JPH0799724B2 - Uniform magnetic field generator - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a uniform magnetic field generator that uses a correction technique of a magnetic field distribution in order to enhance the spatial homogeneity of a magnetic field.

[Conventional technology]

11 to 14 show a conventional uniform magnetic field generator disclosed in, for example, Japanese Patent Laid-Open No. 59-99708. In FIG. 11, (1) is the main solenoid coil. A magnetic field correction coil (2) is mounted on the outer circumference of the main solenoid coil (1). A highly uniform magnetic field region (3) is shown in the center of the main solenoid coil (1) and the coordinate axis Z-X is shown.

FIG. 12 is a diagram showing in detail one type of the magnetic field correction coil (2) shown in FIG. In the figure, (2A) is a Z ¹ shim coil, and each Z ¹ shim coil (2A) is a circular coil (circular current loop), which is arranged in plane symmetry with the Z = O plane as the target plane. In the figure, a mounting distance 2Zo1 of Z ¹ shim coil (2A), showed diameters 2a, Z ¹ shim coil (2
The position of A) is | Zo1 / a | = 0.866, or close enough to this | Zo1 / a |). The ampere-turns of the two Z ¹ shim coils (2A) are equal, and the direction of current flow is opposite in each coil. The direction of the electric current is indicated by an arrow in the Z ¹ shim coil (2A) in FIG. The main solenoid coil (1) and the Z ¹ shim coil (2A) are coaxial.

Next, an analysis method for determining the mounting position of the Z ′ shim coil will be described. In the following description, the magnetic velocity density obtained by multiplying the magnetic field by the magnetic permeability is used.

The magnetic velocity density Bz (z) in the Z-axis direction created by the circular current loop attached to the Z = Zo plane at the arbitrary point Z on the Z-axis is expressed by the following equation.

Here, I is the total current value flowing in the circular current loop, which is equal to ampere-turn. a is the radius of the circular current loop, and μ ₀ is the magnetic permeability in vacuum.

Using the formula, the magnetic velocity density created by one circular current loop in the vicinity of Z = 0 on the Z-axis is expressed by Taylor expansion as follows. However, From the formula, the magnetic velocity density obtained by one circular current loop at an arbitrary point on the Z axis was obtained. In one embodiment described here, we deal with the Z ¹ shim coil, which has And is a shim coil having only an output proportional to the coordinate Z. In general, the shim coil needs to generate only a specific order output of a specified variable, eg variable Z. If unspecified output occurs at the same time, the output is
Quite contrary to the correction of the magnetic field, the homogeneity of the magnetic field may be deteriorated.

Therefore, even when a plurality of types of shim coils are mounted, each shim coil output must be completely independent. Considering the symmetry of the shape of the main solenoid coil (1), there is a strong possibility that the non-uniform magnetic field will also be symmetric with respect to the Z = o plane, so the output of the magnetic field correction coil (2) with respect to the Z = o plane. Must be symmetric. Therefore, the magnetic field correction coil (2) is
= Installed symmetrically with respect to the o plane. For example, the magnetic velocity density created by two circular current loops at positions ± Zo near Z = o
Bz (z) is given by the following equation. However, the ampere-turn of each coil is the same.

The subscripts + and-in the equations indicate that the Z coordinate corresponds to the coil at the positive position and the Z coordinate corresponds to the coil at the negative position, respectively.

When the direction of the current in the circular current loop is opposite, the following output is obtained using the equation.

Similarly, when the currents in the circular current loop flow in the same direction, the following equation is obtained.

, If the subscript + attached to Bo and εn (n = 0, 1, 2 ...) In the formula is omitted, each symbol is the same as in the formula. Hereinafter, the + sign is omitted for simplicity.

To make the Z ¹ shim coil (2A) described here,
The first term on the right side of the equation, Should only generate. Therefore, the third-order term that has the greatest effect on the first term Need to be erased. For that purpose, ε ₃ = 0 is sufficient, but from the equation, it is understood that β that satisfies the following equation should be present.

However, According to the equation, ε ₁ is also set to 0 from the equation, and the output required here cannot be obtained. Therefore, it cannot be used here. Therefore, the position of the Z ¹ shim coil (2A) is given by the following equation using the solution of the equation.

The output of the Z ¹ shim coil (2A) when using β in the equation is as follows.

From the equation, the Z ¹ shim coil (2A) generates not only the primary output but also an odd-numbered output of 5 or more. However, | Z / a |
When used only in the vicinity of Z = 0 such that <0.3, the order difference between the first and fifth terms is the fourth order. Therefore, the 5th-order term is less than 1% of the magnitude of the 1st-order term, and does not pose any problem in practical use. Where ε ₁ and ε
_{It is known that 5} is about the same size.

