconducting shield coils may have a larger magnetomotive force in absolute value than the other. As described above, the superconducting shield coils in this embodiment can control the higher order components of the leakage magnetic field to provide the leakage magnetic field lower than that in the conventional magnets described above. 
   Another embodiment of the present invention will be described below. 
     FIG. 2  shows a cross sectional view of the superconducting magnets in the open-type MRI apparatus according to another embodiment of the present invention. In this embodiment, the upper and lower magnet assemblies  19 ,  20  each include three superconducting shield coils. The superconducting main coils  21 ,  22 ,  23 , and  24  are contained in a low-temperature enclosure  25 , which is in turn involved in a vacuum chamber  26 . Although not shown in  FIG. 2  for simplicity, the device also has a support structure for the superconducting coils and a heat shield between the vacuum chamber and low-temperature enclosure to prevent the penetration of heat radiation. The low-temperature enclosure contains liquid helium, which can cool the superconducting coils to a cryogenic temperature (4.2 K) to keep them in the superconducting state. 
   Connecting tubes  27 ,  28  between the upper and lower vacuum chambers can hold the chambers at a predetermined distance. 
   These connecting tubes  27 ,  28  can mechanically support the upper and lower vacuum chambers. The tubes  27 ,  28  may also thermally connect the upper and lower low-temperature enclosures. This can replace the upper and lower cooling machines in the system with one cooling machine. The number of the connecting tubes  27 ,  28  does not need to be limited to two as shown in FIG.  2  and may be three or four or more, and may be one to support the vacuum chambers on one side to provide a greater sense of openness between the magnets. 
   The upper and lower magnet assemblies each include three superconducting shield coils for suppressing the leakage magnetic field. The upper magnet assembly  19  will be described below. The low-temperature enclosure  25  contains the superconducting shield coils  29 ,  30 , and  31  and the liquid helium cools the coils to 4.2 K to keep them in the superconducting state. The main coils  21 ,  22 ,  23 ,  24 , and the superconducting shield coils  29 ,  30 ,  31  are almost concentric with respect to the center axis  32  denoted as the z-axis in FIG.  2 . The center axis (z-axis)  32  passes through the center  33  of the magnets. 
   In the cross section of  FIG. 2 , i.e., the cross section including the center axis (z-axis)  32 , θ1, θ2, and θ3 are defined as angles  35 ,  37 , and  39  between the center axis (z-axis)  32  and half lines  34 ,  36 , and  38 , respectively, the half lines  34 ,  36 , and  38  extending from the center  33  to the cross section geometric center of each of the superconducting shield coils  29 ,  30 , and  31 , respectively, and the θ1, θ2, and θ3 are in a relation of θ1&lt;θ2&lt;θ3. If the superconducting main coil  24  is defined to have a positive current direction, then the superconducting shield coils  29 ,  30 , and  31  corresponding to θ1, θ2, and θ3, respectively, will have negative, positive, and negative current directions, respectively. 
   This can be generalized in that the superconducting shield coils will have alternately positive and negative current directions with increasing value of the θn. The superconducting shield coil  31  with the largest radius of the three superconducting shield coils may have a larger magnetomotive force in absolute value than the others. As described above, the superconducting shield coils in this embodiment can control the higher order components of the leakage magnetic field to provide the leakage magnetic field lower than that in the conventional magnets described above. 
     FIG. 3  shows a cross sectional view of the superconducting magnets in the open-type MRI apparatus according to another embodiment of the present invention. This embodiment uses one superconducting main coil  40  and a magnet pole  52  to produce a uniform magnetostatic field. The upper and lower magnet assemblies  53 ,  54  each include two superconducting shield coils. The superconducting main coil  40  and the magnet pole  52  are contained in a low-temperature enclosure  41 , which is in turn involved in a vacuum chamber  42 . Although not shown in  FIG. 3  for simplicity, the device also has a support structure for the superconducting coils and magnet pole and has a heat shield between the vacuum chamber and low-temperature enclosure to prevent the penetration of heat radiation. The low-temperature enclosure contains liquid helium, which can cool the superconducting coils to a cryogenic temperature (4.2 K) to keep them in the superconducting state. 
   Connecting tubes  43 ,  44  between the upper and lower vacuum chambers can hold the chambers at a predetermined distance. These connecting tubes  43 ,  44  can mechanically support the upper and lower vacuum chambers. The tubes  43 ,  44  may also thermally connect the upper and lower low-temperature enclosures. This can replace the upper and lower cooling machines in the system with one cooling machine. The number of the connecting tubes  43 ,  44  does not need to be limited to two as shown in FIG.  3  and may be three or four or more, and may be one to support the vacuum chambers on one side to provide a greater sense of openness between the magnets. 
