CN113030811A - Design method of cylindrical shimming coil - Google Patents

Design method of cylindrical shimming coil Download PDF

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CN113030811A
CN113030811A CN202110548675.XA CN202110548675A CN113030811A CN 113030811 A CN113030811 A CN 113030811A CN 202110548675 A CN202110548675 A CN 202110548675A CN 113030811 A CN113030811 A CN 113030811A
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current density
coil
cylindrical
grid
magnetic field
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CN113030811B (en
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陈方
樊萌
刘朝阳
张志�
冯继文
陈俊飞
陈黎
程鑫
鲍庆嘉
汪慧娟
王佳鑫
杨李泽
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Institute of Precision Measurement Science and Technology Innovation of CAS
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    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
    • G01R33/28—Details of apparatus provided for in groups G01R33/44 - G01R33/64
    • G01R33/32—Excitation or detection systems, e.g. using radio frequency signals
    • G01R33/34—Constructional details, e.g. resonators, specially adapted to MR
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Abstract

The invention discloses a design method of a cylindrical shimming coil, which comprises the following steps of firstly, carrying out grid division on the cylindrical shimming coil to obtain each grid node; selecting a target point on the target spherical surface; establishing a finite difference relation between a grid node current density flow function and a grid node current density; setting the magnetic field intensity of a target point; establishing and solving an equation set between a grid node current density flow function and a component of a target point magnetic field intensity in the z-axis direction; and (4) arranging the equipotential lines distributed on the corresponding cylindrical surface of the coil in an equal difference manner to obtain the winding mode of the shimming coil. The method is simple and effective, provides a new idea for designing the cylindrical shimming coil, and can effectively eliminate the uneven magnetic field components of each order of the main magnetic field introduced by the cylindrical magnet system due to production and manufacturing errors, thereby improving the uniformity of the main magnetic field of the cylindrical magnet system.

Description

Design method of cylindrical shimming coil
Technical Field
The invention belongs to the technical field of magnetic resonance imaging coils, and particularly relates to a design method of a cylindrical shimming coil.
Background
According to the working principle and the application field, the magnetic resonance instrument system can be divided into a Nuclear Magnetic Resonance (NMR) instrument, a Magnetic Resonance Imaging (MRI) instrument, an Electron Paramagnetic Resonance (EPR) instrument and the like, a magnet is one of the most important components of the magnetic resonance instrument system, and the performance of the magnetic resonance instrument depends on the main magnetic field B of the magnet to a great extent0The higher the homogeneity of the main magnetic field of the magnet, the higher the signal-to-noise ratio and resolution of the NMR signal obtained by the NMR instrument, and the higher the quality of the MRI image obtained by the MRI instrument.
Ideally, the main magnetic field strength of the MRI apparatus is B0 However, in the actual magnet manufacturing process, due to engineering errors, uneven magnetic field components of each step are inevitably introduced to affect the main magnetic field uniformity. In magnetic resonance systems, however, the quality of the Nuclear Magnetic Resonance (NMR) signals and MRI images is largely dependent on the homogeneity of the main magnetic field. Methods for improving the uniformity of a main magnetic field are divided into active shimming and passive shimming, wherein the active shimming is realized by shimming coils with specific current distribution.
The invention provides a method for designing a cylindrical shimming coil for magnetic resonance imaging, aiming at solving the problem of main magnetic field nonuniformity of a cylindrical magnet system (such as a superconducting magnet, a conventional electromagnet and the like), wherein the shimming coil designed by the method can eliminate nonuniform magnetic field components of each step of the main magnetic field of the cylindrical MRI magnet system and improve the uniformity of the main magnetic field (as shown in figure 1).
Disclosure of Invention
The invention aims to solve the problems in the prior art, and provides a design method of a cylindrical shimming coil, which can eliminate the uneven magnetic field component of each order of the main magnetic field of a cylindrical magnet system and improve the uniformity of the main magnetic field.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a design method of a cylindrical shimming coil comprises the following steps:
step 1, firstly, carrying out grid division on a coil cylindrical surface where a cylindrical shimming coil is located to obtain each grid node;
step 2, selecting a target point on the target spherical surface;
step 3, establishing a current density flow function of the grid node
Figure 937758DEST_PATH_IMAGE001
And finite difference relationship of grid node current density;
step 4, setting the magnetic field intensity of a target point;
step 5, establishing a grid node current density flow function
Figure 342194DEST_PATH_IMAGE002
And the z-axis direction component of the magnetic field strength of the target point;
step 6, constructing a power consumption constraint function H, obtaining a constraint matrix L according to the power consumption constraint function H, and solving the grid node current density flow function in the step 5 by utilizing a Tikhonov regularization method
Figure 191202DEST_PATH_IMAGE002
And the z-axis direction component of the magnetic field intensity of the target point to obtain a grid node current density flow function
Figure 972076DEST_PATH_IMAGE002
The specific numerical values of (a);
Figure 488508DEST_PATH_IMAGE003
wherein R1 is the bottom surface radius of the coil cylindrical surface,
Figure 565311DEST_PATH_IMAGE004
is the height of the cylindrical surface of the coil,
Figure 901614DEST_PATH_IMAGE005
the grid current density is the angular direction around the circumference,
Figure 220600DEST_PATH_IMAGE006
is the grid current density in the z-axis direction, zs is the z-axis height variable of the grid node,
Figure 325959DEST_PATH_IMAGE007
is the azimuthal variation of the axial dividing line,
and 7, arranging the distributed equipotential lines of the current density flow function of each grid node on the corresponding coil cylindrical surface in an equal difference mode to obtain the winding mode of the shimming coil.