As described above, a current having the same ampere turn and the opposite direction is applied to each coil of the Z ¹ shim coils (2A) mounted at appropriate positions. Also, the ampere turn is
The primary nonuniform magnetic field in the highly uniform magnetic field region (3) as shown in FIG. 11, that is, the nonuniform magnetic field proportional to the coordinate Z is adjusted to be the minimum. In some cases, it is necessary to reverse all the initially set current directions.

In the description, the current value and the ampere-turn are used in the same meaning, so the current value when the coil has a plurality of turns is the current flowing through one coil conductor multiplied by the number of coil turns.

Although the Z ¹ shim coil (2A) has been described in the above embodiment, the Z ² shim coil for correcting the secondary magnetic field component can be manufactured in the same manner as in the above embodiment.

The Z ² shim coil is based on the equation when current flows in the same direction in the circular current loop. The unnecessary terms having the greatest influence on the second-order term having ε ₂ are the 0th-order term and the 4th-order term. First, a method of erasing the fourth-order term will be described. In order to eliminate this term, it is necessary to set ε ₄ = 0. ε ₄ is given by the following equation when obtained in the same manner as the terms shown in the equation.

Therefore, β with ε ₄ = 0 can be obtained from the following equation.

1-12β ² + 8β ⁴ = 0. By solving the above equation for β, the following equation is obtained.

Therefore, a Z ² shim coil in which the 4th order term is eliminated need only have an equation or a pair of circular coils that satisfy the equation, but then the 0th order term must also be eliminated. In order to eliminate the 0th-order term, a method of canceling the 0th-order term is applied by passing currents in opposite directions to the coil pair at Zo ₁ / a and the coil pair at Zo ₂ / a. At this time, the secondary magnetic field component required here can be taken out as the difference between the outputs of the two coil pairs. From the equation, it is understood that the condition that does not generate the 0th-order output is the current ratio that satisfies the following equation.

Solving the formula, I ₁ and I ₂ represent the ampere turns of the coils at the positions Zo ₁ / a and Zo ₂ / a, respectively.

The above results are summarized in Fig. 13. In Fig. 13 (2B)
Current value I ₁ in the Z ² shim coil, Z ² shim coils (2B), I ₂
And the direction of the current in each coil is indicated by an arrow. Also,
The position of the Z ² shim coil (2B) is indicated by 2Zo1 and 2Zo2. By installing the Z ² shim coil (2B), it is possible to correct a non-uniform magnetic field component proportional to Z ² . The output of the Z ² shim coil (2B) includes an even-order term of 6th order or more in addition to the 2nd order term required for magnetic field correction, but there is a difference of 4th order or more with respect to the 2nd order term. Therefore, if a high uniform magnetic field region (3) of | Z / a | <0.3 is used as in the case of the Z ′ shim coil, there is no problem in practical use.

Then, the third-order magnetic field components, i.e., for the shim coils to correct the non-uniform magnetic field component proportional to Z ^3, can be manufactured similarly to the above embodiment, with respect to non-uniform magnetic field component proportional to Z ^3, the above-described It has the same effect as the example. FIG. 14 shows such a magnetic field correction coil. In the figure, (2C) is
In Z ³ shim coils, a magnetic field correction coils has an effect of removing a non-uniform magnetic field component which varies in proportion to Z ^3. The configuration of the Z ³ shim coil (2C) will be described. Where ε
Absolute value third order terms having ₃ that the closest is the fifth-order term and first-order terms. Therefore, it can be said that the terms that have the greatest influence on the third-order terms are the fifth-order terms and the first-order terms.
Consider a coil arrangement with the following terms removed. ε ₅ is
The following equation can be obtained by obtaining in the same manner as the terms shown in the equation.

Therefore, β with ε ₅ = 0 is given by the following equation.

β = 0 35-140β ² + 56β ⁴ = 0 Since the expression also sets ε ₃ to 0, the third-order output magnetic field required here cannot be used, either. When the equation is solved for β, the following equation is obtained.

Therefore, the Z ³ shim coil (2C) in which the fifth-order term is deleted is
Either the equation or a pair of circular coils satisfying the equation is needed, but then the first order terms must also be eliminated. In order to eliminate the first-order term, each coil current is made to flow so that the currents of the adjacent coils are all in the opposite directions as shown by the arrows in FIG. 14, so that the coil pair at position Zo ₁ / a A method is used in which the coil pair at the position Zo ₂ / a cancels the first-order term that occurs. From the equation, it can be seen that the condition that the primary output is not generated is the current ratio that satisfies the following equation.

Solving the formula, I ₁ and I ₂ represent the ampere-turns of the coils at positions Zo ₁ / a and Zo ₂ / a, respectively.