   The upper and lower magnet assemblies each include two superconducting shield coils for suppressing the leakage magnetic field. The upper magnet assembly  53  will be described below. The low-temperature enclosure  41  contains the superconducting shield coils  45 ,  46  and the liquid helium cools the coils to 4.2 K to keep them in the superconducting state. The main coil  40  and superconducting shield coils  45 ,  46  are almost concentric with respect to the center axis  55  denoted as the z-axis in FIG.  3 . 
   The center axis (z-axis)  55  passes through the center  47  of the magnets. In the cross section of  FIG. 3 , i.e., the cross section including the center axis (z-axis)  55 , θ1, θ2 are defined as angles  49 ,  51  between the center axis (z-axis)  55  and half lines  48 ,  50 , respectively, the half lines  48 ,  50  extending from the center  55  to the cross section geometric center of each of the superconducting shield coils  45 ,  46 , respectively, and the θ1, θ2 are in a relation of θ1&lt;θ2. If the superconducting main coil  40  is defined to have a positive current direction, then the superconducting shield coils  45  and  46  corresponding to θ1 and θ2, respectively, will have positive and negative current directions, respectively. 
   This can be generalized in that the superconducting shield coils will have alternately positive and negative current directions with increasing value of the θn. The superconducting shield coil  46  with the largest radius of the two superconducting shield coils may have a larger magnetomotive force in absolute value than the other. As described above, the superconducting shield coils in this embodiment can control the higher order components of the leakage magnetic field to provide the leakage magnetic field lower than that in the conventional magnets described above. This embodiment uses the magnet pole  52  to produce a uniform magnetostatic field so that the superconducting main coil  40  may have a smaller magnetomotive force in absolute value than the superconducting main coils in the embodiments shown in  FIGS. 1 and 2 . The superconducting shield coils  45 ,  46  may then also have a smaller magnetomotive force in absolute value than the superconducting shield coils in the embodiments in  FIGS. 1 and 2 . Thus, the each shield coil may have a smaller electromagnetic force. 
     FIG. 4  shows a cross sectional view of the superconducting magnets in the open-type MRI apparatus according to another embodiment of the present invention. This embodiment uses one superconducting main coil  58  and a magnet pole  59  to produce a uniform magnetostatic field. The upper and lower magnet assemblies  56 ,  57  each include three superconducting shield coils. The superconducting main coil  58  and the magnet pole  59  are contained in a low-temperature enclosure  60 , which is in turn involved in a vacuum chamber  61 . Although not shown in  FIG. 4  for simplicity, the device also has a support structure for the superconducting coils and magnet pole and has a heat shield between the vacuum chamber and low-temperature enclosure to prevent the penetration of heat radiation. The low-temperature enclosure contains liquid helium, which can cool the superconducting coils to a cryogenic temperature (4.2 K) to keep them in the superconducting state. 
   Connecting tubes  62 ,  63  between the upper and lower vacuum chambers can hold the chambers at a predetermined distance. These connecting tubes  62 ,  63  can mechanically support the upper and lower vacuum chambers. The tubes  62 ,  63  may also thermally connect the upper and lower low-temperature enclosures. This can replace the upper and lower cooling machines in the system with one cooling machine. The number of the connecting tubes  62 ,  63  does not need to be limited to two as shown in FIG.  4  and may be three or four or more, and may be one to support the vacuum chambers on one side to provide a greater sense of openness between the magnets. 
   The upper and lower magnet assemblies each include three superconducting shield coils for suppressing the leakage magnetic field. The upper magnet assembly  56  will be described below. The low-temperature enclosure  60  contains the superconducting shield coils  64 ,  65 , and  66  and the liquid helium cools the coils to 4.2 K to keep them in the superconducting state. The superconducting main coil  58  and superconducting shield coils  64 ,  65 , and  66  are almost concentric with respect to the center axis  67  denoted as the z-axis in FIG.  4 . 
   The center axis (z-axis)  67  passes through the center  68  of the magnets. In the cross section of  FIG. 4 , i.e., the cross section including the center axis (z-axis)  67 , θ1, θ2, and θ3 are defined as angles  70 ,  72 , and  74  between the center axis (z-axis)  67  and half lines  69 ,  71 , and  73 , respectively, the half lines  69 ,  71 , and  73  extending from the center  68  to the cross section geometric center of each of the superconducting shield coils  64 ,  65 , and  66 , respectively, and the θ1, θ2, and θ3 are in a relation of θ1&lt;θ2&lt;θ3. If the superconducting main coil  58  is defined to have a positive current direction, then the superconducting shield coils  64 ,  65 , and  66  corresponding to θ1, θ2, and θ3, respectively, will have negative, positive, and negative current directions, respectively. This can be generalized in that the superconducting shield coils will have alternately positive and negative current directions with increasing value of the θn. The superconducting shield coil  66  with the largest radius of the three superconducting shield coils may have a larger magnetomotive force in absolute value than the others. 