In step 1 as described above:
selecting one of axial dividing lines of the cylindrical surface of the coil where the cylindrical shimming coil is positioned as a starting axial dividing line, numbering each axial dividing line in a clockwise or reverse time mode, and indicating the number of the axial dividing line by i;
and selecting one end to the other end of the cylindrical surface of the coil where the cylindrical shimming coil is positioned to number each circumferential division circle of the cylindrical surface of the coil where the cylindrical shimming coil is positioned, wherein the number of the circumferential division circle is represented by j.
In step 3, as described above, the grid node current density comprises the grid current density in the angular direction around the circumference
Figure 337777DEST_PATH_IMAGE005
And zAxial grid current density
Figure 161377DEST_PATH_IMAGE006
Grid current density in angular directions around the circumference
Figure 18475DEST_PATH_IMAGE005
And z-axis grid current density
Figure 509499DEST_PATH_IMAGE006
The relationship between them is:
Figure 426639DEST_PATH_IMAGE008
in the above formula, the first and second carbon atoms are,
Figure 737535DEST_PATH_IMAGE009
as a mesh node
Figure 398323DEST_PATH_IMAGE010
The grid current density is at an angular orientation around the circumference,
Figure 478275DEST_PATH_IMAGE011
as a mesh node
Figure 333361DEST_PATH_IMAGE012
The grid current density in the direction of the z axis,
Figure 865973DEST_PATH_IMAGE013
as a mesh node
Figure 330452DEST_PATH_IMAGE014
The radius of the cylindrical surface of the coil on which the coil is located,
Figure 530490DEST_PATH_IMAGE015
is the angular difference between the azimuths of adjacent axial divisions of the cylindrical surfaces of the coils,
Figure 789433DEST_PATH_IMAGE016
the spacing between circles is divided for adjacent circumferential directions of the cylindrical surfaces of the coils,
Figure 74920DEST_PATH_IMAGE017
representing the current density flow function at the grid node (i, j),
Figure 343091DEST_PATH_IMAGE018
representing the current density flow function at the grid node (i +1, j),
Figure 132055DEST_PATH_IMAGE019
representing the current density flow function at the grid node (i, j + 1).
Step 5 as described above comprises the steps of:
step 5.1, establishing the component of the target point magnetic field intensity in the z-axis direction
Figure 827479DEST_PATH_IMAGE020
Discrete equations of the governing equation of (1);
Figure 334683DEST_PATH_IMAGE021
in the above formula, zs is the z-axis height variable of the mesh node,f = 1，2…N，
Figure 140965DEST_PATH_IMAGE022
is as followsfCoordinate values of the target points under the rectangular coordinate system,
Figure 551480DEST_PATH_IMAGE023
step 5.2, according to the component of the magnetic field intensity of the target point in the z-axis direction
Figure 417805DEST_PATH_IMAGE024
The discrete equation of the control equation of (1) and the current density flow function of the grid node
Figure 412306DEST_PATH_IMAGE002
And z-axis direction component of the magnetic field strength at the target point:
Figure 22279DEST_PATH_IMAGE025
Figure 520256DEST_PATH_IMAGE026
for the first mesh node to mth mesh node current density flow function,
Figure 823062DEST_PATH_IMAGE027
，……，
Figure 39280DEST_PATH_IMAGE028
m is the total number of all grid nodes obtained by grid division of the cylindrical surface of the coil, N is the total number of target points,
Figure 187364DEST_PATH_IMAGE029
the z-axis direction components of the magnetic field strengths of the first target point to the Nth target point.
Compared with the prior art, the invention has the following beneficial effects:
the method is simple and effective, provides a new idea for designing the cylindrical shimming coil, and can effectively eliminate the uneven magnetic field components of each order of the main magnetic field introduced by the cylindrical magnet system due to production and manufacturing errors, thereby improving the uniformity of the main magnetic field of the cylindrical magnet system.
Drawings
Fig. 1 is a schematic diagram of the front and rear configurations of cylindrical shim coils.