[Problems to be solved by the invention]

Since the conventional uniform magnetic field generator is configured as described above, the same number of shim coils as the types of magnetic field components to be generated are required. Therefore, when the magnetic field component required for magnetic field correction increases, the number of shim coils must be increased, which not only makes the device significantly expensive, but also installs the device. There was a problem such as requiring a large space.

The present invention has been made in order to solve the above-mentioned problems, and by reducing the number of shim coils without reducing the types of generated magnetic field components, the cost is reduced and the size is reduced. It is an object of the present invention to obtain a uniform magnetic field generating device in which the accuracy of the output magnetic field such as once or spatial linearity is remarkably improved.

[Means for solving problems]

In the uniform magnetic field generator according to the present invention, one type of shim coil composed of a plurality of current loop pairs is installed, and the direction of the current flowing through each current loop pair and the current ratio thereof are set to various ratios.

[Action]

By changing the direction and the current ratio of the current flowing in each current loop pair of one type of shim coil composed of a plurality of current loop pairs,
The generated magnetic field component changes. That is, a winding of one type of shim coil, for example, a Z ⁴ shim coil is arranged. Then, by changing the current direction and the current ratio of each current loop pair of the Z ⁴ shim coil, three kinds of magnetic fields Z ⁰ , Z ² and Z ⁴ can be arbitrarily generated. Also, AZ ⁰ + BZ ² + CZ
Magnetic fields of ⁴ (A, B, C ... arbitrary coefficients) can be generated simultaneously. Furthermore, the Z ⁰ and Z ² magnetic fields can be generated with extremely high accuracy by disposing the Z ⁴ shim coil. The same applies to the case where the Z ⁵ shim coil is arranged and three types of magnetic fields Z ′, Z ³ and Z ⁵ are generated.

〔Example〕

Hereinafter, one embodiment of the present invention will be described. First,
The principle of the present invention will be described. In FIG. 8, (5) is a circular current loop, in which the current I flows at the radius a as shown by the arrow. The Z axis is shown in the figure, and the circular current loop (5) is mounted at a position of Z = -Zo in a plane perpendicular to the Z axis. One circular current loop (5) mounted in the plane perpendicular to the Z axis makes Z at the point q (γ, θ) near the origin.
The axial magnetic field can be expressed by the following equation by Taylor expansion.

In the equation, if the q point is on the Z axis, the equation is the same as the equation. In the following description, an arbitrary point may be set in addition to the Z-axis, and therefore the expression is similar to the conventional example, but will be described again. In the formula, Pn (U) is an n-th order Lujandor polynomial. However, U = cos θ.
Therefore, the equation can be expressed as the following equation.

Where B _z (0,0) is the magnetic field in the Z-axis direction at the origin, ε
_n is an n-th order differential coefficient including n1. B _z (0,0) and ε _n
Is a constant that is determined only by the current I of the circular current loop and the position Z ₀ of the circular current loop, and is shown collectively in Table 1 including some of the conventional examples.

The arrangement of the circular current loop (5) and the direction of the current as shown in FIG. 9 are defined as a symmetrical structure and a symmetrical current, and the case as shown in FIG. 10 is defined as a symmetrical structure and an antisymmetrical current.

The magnetic field output of the pair of circular current loops (5) in the case of FIG. 9 can be expressed by the following equation.

Similarly, in the case of FIG. 10, it can be expressed by the following equation.

Considering the magnetic field output by k pairs of circular current loops, if the m-th pair is represented by the subscript m, the output of each circular current loop pair can be represented by the following equation.

In the case of symmetrical structure and symmetrical current, the following equation is obtained.

Next, in the case of symmetric structure and antisymmetric current, the following equation is obtained.

However, Even-Order Z Shim Coil First, the even-order Z shim coil will be described.

An even-order Z shim coil is Z ^2k (k = 0,
The magnetic field correction coil has a main magnetic field direction that changes in proportion to 1, 2, ..., That is, a magnetic field component in the Z-axis direction. The Z ^2k shim coil is composed of k + 1 pairs of circular current loops.
The number of circular current loop pairs corresponds to all positions where 2k + 2nd order output can be removed for 2kth order output. That is, ε
The solution β of _{2k + 2} = 0 (where β is the distance in the main magnetic field direction standardized by the radius of the circular current loop) is ± β ₁ , ± β ₂ , ... ±
Being β _{k + 1} , a circular current loop is installed at these (2k + 1) positions. The magnetic field output at this time is expressed by the following equation.

R _{m, 2k} is a high-order error term for the specified output of the shim coil, If so, the ratio to the specified output is sufficiently small and can be ignored. When ignoring the term of R _2k, the following 2 (k + 1) elements determine B _z (γ, θ).