   As described above, the superconducting shield coils in this embodiment can control the higher order components of the leakage magnetic field to provide the leakage magnetic field lower than that in the conventional magnets described above. In particular, this embodiment uses three pairs of the shield coils to control even higher order components of the leakage magnetic field to provide the lower leakage magnetic field than the embodiment disclosed in FIG.  3 . This embodiment also uses the magnet pole  59  to produce a uniform magnetostatic field so that the superconducting main coil  58  may have a smaller magnetomotive force in absolute value than the superconducting main coils in the embodiments shown in  FIGS. 1 and 2 . The superconducting shield coils  64 ,  65 , and  66  may then also have a smaller magnetomotive force in absolute value than the superconducting shield coils in the embodiments in  FIGS. 1 and 2 . Thus, the each shield coil may have a smaller electromagnetic force. 
     FIG. 5  shows a cross sectional view of the superconducting magnets in the open-type MRI apparatus according to another embodiment of the present invention. This embodiment adds a superconducting correction coil to the embodiment disclosed in  FIG. 3  to further improve the uniformity of the magnetic field. The superconducting correction coils  90 ,  91 , which are contained in a low temperature disclosure  78 , can correct the magnetostatic field from the superconducting main coil  76  and magnetic pole  77  to further uniform the magnetic field. The superconducting shield coils  82 ,  83  are arranged in the same way as the shield coils in FIG.  3  and can control the higher order components of the leakage magnetic field to reduce the leakage magnetic field. 
     FIG. 6  shows a cross sectional view of the superconducting magnets in the open-type MRI apparatus according to another embodiment of the present invention. This embodiment adds a superconducting correction coil to the embodiment disclosed in  FIG. 4  to further improve the uniformity of the magnetic field. The superconducting correction coils  109 ,  110  which are contained in a low temperature disclosure  94  can correct the magnetostatic field from the superconducting main coil  92  and magnetic pole  93  to further uniform the magnetic field. The superconducting shield coils  98 ,  99 , and  100  are arranged in the same way as the shield coils in FIG.  4  and can control the higher order components of the leakage magnetic field to realize the lower leakage magnetic field. 
     FIG. 7  shows a cross sectional view of the superconducting magnets in the open-type MRI apparatus according to another embodiment of the present invention. This embodiment uses a pair of the main coils and a pair of the magnet poles to produce a uniform magnetic field as with the embodiments in  FIGS. 3  to  6 . This embodiment, however, has the magnetic poles on the ambient temperature space side of the vacuum chamber  116  unlike the embodiments in  FIGS. 3  to  6 . In the upper magnet assembly  111 , the superconducting main coil  113  and the two superconducting shield coils  119 ,  120  are contained in a low-temperature enclosure  115 , which is in turn involved in a vacuum chamber  116 . 
   Although not shown in  FIG. 7  for simplicity, the device also has a support structure for the superconducting coils and has a heat shield between the vacuum chamber and low-temperature enclosure to prevent the penetration of heat radiation. The low-temperature enclosure contains liquid helium, which can cool the superconducting coils to a cryogenic temperature (4.2 K) to keep them in the superconducting state. The magnet pole  114  is on the ambient temperature space side of the vacuum chamber  116  and can produce a uniform magnetostatic field together with the superconducting main coil  113 . The superconducting main coil  113  and superconducting shield coils  119 ,  120  are almost concentric with respect to the center axis  121  denoted as the z-axis in FIG.  4 . 
   The center axis (z-axis)  121  passes through the center  122  of the magnets. In the cross section of  FIG. 7 , i.e., the cross section including the center axis (z-axis)  121 , θ1, θ2 are defined as angles  124 ,  126  between the center axis (z-axis)  121  and half lines  123 ,  125 , respectively, the half lines  123 ,  125  extending from the center  122  to the cross section geometric center of each of the superconducting shield coils  119 ,  120 , respectively, and the θ1, θ2 are in a relation of θ1&lt;θ2. If the superconducting main coil  113  is defined to have a positive current direction, then the superconducting shield coils  119 ,  120  corresponding to θ1, θ2, respectively, will have positive and negative current directions, respectively. This can be generalized in that the superconducting shield coils will have alternately positive and negative current directions with increasing value of the θn. 
   The superconducting shield coil  120  with the largest radius of the two superconducting shield coils may have a larger magnetomotive force in absolute value than the other. As described above, the superconducting shield coils in this embodiment can control the higher order components of the leakage magnetic field to provide the leakage magnetic field lower than that in the conventional magnets described above. This embodiment also uses the magnet pole  114  to produce a uniform magnetostatic field so that the superconducting main coil  113  may have a smaller magnetomotive force in absolute value than the superconducting main coils in the embodiments described above. The superconducting shield coils  119 ,  120  may then also have a smaller magnetomotive force in absolute value than the superconducting shield coils in the embodiments described above. Thus, the each shield coil may have a smaller electromagnetic force. 