1-a cylindrical magnet; 2-the distribution of the magnetic lines before the shimming coil is added is indicated; 3-cylindrical shim coils; 4-the distribution of magnetic lines of force is indicated after the cylindrical shimming coil is added; b is0 -main magnetic field direction.
Fig. 2 is a grid node division of the coil cylinder surface.
FIG. 3 shows a target point selected from the target sphere.
Fig. 4 shows a winding mode of the cylindrical shim coil on the cylindrical surface of the coil.
FIG. 5 shows a winding pattern of a second cylindrical shim coil on the cylindrical surface of the coil.
Fig. 6 is an overall schematic diagram of mesh nodes of two coil cylindrical surfaces and target points of a target spherical surface.
Detailed Description
The present invention will be described in further detail with reference to examples for the purpose of facilitating understanding and practice of the invention by those of ordinary skill in the art, and it is to be understood that the present invention has been described in the illustrative embodiments and is not to be construed as limited thereto.
In this embodiment, the invention will be used to counteract
Figure 71006DEST_PATH_IMAGE030
Coil for cancelling out inhomogeneous components of interest
Figure 279134DEST_PATH_IMAGE031
The coils of the relevant inhomogeneous components are respectively defined as a first cylindrical shimming coil and a second cylindrical shimming coil, and a design method of the cylindrical shimming coil for magnetic resonance imaging is introduced by taking two groups of 2-order cylindrical shimming coils of the first cylindrical shimming coil and the second cylindrical shimming coil as design examples. The first cylindrical shimming coil and the second cylindrical shimming coil can be independently implemented according to the following steps 1-7.
The cylindrical coils are distributed on a cylindrical surface with the z axis as the central axis, and the target region of the shimming is a target spherical surface with the origin as the spherical center. In this embodiment, the height of the coil cylinder is 0.42m, the radius of the bottom surface is 0.1m, and the radius of the target cylinder surface is 0.025 m.
A design method of a cylindrical shimming coil comprises the following steps:
step 1, firstly, grid division is carried out on the cylindrical surfaces of coils where the cylindrical shimming coil I and the cylindrical shimming coil II are respectively located to obtain each grid node.
As shown in fig. 2, the coil cylindrical surface is divided by a plurality of axial division lines each of which is located on the coil cylindrical surface and is parallel to the central axis of the coil cylindrical surface, and a plurality of circumferential division circles each of which is located on the coil cylindrical surface and is perpendicular to the central axis of the coil cylindrical surface, an angle difference between azimuth angles of adjacent axial division lines being
Figure 248227DEST_PATH_IMAGE032
The azimuth angle of the axial dividing line means the azimuth angle of the axial dividing line in the circumferential direction of the cylindrical surface of the coil, and the interval between adjacent circumferential dividing circles is
Figure 200002DEST_PATH_IMAGE033
In the present embodiment, the first and second electrodes are, in this embodiment,
Figure 174037DEST_PATH_IMAGE032
=360°/60，
Figure 818645DEST_PATH_IMAGE033
=
Figure 9455DEST_PATH_IMAGE034
/60，
Figure 764921DEST_PATH_IMAGE034
the height of the cylindrical surface of the coil.
Selecting one of the axial dividing lines of the cylindrical surface of the coil where the first cylindrical shimming coil is located as a starting axial dividing line, numbering the axial dividing lines clockwise or anticlockwise, selecting one of the axial dividing lines of the cylindrical surface of the coil where the second cylindrical shimming coil is located as a starting axial dividing line, numbering the axial dividing lines clockwise or anticlockwise, and indicating the numbering of the axial dividing lines by i;
numbering each circumferential dividing circle of the cylindrical shimming coil I from one end to the other end of the cylindrical shimming coil I; and numbering each circumferential division circle of the cylindrical shimming coil II from one end to the other end of the cylindrical shimming coil II, wherein the number of the circumferential division circle is represented by j.
The central axis of the coil cylindrical surface of the first cylindrical shim coil, the central axis of the coil cylindrical surface of the second cylindrical shim coil and the z axis are parallel.
The intersection points of the axial dividing lines and the circumferential dividing circles are grid nodes, and the serial numbers of the grid nodes can be represented by (i, j).
And 2, selecting a target point on the target spherical surface.
And extracting the coordinate value of the target point under the rectangular coordinate system
Figure 357577DEST_PATH_IMAGE035
The target point on the target spherical surface is selected by the following steps: 59 wefts are taken at equal intervals on the target spherical surface, the equal intervals refer to the shortest interval between adjacent wefts along the target spherical surface, 60 target points are uniformly selected on each weft,fthe number of the target point.
Step 3, establishing a current density flow function of the grid node
Figure 907507DEST_PATH_IMAGE036
And finite difference relationship of the current density of the grid nodes.