During the magnetic field output of all circular current loops with k + 1 pairs, 2k +
In order not to include the quadratic term, it is essential that the coil mounting positions are ± β ₁ , ..., ± β _{k + 1} . Therefore,
There is no freedom regarding the coil attachment position β. However, the coil current has k + 1 degrees of freedom and will be used hereafter to define the magnetic field output. Since the output of the shim coil is used for the correction of the magnetic field, the different types of magnetic field outputs must be independent. Let ε _{2k + 2} = 0 and R
The magnetic field output of the shim coil ignoring _2k can be expressed by the following equation.

When realizing a Z ^2k shim coil, all the terms other than the 2kth order are unnecessary, and all the terms from the 0th order to the (2k-2) th order must be deleted. For that purpose, only the coil current shown in the equation (see Table 1) is used as a variable for an arbitrary position γ.
(However, In, the following formula must hold.

The above equation is k simultaneous equations, but the variable I is I _{1 to} I _{k + 1.}
There are k + 1 up to. Therefore, k variables Holds for. That is, by determining the current ratio between the coils, it is possible to obtain a magnetic field output having only a predetermined order of 2k, and the magnitude of the magnetic field output depends on the coil current I ₁
It can be arbitrarily selected by changing the absolute value of.

From the general theory described here, it can be seen that other independent magnetic fields can be generated with the same arrangement. This point will be described subsequently.

From the formula, in order for B _z (γ, θ) ≡ 0 to hold for any position (γ, θ), Since it has to be 0, the sum of the coefficients by the degree at any position (γ, θ) must be 0.

The above equation is k + 1 simultaneous equations, and k + 1 solutions I ₁ ~
Although it is uniquely determined by I _{k + 1} , it can be established as k simultaneous equations excluding any one equation,
The number of solutions at this time is k in the following equation.

Alternatively, the following solution of k may be used.

That is, To summarize the above results, by using the k + 1 pairs of circular current loops mounted to obtain the Z ^2k shim coil output, it is possible to obtain only one arbitrary even-order output within the 2k-th order. Also, by overlapping the currents,
It is possible to generate k + 1 types of shim coil outputs up to the 2k-th order completely independently without attaching a new coil. The lowest order error term contained in these magnetic field outputs is 2k + 4th order. In the conventional uniform magnetic field generator, the necessary magnetic field output + the fourth-order term are included as error terms. However, according to the above, since it is irrelevant to the magnetic field output and depends only on the number of attached coil pairs, the lower order cis coil, which is expected to have a higher utilization rate, has higher magnetic field accuracy, and also has a different magnetic field. It is not necessary to provide different coils for each output.

Odd-order Z sis coil Next, the odd-order Z shim coil will be described. An odd-numbered Z shim coil is Z ^{2k + 1} (k = 0,1,2, ...) in the Z-axis direction.
It is a magnetic field correction coil having a Z-axis direction magnetic field component that changes in proportion to. Regarding the odd-order Z shim coil, the same idea as that of the even-order Z shim coil may be used. The power of the even-order Z ^2k shim coil is changed to Z ^{2k + 1, and} it is constituted by a circular current loop of k + 1 pairs. The order of the odd-ordered shim coil is higher by one order than the same number of coils is that ε _{2k + 1} = 0 (k = 0,1,
Solution that satisfies the required magnetic field output to 0
This is because 0 is included and therefore this solution is not included as a solution for determining the coil attachment position. The general formula of the magnetic field output is as follows.

The simultaneous equations that determine any one type of order output are as follows.

1 corresponding to the required magnetic field output in k + 1 equations
K equations other than Is established by.

The above is the principle of the uniform magnetic field generator according to the present invention. It is possible to generate a plurality of completely independent magnetic field outputs with one type of coil arrangement, and to increase the logarithm of the circular current loop. It is possible to obtain a magnetic field in which the accuracy of the output magnetic field such as uniformity or linearity is remarkably good.

Next, an embodiment of the uniform magnetic field generator of the present invention will be described.

Eighth-Order Compensated Even-Order Shim Coil First, an eighth-order compensated even-order shim coil will be described as an even-order shim coil. Here, the nth order compensation shim coil (n
= 1,2,3 ...) is defined as a shim coil that does not include all the magnetic field components of the 0th order to the (n-1) th order except the required magnetic field components. For the eighth-order compensation even-order shim coil, the Z ⁴ shim coil arrangement is used as a reference, and k = 2 is substituted into each equation described in the principle. Z ⁴ shim coils requires circular current loop of three pairs, placing each circle current loops in a position to remove the 6-order term. The error term is generated from the 8th order term. The circular current loop is a solution that satisfies ε ₆ = 0 β = ± β ₁ , ± β ₂ ,
Install at 6 locations of ± β ₃ . The magnetic field output is given by the following equation.

Is used as an application area, and the error terms R _1,4 , R _2,4 and R _3,4 are ignored. The external elements that determine the magnetic field output Bz (γ, θ) are the respective circular current loops vs. the currents I ₁ , I ₂ , I ₃ . The currents I _{1 to} I ₃ with Bz (γ, θ) ≡ 0 are obtained from the following equation.