     FIG. 8  shows a cross sectional view of the superconducting magnets in the open-type MRI apparatus according to another embodiment of the present invention. This embodiment uses a pair of the main coils and a pair of the magnet poles to produce a uniform magnetic field as with the embodiments in  FIG. 7 , and has the magnetic poles on the ambient temperature space side of the vacuum chamber  132 . In the upper magnet assembly  127 , the superconducting main coil  129  and the three superconducting shield coils  135 ,  136 , and  137  are contained in a low-temperature enclosure  131 , which is in turn involved in a vacuum chamber  132 . 
   Although not shown in  FIG. 8  for simplicity, the device also has a support structure for the superconducting coils and has a heat shield between the vacuum chamber and low-temperature enclosure to prevent the penetration of heat radiation. The low-temperature enclosure contains liquid helium, which can cool the superconducting coils to a cryogenic temperature (4.2 K) to keep them in the superconducting state. The magnet pole  130  is on the ambient temperature space side of the vacuum chamber  132  and can produce a uniform magnetostatic field together with the superconducting main coil  129 . The superconducting main coil  129  and superconducting shield coils  135 ,  136 , and  137  are almost concentric with respect to the center axis  138  denoted as the z-axis in FIG.  8 . 
   The center axis (z-axis)  138  passes through the center  139  of the magnets. In the cross section of  FIG. 8 , i.e., the cross section including the center axis (z-axis)  138 , θ1, θ2, and θ3 are defined as angles  141 ,  143 , and  145  between the center axis (z-axis)  138  and half lines  140 ,  142 , and  144 , respectively, the half lines  140 ,  142 , and  144  extending from the center  139  to the cross section geometric center of each of the superconducting shield coils  135 ,  136 , and  137 , respectively, and the θ1, θ2, and θ3 are in a relation of θ1&lt;θ2&lt;θ3. If the superconducting main coil  129  is defined to have a positive current direction, then the superconducting shield coils  135 ,  136 , and  137  corresponding to θ1, θ2, and θ3, respectively, will have negative, positive, and negative current directions, respectively. This can be generalized in that the superconducting shield coils will have alternately positive and negative current directions with increasing value of the θn. 
   The superconducting shield coil  137  with the largest radius of the three superconducting shield coils may have a larger magnetomotive force in absolute value than the others. As described above, the superconducting shield coils in this embodiment can control the higher order components of the leakage magnetic field to provide the leakage magnetic field lower than that in the conventional magnets described above. This embodiment also uses the magnet pole  130  to produce a uniform magnetostatic field so that the superconducting main coil  129  may have a smaller magnetomotive force in absolute value than the superconducting main coils in the embodiments described above. The superconducting shield coils  135 ,  136 , and  137  may then also have a smaller magnetomotive force in absolute value than the superconducting shield coils in the embodiments described above. Thus, the each shield coil may have a smaller electromagnetic force. 
     FIG. 9  shows a cross sectional view of the superconducting magnets in the open-type MRI apparatus according to another embodiment of the present invention. This embodiment uses a pair of permanent magnets  148 ,  149  as the magnetomotive force sources for the magnetostatic field. This embodiment also uses a pair of magnet poles  150 ,  151  as a means to make the magnetic field uniform. This embodiment has the permanent magnets  148 ,  149  and magnet poles  150 ,  151  on the ambient temperature space side of the vacuum chamber  153 ,  164 , respectively. 
   The upper magnet assembly  146  will be described below. The superconducting shield coils  156 ,  157  are contained in a low-temperature enclosure  152 , which is in turn involved in a vacuum chamber  153 . Although not shown in  FIG. 9  for simplicity, the device also has a support structure for the superconducting coils and has a heat shield between the vacuum chamber and low-temperature enclosure to prevent the penetration of heat radiation. The low-temperature enclosure contains liquid helium, which can cool the superconducting coils to a cryogenic temperature (4.2 K) to keep them in the superconducting state. The superconducting shield coils  156 ,  157  are almost concentric with respect to the center axis  158  denoted as the z-axis in FIG.  9 . The center axis (z-axis)  158  passes through the center  159  of the magnets. 
   In the cross section of  FIG. 9 , i.e., the cross section including the center axis (z-axis)  158 , θ1, θ2 are defined as angles  161 ,  163  between the center axis (z-axis)  158  and half lines  160 ,  162 , respectively, the half lines  160 ,  162  extending from the center  158  to the cross section geometric center of each of the superconducting shield coils  156 ,  157 , respectively, and the θ1, θ2 are in a relation of θ1&lt;θ2. The permanent magnets  148 ,  149  are magnetized almost in a positive direction along the z-axis, and can produce, together with the magnet poles  150 ,  151 , a uniform magnetic field in a positive direction along the z-axis in the imaging space. To produce such a magnetic field direction with a coil concentric with respect to the z-axis, a current clockwise around the z-axis, such as the superconducting shield coil  156 , may be provided. Thus, if the current direction equivalent to the magnetization direction of the permanent magnets  148 ,  149 , i.e., the clockwise direction around the z-axis is defined as the positive current direction, the superconducting shield coils  156 ,  157  corresponding to θ1, θ2, respectively, will have positive and negative current directions, respectively. 
   This can be generalized in that the superconducting shield coils will have alternately positive and negative current directions with increasing value of the θn. The superconducting shield coil  157  with the largest radius of the two superconducting shield coils may have a larger magnetomotive force in absolute value than the other. As described above, the superconducting shield coils in this embodiment can control the higher order components of the leakage magnetic field to provide the lower leakage magnetic field. Although not shown in  FIG. 7 , the vacuum chambers  153 ,  164  and connecting tubes  154 ,  155  mechanically support the permanent magnets  148 ,  149  and magnet poles  150 ,  151 . However, a T-shape structure may also hold the upper and lower permanent magnets  148 ,  149  and magnet poles  150 ,  151 . It should be appreciated that the present embodiment does not limit the mechanical structure of the magnets. 
     FIG. 10  shows a cross sectional view of the superconducting magnets in the open-type MRI apparatus according to another embodiment of the present invention. Unlike the embodiment disclosed in  FIG. 9 , the present embodiment uses three pairs of the superconducting shield coils. The upper magnet assembly  165  will be described below. The superconducting shield coils  176 ,  177 , and  178  are almost concentric with respect to the center axis  179  denoted as the z-axis in FIG.  10 . The center axis (z-axis)  179  passes through the center  180  of the magnets. 
   In the cross section of  FIG. 10 , i.e., the cross section including the center axis (z-axis)  179 , θ1, θ2, and θ3 are defined as angles  182 ,  184 , and  186  between the center axis (z-axis)  179  and half lines  181 ,  183 , and  185 , respectively, the half lines  181 ,  183 , and  185  extending from the center  180  to the cross section geometric center of each of the superconducting shield coils  176 ,  177 , and  178 , respectively, and the θ1, θ2, and θ3 are in a relation of θ1&lt;θ2&lt;θ3. The permanent magnets  167 ,  168  are magnetized almost in a positive direction along the z-axis, and can produce, together with the magnet poles  169 ,  170 , a uniform magnetic field in a positive direction along the z-axis in the imaging space. 
   To produce such a magnetic field direction with a coil concentric with respect to the z-axis, a current clockwise around the z-axis, such as the superconducting shield coil  177 , may be provided. Thus, if the current direction equivalent to the magnetization direction of the permanent magnets  167 ,  168 , i.e., the clockwise direction around the z-axis is defined as the positive current direction, the superconducting shield coils  176 ,  177 , and  178  corresponding to θ1, θ2, and θ3 respectively, will have negative, positive, and negative current directions, respectively. This can be generalized in that the superconducting shield coils will have alternately positive and negative current directions with increasing value of the θn. 
   The superconducting shield coil  178  with the largest radius of the three superconducting shield coils may have a larger magnetomotive force in absolute value than the others. As described above, the superconducting shield coils in this embodiment can control the higher order components of the leakage magnetic field to provide the lower leakage magnetic field. Although not shown in  FIG. 10 , the vacuum chambers  172 ,  173  and connecting tubes  174 ,  175  mechanically support the permanent magnets  167 ,  168  and magnet poles  169 ,  170 . However, a T-shape structure may also hold the upper and lower permanent magnets  167 ,  168  and magnet poles  169 ,  170 . It should be appreciated that the present embodiment does not limit the mechanical structure of the magnets. 
   The superconducting magnets in the open-type MRI apparatus according to the embodiments of the present invention have been disclosed. The description below will disclose the coil arrangement and the leakage magnetic field distribution, which are derived from a computer program using the equation (3), for the air-core magnets shown in  FIGS. 1 and 2 . The coil arrangement will be disclosed for the z&gt;0 area of the mirror symmetric space with respect to the z=0 plane. The calculation condition is that the central magnetic field strength is 0.75T, the magnetic field is uniform to such an extent that the expansion coefficients of the second to tenth order in the equation (2) vanish in the uniform magnetic field area, and every case will have ±3 ppm/45 cm DSV. 
     FIG. 11  illustrates the coil arrangement where the shield coils are not used, i.e., the leakage magnetic field is not controlled. Five main coils  187 ,  188 ,  189 ,  190 ,  191  are arranged such that they have alternately positive and negative current directions. The foregoing patent “MAGNET APPARATUSAND MRI APPARATUS” discloses such a main coils arrangement. There are symbols near the coils to show the coils&#39; electric current directions. 