The above equation is a simultaneous equation with _three elements and is uniquely determined by _three solutions I ₁ , I ₂ , and I ₃ . When only two simultaneous equations except one arbitrary equation are satisfied, the current ratio becomes a solution, and _two solutions of I ₂ / I ₁ and I ₃ / I _{1 form} two arbitrary equations. However, the remaining one expression has a finite value. Therefore, the optimum current ratio can be obtained by solving the equation except for the equation that gives the required magnetic field output of the order. ~ The formula is specifically shown.

Collected by variables I ₂ / I ₁ and I ₃ / I ₁ .

If the current ratio that satisfies any of the two expressions is obtained, the remaining one expression becomes the required order output.

For the 0th order output, the current ratio is obtained from the following determinant.

The secondary and quaternary outputs can be similarly obtained. First, a solution satisfying ε ₆ = 0 is given by the following equation.

Each numerical value is shown within a practically sufficient range. After that, the same concept is applied to the part where numerical values are substituted. Therefore, both sides of the equation are not equal in the exact mathematical sense.

Next, the current ratio corresponding to each order output is shown.

0th output Secondary output 4th output From the above equation, when I ₁ is the current direction, the direction of the current in the ε-order compensation even-order shim coil is as shown in Table 2.

FIGS. 1a to 1c show one embodiment of the present invention based on equations. In each figure, (2D) is an eighth-order compensation even-order shim coil, and the arrangement position of each circular current loop pair of the eighth-order compensation even-order shim coil (2D), the current ratio, and the direction of current flow are shown. Figure 1a shows the 0th order output, namely Z ^0.
This is a case where a Z-axis direction magnetic field output proportional to is obtained. FIG. 1b shows a case where a secondary output, that is, a magnetic field output in the Z-axis direction proportional to Z ² is obtained. FIG. 1c shows a case where a fourth-order output, that is, a Z-axis direction magnetic field output proportional to Z ⁴ is obtained. The positions of the circular current loop pairs shown in FIGS. 1a to 1c are exactly the same, and only the current ratio of the currents flowing in each loop pair and the direction of the currents are changed. Therefore, if the 0th-order output, the 2nd-order output, and the 4th-order output required for magnetic field compensation are determined, the sum of the currents required for each order may be passed to each circular current loop pair. For example, 0th-order output that requires I ₁ = 1 [A] and I ₁ = 1
When there is a secondary output that requires [A] and a quaternary output that requires I ₁ = 1 [A], the currents flowing in each circular current loop pair are as shown in Table 3. That is, three types of magnetic field outputs of which the magnitudes of the respective magnetic field outputs are completely arbitrary can be realized by one type of shim coil arrangement.

Ninth-Order Compensated Odd-Order Shim Coil Next, a ninth-order compensated odd-order shim coil will be described as an odd-order shim coil. This 9th order compensation odd order shim coil
Based on the Z ⁵ shim coil arrangement, k in each equation of the principle
= 2 is substituted. The Z ⁵ shim coil places each circular current loop in a position that requires three pairs of circular current loops and eliminates the 7th order term. The error term is generated from the 9th order term. The circular current loop is installed at six positions of solution β = ± β ₁ , ± β ₂ , ± β ₃ which satisfies ε ₇ = 0. The solution β = 0 is excluded because it does not generate an odd-order magnetic field output. A general formula giving the optimum current ratio is shown.

If the current ratio that satisfies any two equations in the above equation is obtained, the remaining one equation becomes the required order output. First, ε ₇ =
When a solution that satisfies 0 is obtained, the following equation is obtained.

Next, the current ratio corresponding to each order output is shown.

Primary output Tertiary output 5th output Taking I ₁ as the direction, the direction of each order current is as shown in Table 4.

The current of each current loop pair is antisymmetric with respect to the Z = 0 plane. 2a to 2c show the arrangement of the circular current loop of the 9th order compensation odd order shim coil based on the above description. In each drawing, (2E) is a ninth-order compensation odd-order shim coil, and similarly to FIGS. 1a to 1c, the arrangement position of the circular current loop pair, the current ratio, and the current flowing direction are shown. Figure 2a shows a primary output, ie a magnetic field output proportional to Z ¹ , Figure 2b shows a tertiary output ie a magnetic field output proportional to Z ⁵ , and Figure 2c shows a 5th order output. , Ie Z ³
This is for obtaining a magnetic field output proportional to. Therefore,
The arrangement of the pair of circular current loops is exactly the same, and three types of magnetic field outputs of primary, tertiary and quintic can be obtained by simply changing the current ratio of each current loop pair.

In addition, as shown in Table 3 for the eighth-order compensation even-order shim coil, the ninth-order compensation odd-order shim coil also has
It goes without saying that if the sum of the currents required to obtain the magnetic field outputs of the respective orders is passed through the circular current loop pairs, the magnetic field outputs of the respective orders can be obtained simultaneously.

Sixth-Order Compensated Even-Order Shim Coil and Seventh-Order Compensated Odd-Order Shim Coil In the above embodiment, even-numbered and odd-ordered shim coils consisting of three pairs of circular current loops are shown, but the number of circular current loop pairs may be increased or decreased. Similar effects are obtained. However, when the number of circular current loop pairs increases, the type of generated magnetic field output increases, and when the number of circular current loop pairs decreases, the type of generated magnetic field output decreases. FIGS. 3a, 3b, 4a and 4b each show an embodiment in which there are two pairs of circular current loops. In Figures 3a and 3b, (2F) is 6
Third-order compensation even-order shim coil, Fig. 3a shows 0th-order output,
Ie to obtain a magnetic field output proportional to Z ⁰ , and 3b
The figure is for obtaining a secondary output, that is, a magnetic field output proportional to Z ² . Further, in FIGS. 4a and 4b, (2G) is a seventh-order compensation odd-order shim coil, FIG. 4a shows a primary output, that is, a magnetic field output proportional to Z ^1, and FIG. This is for obtaining a tertiary output, that is, a magnetic field output proportional to Z ³ . Even in the case of these two pairs of circular current loops, as in the case of the above-mentioned three pairs, if the sum of the currents necessary to obtain the magnetic field outputs of the respective orders is passed through the respective pairs of circular current loops, the respective orders will be It goes without saying that the magnetic field outputs of 1 and 2 can be obtained simultaneously and independently.

Regarding homogeneity and linearity of magnetic field output Next, the relationship between the same magnetic field output and the number of circular current loop pairs will be described. As an example, the zero-order output of the even-order shim coils, namely the case of obtaining a magnetic field proportional to Z ⁰ output (Z ⁰ magnetic field) will be described. FIG. 5 shows the coil used for the numerical calculation. In the figure, (6) is a rectangular cross-section circular coil, and the cross-sectional area of the coil is 2 mm (millimeter) x 2
mm, the radius of the coil is 500 mm. The center of the coil cross section is designated as the designated position for each of the positions based on the 1-pair type (β = 0.5) called Helmholtz coil, 2-pair type shown in FIG. 3a, and 3-pair type shown in FIG. 1a. I made it equal. The results are shown in FIG. In FIG. 6, the vertical axis represents the uniformity and the horizontal axis represents the area indicated by the distance Z (m) from the center point of the main solenoid coil. From the figure, it is clear that even when the same magnetic field output is obtained, the uniformity increases as the number of circular current loops increases. For example,
The three-pair type circular current loop is about 1000 times better in uniformity than the one-pair type. As another example, the primary output of the odd-order shim coils, namely the case of obtaining a magnetic field proportional to Z ¹ output (Z ¹ field) will be explained. A coil having the same shape as the rectangular cross-section circular coil (6) of FIG. 5 was used, and the one-pair type (β = 0.866) of odd-order shim coils and the two-pair type arrangement shown in FIG. 4a were used as references. The results are shown in FIG. In FIG. 7, the vertical axis represents the linearity, and the horizontal axis represents the area indicated by the distance Z (m) from the center point of the main solenoid coil. From the figure, using a 2-pair circular current loop,
It can be seen that the linearity is improved more than 300 times that of the one-pair type.

In the above embodiment, the homogeneity of the Z ⁰ magnetic field output up to 3-pair type was shown, but if the logarithm of the circular current loop is further increased,
The homogeneity of the Z ⁰ magnetic field output is further improved. In this case, it goes without saying that the position of each current loop pair follows the arrangement of the even-order shim coils described above. Further, in the above embodiment,
The linearity of the Z ¹ magnetic field output up to the 2-pair type was shown, but the linearity of the Z ¹ magnetic field output is further improved as the number of logarithms of the circular current loop increases. In this case, the position of each current loop pair is
It goes without saying that the arrangement of the odd-order shim coils described above is followed. Further, in the above embodiment, only the Z ⁰ magnetic field output and the Z ¹ magnetic field output are shown, but magnetic field outputs of other arbitrary orders may be used. Also in this case, increasing the logarithm of the circular current loop improves the accuracy of the magnetic field output of each order.

Further, in the above embodiment, the shim coil installed on the outer circumference of the main solenoid coil, that is, the magnetic field correction coil has been described, but the magnetic field correction coil may be on the inner circumference of the main solenoid coil, similar to the above embodiment. Produce an effect.

Further, although the magnetic field correction coil is circular in the above-mentioned embodiment, it may be a rectangular coil installed on the ball piece of the permanent magnet, and the same effect as that of the above-mentioned embodiment is obtained.