     FIG. 12  shows a leakage magnetic field distribution from the coil arrangement in FIG.  11 .  FIG. 12  shows the contour plot of the leakage magnetic field strength including, from the inside, the 1000 gauss contour  192 , 500 gauss contour  193 , 100 gauss contour  194 , 50 gauss contour  195 , 10 gauss contour  196 , and 5 gauss contour  197 . One guideline for the MRI apparatus installation in the hospital is that the 5 gauss contour of the leakage magnetic field is within 3 meters from the origin.  FIG. 12  shows the 5 gauss contour  197  of the leakage magnetic field far beyond 10 meters along the z-axis. 
     FIG. 13  shows a coil arrangement derived with an additional condition that first order component of the leakage magnetic field expanded in the equation (3) only vanishes. In addition to the main coils  198 ,  199 ,  200 ,  201 , and  202  corresponding to the main coils in  FIG. 11 , the arrangement includes a pair of shield coils  203 . Each main coil has a larger magnetomotive force in absolute value than the main coils in  FIG. 11 , and the central magnetic field strength and magnetic field uniformity are the same as those in FIG.  11 . 
     FIG. 14  shows a leakage magnetic field distribution from the coil arrangement in FIG.  13 . The distribution includes, from the inside, the 1000 gauss contour  204 , 500 gauss contour  205 , 100 gauss contour  206 , 50 gauss contour  207 , 10 gauss contour  208 , 5 gauss contour  209 , and 1 gauss contour  210 . The 5 gauss contour  209  is smaller than that when the shield coils are not used as shown in  FIG. 12 , but is still 5 meters which is too large to install the MRI apparatus in the hospital. The conventional shield coil arrangements described above are all similar to the coil arrangement shown in  FIG. 13  so that they can significantly increase the third order component of the leakage magnetic field as described above and have the large leakage magnetic field distribution as shown in FIG.  14 . The leakage magnetic field in  FIG. 14  expanded in the equation (3) shows a dominant third order component and has a magnetic field distribution which decreases in proportion to the fifth negative power of distance from the origin. 
     FIG. 15  shows a coil arrangement under the condition that the magnetic field is uniform and the additional condition that the first and third order components of the leakage magnetic field expanded in the equation (3) vanish. In addition to the main coils  211 ,  212 ,  213 ,  214 , and  215  corresponding to the main coils in  FIG. 11 , the arrangement includes three pairs of shield coils  216 ,  217 , and  218 . Each main coil has a larger magnetomotive force in absolute value than the main coils in  FIG. 11 , and the central magnetic field strength and magnetic field uniformity are the same as those in FIG.  11 . 
     FIG. 16  shows a leakage magnetic field distribution from the coil arrangement in FIG.  15 . The distribution includes, from the inside, the 1000 gauss contour  219 , 500 gauss contour  220 , 100 gauss contour  221 , 50 gauss contour  222 , 10 gauss contour  223 , 5 gauss contour  224 , and 1 gauss contour  225 . The leakage magnetic field is successfully significantly decreased and the 5 gauss contour  224  is between 3 and 3.5 meters. The 1 gauss contour  225  is also very small. In this embodiment, the first and third order components of the leakage magnetic field expanded in the equation (3) vanish, so that the fifth order component of the leakage magnetic field is dominant and the leakage magnetic field strength decreases very rapidly in proportion to the seventh negative power of distance from the origin. 
   In this embodiment, θ1, θ2, and θ3 are defined as angles between the z-axis  226  and half lines  228 ,  230 , and  232 , respectively, the half lines  228 ,  230 , and  232  extending from the origin  227  to the cross section geometric center of each of the superconducting shield coils  216 ,  217 , and  218 , respectively, and the θ1, θ2, and θ3 are in a relation of θ1&lt;θ2&lt;θ3. The corresponding shield coils have alternately positive and negative current directions. The shield coil  218  with the largest radius of the shield coils has a larger magnetomotive force in absolute value than the others. In this embodiment he shield coil  218  with the largest radius has a larger average radius than the main coil  211  of the largest average radius. 
     FIG. 25  shows the superconducting magnets in the open-type MRI apparatus according to another embodiment of the present invention, which has the leakage magnetic field performance equivalent to that of the magnets in FIG.  7 . The superconducting shield coil  120  in  FIG. 7  is divided into two superconducting shield coils  281 ,  282  in the embodiment in FIG.  25 . Alternatively, it may be conceived that a superconducting shield coil  282  of a lower magnetomotive force replaces the superconducting shield coil  120 , and another superconducting shield coil  281  is added. 
   It is well-known to those skilled in the art that if an electromagnetic force or the maximum empirical magnetic field for one superconducting coil is too large to form a superconducting coil, the coil can be divided into more than one coil as in this embodiment to reduce the electromagnetic force or the maximum empirical magnetic field. The present invention also meets the following condition to reduce the leakage magnetic field from the divided coils as described above. 
   The superconducting main coils are defined to have a positive current direction. The shield coils  280 ,  281  of positive current directions make up a first group of shield coils. The shield coils  282 ,  283  of negative current directions make up a second group of shield coils. θ1 is defined as an angle  287  between the z-axis  284  and a half line  286  extending from the origin  285  to the cross section geometric center  290  of the shield coils  280 ,  281  of the first group. θ2 is defined as an angle  289  between the z-axis  284  and a half line  288  extending from the origin  285  to the cross section geometric center  291  of the shield coils  282 ,  283  of the second group. The θ1, θ2 are in a relation of θ1&lt;θ2, and the corresponding groups of shield coils have alternately positive and negative current directions. The second group of shield coils including the largest radius shield coil  283  has a larger sum of the magnetomotive force in absolute value than the other groups. 
     FIG. 26  shows a normal conducting shield coil according to another embodiment of the present invention. The MRI magnets  292  are disposed in the MRI scan room  293  in a hospital. In this embodiment, the magnets  292  are open-type magnets and produce a uniform magnetic field in the imaging space along the magnet center axis  297  denoted as the z-axis in FIG.  26 . The coils in the open-type magnet  292  are almost concentric with respect to the magnet center axis  297  denoted as the z-axis. The normal conducting shield coils  294 ,  295 , and  296  are on the ambient temperature side of the vacuum chamber for the superconducting magnets almost concentrically with respect to the center axis  297 . This embodiment has the normal conducting shield coils around the ceiling of the MRI scan room. 
   If θ1, θ2, and θ3 are defined as angles  300 ,  302 , and  304  between the center axis  297  and half lines  299 ,  301 , and  303 , respectively, the half lines  299 ,  301 , and  303  extending from the magnet center  298  to each of the normal conducting shield coils  294 ,  295 , and  296 , respectively, then the θ1, θ2, and θ3 are in a relation of θ1&lt;θ2&lt;θ3 and the shield coils corresponding to the θ1, θ2, and θ3 have alternately positive and negative current directions. As described above, the normal conducting shield coils in this embodiment can control the higher order components of the leakage magnetic field to prevent the magnetic field leakage above the MRI scan room  293 . Although not shown in this embodiment, the device also has a support structure for the normal conducting coils which fastens the normal conducting shield coils on the wall of the MRI scan room  293 . Alternatively, the normal conducting shield coils may be fastened on the magnet  292 . 
     FIG. 27  shows a normal conducting shield coil according to another embodiment of the present invention. In this embodiment, more than one group of shield coils make up the shield coils having an effect equivalent to that of the shield coils shown in FIG.  26 . The normal conducting shield coils  307 ,  308  make up a first group of shield coils. The normal conducting shield coils  309 ,  310 , and  311  make up a second group of shield coils. The normal conducting shield coils  312 ,  313  make up a third group of shield coils. θ1 is defined as an angle  320  between the magnet center axis  317  and a half line  319  extending from the magnet center  318  to the cross section geometric center  314  of the first group shield coils. θ2 is defined as an angle  322  between the magnet center axis  317  and a half line  321  extending from the magnet center  318  to the cross section geometric center  315  of the second group shield coils. θ3 is defined as an angle  324  between the magnet center axis  317  and a half line  323  extending from the magnet center  318  to the cross section geometric center  316  of the second group shield coils. The θ1, θ2, and θ3 are in a relation of θ1&lt;θ2&lt;θ3, and the shield coil groups corresponding to θ1, θ2, and θ3 have alternately positive and negative current directions. 
   As described above, the normal conducting shield coils in this embodiment can control the higher order components of the leakage magnetic field to prevent the magnetic field leakage above the MRI scan room  306 . The coils of the magnet  305  and the shield coils are almost concentric with respect to the magnet center axis  317  denoted as the z-axis in FIG.  27 . Although the embodiments shown in  FIGS. 26 and 27  have the normal conducting shield coils only above the magnet, the normal conducting shield coils may be disposed below the magnet in the same manner to reduce the magnetic field leakage below the MRI scan room. 
   The present invention has been described in the specific embodiments. In the embodiments described above, the coils in the magnet are all superconducting coils. However, the present invention is not limited to the superconducting coils and may use any current carrying means such as a coil of copper wire. 
   The present invention can be implemented in a variety of embodiments as described above. However, it should be appreciated that the present invention is not limited by any embodiment disclosed here. 