〔The invention's effect〕

As described above, according to the present invention, the magnetic field compensating coil of the uniform magnetic field generating device has one type of shim coil arrangement, for example, winding arrangement of Z ⁴ shim coils, and the current ratio of the energizing current to each circular current loop pair and the current By changing the direction of Z ⁰ , Z
^2, Z ⁴ three magnetic field independently, and can be generated at the same time, without reducing the types of I connexion generated magnetic field component in this, it is possible to reduce the number of shim coils,
There is an effect that an inexpensive and miniaturized uniform magnetic field generator can be obtained. Furthermore, when the Z ⁰ magnetic field and the Z ² magnetic field are generated by the Z ⁴ shim coil, the effect that the more accurate Z ⁰ magnetic field or Z ² magnetic field can be obtained is obtained.

[Brief description of drawings]

1a, 1b, and 1c are perspective views of a uniform magnetic field generator including an eighth-order compensation even-order shim coil according to an embodiment of the present invention, and FIGS. 2a, 2b, and 2c are FIG. 3a and FIG. 3b are perspective views of a uniform magnetic field generator having a ninth-order compensated odd-order shim coil according to another embodiment of the present invention, and a sixth-order compensated even-order shim coil according to another embodiment of the present invention. FIG. 4a and FIG. 4b are perspective views of a uniform magnetic field generator according to another embodiment of the present invention.
FIG. 5 is a perspective view of a uniform magnetic field generator having odd-order compensation odd-order shim coils, FIG. 5 is a partial sectional perspective view of a rectangular cross-section circular coil used in the numerical calculation of the uniform magnetic field generator of the present invention, and FIG. FIG. 7 is a diagram showing the numerical calculation result of the uniformity of the magnetic field output of the uniform magnetic field generator of the present invention; FIG. 7 is a diagram showing the numerical calculation result of the linearity of the magnetic field output of the uniform magnetic field generator of the present invention; 8, 9 and 10 are explanatory views for explaining the principle of the present invention, and FIG. 11 is a cross-sectional view of a conventional uniform magnetic field generator, FIG. 12, FIG. 13, FIG. FIG. 6 is a perspective view of a conventional uniform magnetic field generator. In the figure, (1) is the main solenoid coil and (2D) is 8
Order-compensated even-order shim coil, (2E) is 9th-order compensated odd-order shim coil, (2F) is 6th-order compensated even-order shim coil, (2G) is 7th-order compensated odd-order shim coil, (5) is circular current loop,
(6) is a circular coil having a rectangular cross section. In each figure, the same reference numerals indicate the same or corresponding parts.

Claims (11)