   The symbols used here are as follows: 
     17 ,  19 ,  53 ,  56 ,  75 ,  92 ,  111 ,  127 ,  146 ,  165 ,  274  . . . upper magneto-static field-generating source;  18 ,  20 ,  54 ,  57 ,  81 ,  93 ,  112 ,  128 ,  147 ,  166 ,  275  . . . lower magneto-static field-generating source;  1 ,  2 ,  3 ,  4 ,  21 ,  22 ,  23 ,  24 ,  40 ,  58 ,  76 ,  94 ,  113 ,  129 ,  276  . . . superconducting main coil;  9 , 10 ,  29 ,  30 ,  31 ,  45 ,  46 ,  64 ,  65 ,  66 ,  82 ,  83 ,  98 ,  99 ,  100 ,  119 ,  120 ,  135 ,  136 ,  137 ,  156 ,  157 ,  176 ,  177 ,  178 ,  280 ,  281 ,  282 ,  283  . . . superconducting shield coil;  90 ,  91 ,  109 ,  110  . . . superconducting correction coil;  148 ,  149 ,  167 ,  168  . . . permanent magnet;  52 ,  59 ,  77 ,  95 ,  114 ,  130 ,  150 ,  151 ,  169 ,  170 ,  277 ,  5 ,  25 ,  41 ,  60 ,  78 ,  96 ,  115 ,  131 ,  152 ,  171 ,  278  . . . low temperature enclosure;  6 ,  26 ,  42 ,  61 ,  79 ,  97 ,  116 ,  132 ,  153 ,  164 ,  172 ,  173 ,  279  . . . vacuum chamber;  7 ,  8 ,  27 ,  28 ,  43 ,  44 ,  62 ,  63 ,  80 ,  117 ,  118 ,  133 ,  134 ,  154 ,  155 ,  174 ,  175  . . . connecting tube;  11 ,  32 ,  55 ,  67 ,  84 ,  101 ,  121 ,  138 ,  158 ,  179 ,  226 ,  252 ,  266 ,  284 ,  297 ,  317  . . . magnet center axis or z-axis;  12 ,  33 ,  47 ,  68 ,  85 ,  102 ,  122 ,  139 ,  159 ,  180 ,  227 ,  253 ,  267 ,  285 ,  298 ,  318  . . . magnet center or origin;  13 ,  15 ,  34 ,  36 ,  38 ,  48 ,  50 ,  69 ,  71 ,  73 ,  86 ,  88 ,  103 ,  105 ,  107 ,  123 ,  125 ,  140 ,  142 ,  144 ,  160 ,  162 ,  181 ,  183 ,  185 ,  228 ,  230 ,  232 ,  254 ,  256 ,  268 ,  270 ,  272 ,  286 ,  288 ,  299 ,  301 ,  303 ,  319 ,  321 ,  323  . . . half line extending from the magnet center or origin to the cross section geometric center of the shield coil;  14 ,  16 ,  35 ,  37 ,  39 ,  49 ,  51 ,  70 ,  72 ,  74 ,  87 ,  89 ,  104 ,  106 ,  108 ,  124 ,  126 ,  141 ,  143 ,  145 ,  161 ,  163 ,  182 ,  184 ,  186 ,  229 ,  231 ,  233 ,  255 ,  257 ,  269 ,  21 ,  273 ,  287 ,  289 ,  300 ,  302 ,  304 ,  320 ,  322 ,  324  . . . angle between magnet center axis or z-axis and half line extending from the magnet center or origin to the cross section geometric center of the shield coil;  187 ,  188 ,  189 ,  190 ,  191 ,  198 ,  199 ,  200 ,  201 ,  202 ,  211 ,  212 ,  213 ,  214 ,  215 ,  242 ,  243 ,  246 ,  247 ,  258 ,  259  . . . main coil;  203 ,  216 ,  217 ,  218 ,  244 ,  245 ,  248 ,  249 ,  250 ,  251 ,  260 ,  261 ,  262 ,  263 ,  264 ,  265 ,  294 ,  295 ,  296 ,  307 ,  308 ,  309 ,  310 ,  311 ,  312 ,  313  . . . shield coil;  192 ,  204 ,  219  . . . 1000 gauss contour of the leakage magnetic field;  193 ,  205 ,  220  . . . 500 gauss contour of the leakage magnetic field;  194 ,  206 ,  221  . . . 100 gauss contour of the leakage magnetic field;  195 ,  207 ,  222  . . . 50 gauss contour of the leakage magnetic field;  196 , 208 ,  223  . . . 10 gauss contour of the leakage magnetic field;  197 ,  209 ,  224  . . . 5 gauss contour of the leakage magnetic field;  210 ,  225  . . . 1 gauss contour of the leakage magnetic field;  234  . . . internal area;  235  . . . external area;  236  . . . coil;  237  . . . magnetic material;  238  . . . space distribution in the external area of the first order component of the leakage magnetic field;  239  . . . space distribution in the external area of the third order component of the leakage magnetic field;  240  . . . space distribution in the external area of the fifth order component of the leakage magnetic field;  241  . . . space distribution in the external area of the seventh order component of the leakage magnetic field;  290 ,  291 ,  314 ,  315 ,  316  . . . the cross section geometric center of one or more shield coils making up the shield coil group;  292 , 305  . . . MRI magnet;  293 , 306  . . . MRI scan room. 
   INDUSTRIAL APPLICABILITY OF THE INVENTION 
   The present invention provides a superconducting magnet device and leakage magnetic field shield assembly for an open-type MRI apparatus, which are lightweight and have an extremely low leakage magnetic field, and a MRI apparatus using them.