[Claims] 1. A main solenoid coil for producing a main magnetic field in an axial direction, and a shim coil provided on the main solenoid coil, the shim coil being k + 1 pairs (k = 1) arranged at a predetermined position of the solenoid coil. , 2, 3, ...) current loops, each current loop pair is provided such that each current loop is equidistant from the center point of the main solenoid coil in the main magnetic field direction and has the same ampere-turn.
By changing the current ratio and the direction of the current of each current loop pair, a magnetic field containing only one arbitrary order of k + 1 even orders of 0 to 2k or k + 1 of 1 to 2k + 1 for the above k + 1 pair. Any one of the odd orders of
A uniform magnetic field generator characterized by generating a magnetic field including only individual orders using a common coil arrangement. 2. A pair of current loops of k + 1 pairs (k = 1,2,3 ...), wherein the current directions of the respective current loops are the same. Item 1. The uniform magnetic field generator according to item 1. 3. A k + 1 pair (k = 1,2,3 ...) of circular current loops is a solution ± β _{1 of} ε _{2k + 2} = 0 which is a 2k + second-order coefficient in a magnetic field generated by these circular current loops. , ± β ₂ , ..., ± β _{k + 1}
Is the sum of the magnetic field generated in the main magnetic field direction other than the higher-order error magnetic field of the circular current loop, which is arranged at the position Where, for any integer l in the range 0 ≦ l ≦ k, However, (0,0): Vector display of coordinates generally represented by (γ, θ) with reference to the center point of the main solenoid coil P _2n (U): Legendre polynomial of 2nth order а: Circle current loop radius β : The currents I ₁ , I ₂ , ..., I _{k + 1} such that the distance in the direction of the main magnetic field normalized by the radius of the circular current loop ε _{m, 0} = 1 U = cos θ The uniform magnetic field generator according to claim 2, wherein a current loop is energized. 4. A pair of current loops of k + 1 pairs (k = 1,2,3 ...) In which the current directions of the respective current loops are opposite to each other. Item 1. The uniform magnetic field generator according to item 1. 5. A k + 1 pair (k = 1,2,3 ...) of circular current loops is a solution ± β _{1 of} ε _{2k + 3} = 0 which is a 2k + third-order coefficient in a magnetic field generated by these circular current loops. , ± β ₂ , ..., ± β _{k + 1}
Is the sum of the coefficients for each order of the magnetic field generated in the main magnetic field direction other than the higher-order error magnetic field of the above-mentioned circular current loop. Is an arbitrary integer l (0 ≦
l ≦ k), However, (0,0): Vector display of coordinates based on the center point of the main solenoid coil P _2n (U): 2nd-order Legendre polynomial а: Radius of circular current loop β: Normalized by radius of circular current loop The currents I ₁ , I ₂ , ..., I _{k + 1} that satisfy the distance U = cos θ in the main magnetic field direction are applied to the circular current loops of each pair. Item 4. The uniform magnetic field generator according to item 4. 6. A main solenoid coil for producing a main magnetic field in an axial direction, and a shim coil provided in the main solenoid coil, the shim coil being k + 1 pairs (k = 1) arranged at a predetermined position of the solenoid coil. , 2, 3, ...) current loops, each current loop pair is provided such that each current loop is equidistant from the center point of the main solenoid coil in the main magnetic field direction and has the same ampere-turn.
The uniform magnetic field generator according to claim 1, wherein a magnetic field composed of primary coupling of magnetic fields of a specific order can be generated by causing a current having a predetermined current ratio to flow in each pair of current loops. . 7. A pair of current loops of k + 1 pairs (k = 1,2,3 ...), wherein the current directions of the respective current loops are both in the same direction. Item 6. The uniform magnetic field generator according to item 6. 8. A k + 1 pair (k = 1,2,3 ...) of circular current loops is a solution ± β _{1 of} ε _{2k + 2} = 0 which is a 2k + second-order coefficient in a magnetic field generated by these circular current loops. , ± β ₂ , ..., ± β _{k + 1}
Is the sum of the magnetic field generated in the main magnetic field direction other than the higher-order error magnetic field of the circular current loop, which is arranged at the position , For any integer l in the range 0 ≦ l ≦ k For an integer j (0 ≦ j ≦ k) different from the currents I ₁ , I ₂ , ..., I _{K + 1} , and l However, (0,0): Vector display of coordinates generally represented by (γ, θ) with reference to the center point of the main solenoid coil P _2n (U): Legendre polynomial of 2nth order а: Circle current loop radius β : current I such that the normalized distance the main field direction _{ε m, 0 = 1 U =} cosθ in a circle current loops _{radius' 1, I '2, ...} , each superposed I' _{k + 1} In the pair of circular current loops, I ₁ + I ' ₁ , I ₂ + I' ₂ ,
The uniform magnetic field generator according to claim 7, wherein a current of Ik _{+ 1} + _{I'k + 1} is passed. 9. A pair of current loops of k + 1 pairs (k = 1,2,3 ...) In which the current directions of the respective current loops are opposite to each other. Item 6. The uniform magnetic field generator according to item 6. 10. A k + 1 pair (k = 1,2,3 ...) of circular current loops is a solution ± β _{1 of} ε _{2k + 3} = 0 which is a 2k + third-order coefficient in a magnetic field generated by these circular current loops. , ± β ₂ ,…, ± β
_The following equation, which is located at the position of _{k + 1} and is the sum of the coefficients for each order of the main magnetic field direction generated magnetic field other than the higher-order error magnetic field of the circular current loop Is an arbitrary integer l (0 ≦
for l ≤ k) For currents I ₁ , I ₂ , ..., I _{K + 1} and l that are different from each other, for an integer j (0 ≦ j ≦ k) However, (0,0): Vector display of coordinates based on the center point of the main solenoid coil P _2n (U): 2nd-order Legendre polynomial а: Radius of circular current loop β: Normalized by radius of circular current loop has been the main magnetic field direction of the distance _{ε m, 0 = 1 U =} cosθ become such a current _{I '1, I' 2,} ..., respectively circular current loop of each pair superposed I _{'k + 1} I ₁ + I ' ₁ , I ₂ + I' ₂ ,
The uniform magnetic field generator according to claim 9, wherein a current of Ik _{+ 1} + _{I'k + 1} is passed. 11. A main solenoid coil for producing a main magnetic field in an axial direction, and a shim coil provided in the main solenoid coil, the shim coil being k + 1 pairs (k = 1) arranged at a predetermined position of the solenoid coil. , 2,3 ...) current loops, each current loop pair is provided such that each current loop is equidistant from the center point of the main solenoid coil in the main magnetic field direction and has the same ampere-turn. 7. The uniform magnetic field generator according to claim 1, wherein the shim coil is capable of generating a magnetic field of a higher order than the order of the magnetic field to be generated among the specific orders.