The numbers (i, j) of mesh nodes generated by meshing the coil cylindrical surface are represented by i =1, 2, … …, 60, j =1, 2, … …, 60. It is specially stated that the grid node
Figure 851192DEST_PATH_IMAGE037
Representing intermediate nodes between mesh node (i, j) and mesh node (i, j + 1), mesh node
Figure 144770DEST_PATH_IMAGE038
Representing intermediate nodes between mesh node (i, j) and mesh node (i +1, j).
The mesh node current density includes the angular mesh current density around the circumference according to the finite difference flow function concept
Figure 591932DEST_PATH_IMAGE039
And z-axis grid current density
Figure 578342DEST_PATH_IMAGE040
Grid current density in angular directions around the circumference
Figure 478165DEST_PATH_IMAGE039
The differential relation between the grid node current density flow function and the grid node current density flow function is shown in formula (2), and the grid current density in the z-axis direction
Figure 88618DEST_PATH_IMAGE040
The differential relationship with the mesh node current density flow function is shown in equation (3):
Figure 655865DEST_PATH_IMAGE041
wherein, in the formula (2) and the formula (3),
Figure 547598DEST_PATH_IMAGE042
as a mesh node
Figure 200296DEST_PATH_IMAGE043
The grid current density is at an angular orientation around the circumference,
Figure 835677DEST_PATH_IMAGE044
as a mesh node
Figure 257431DEST_PATH_IMAGE045
The grid current density in the direction of the z axis,
Figure 585644DEST_PATH_IMAGE046
as a mesh node
Figure 460059DEST_PATH_IMAGE047
The radius of the cylindrical surface of the coil is positioned, zs is the height variable of the z axis of the grid node,
Figure 899131DEST_PATH_IMAGE048
is the azimuthal variation of the axial division line.
According to the finite difference concept, the formula (2) and the formula (3) can be expressed as the formula (4) and the formula (5) in the finite difference form, and then the current density flow function of the grid node is obtained
Figure 175391DEST_PATH_IMAGE036
And finite difference relationship of grid node current density:
Figure 408927DEST_PATH_IMAGE049
wherein, in the formulas (4) and (5), the grid nodes
Figure 770638DEST_PATH_IMAGE050
Representing intermediate nodes between mesh node (i, j) and mesh node (i, j + 1), mesh node
Figure 514865DEST_PATH_IMAGE051
Representing intermediate nodes between mesh node (i, j) and mesh node (i +1, j),
Figure 645632DEST_PATH_IMAGE052
representing the current density flow function at the grid node (i, j),
Figure 50069DEST_PATH_IMAGE053
representing the current density flow function at the grid node (i +1, j),
Figure 164655DEST_PATH_IMAGE054
representing the current density flow function at the grid node (i, j + 1).
Step 4, setting the magnetic field intensity of a target point corresponding to the cylindrical shimming coil I and the magnetic field intensity of a target point corresponding to the cylindrical shimming coil II, wherein in the embodiment, the magnetic field intensity of the target point corresponding to the cylindrical shimming coil I is
Figure 945529DEST_PATH_IMAGE055
The magnetic field intensity of a target point corresponding to the cylindrical shimming coil II is
Figure 196382DEST_PATH_IMAGE056
。
Step 5, establishing current density flow functions of all grid nodes by using the Biot-savart theorem
Figure 771720DEST_PATH_IMAGE057
And z-axis component of the magnetic field strength at the target point
Figure 108023DEST_PATH_IMAGE058
A system of equations in between;
for any target point, the direction of the main magnetic field is defined as the direction of the z axis, and the component of the magnetic field strength of the target point in the direction of the z axis can be obtained by utilizing the Biot-Saval theorem
Figure 692589DEST_PATH_IMAGE058
Is shown in equation (6):
Figure 797948DEST_PATH_IMAGE059
in the formula (2) and the formula (4),
Figure 544187DEST_PATH_IMAGE060
in order to achieve a magnetic permeability in a vacuum,
Figure 134831DEST_PATH_IMAGE061
is the angular variation of the mesh nodes around the circumference. Substituting the formula (4) into the formula (6) can obtain the component of the magnetic field intensity of the target point in the z-axis direction
Figure 991928DEST_PATH_IMAGE058
The discrete equation of the control equation of (2) is shown in equation (7):
Figure 217373DEST_PATH_IMAGE062
zs is the z-axis height variable of the mesh node,f =1, 2 … N, intermediate variable
Figure 400093DEST_PATH_IMAGE063
The value of (c) is shown in equation (8):
Figure 445409DEST_PATH_IMAGE064
considering that the magnetic field intensity of each target point is the vector sum of the current density flow functions of all grid nodes on the cylindrical surface of the coil and the magnetic field generated by the target point, the following equation system can be obtained by the formula (7) to obtain the current density flow function of the grid nodes
Figure 106198DEST_PATH_IMAGE036
And z-axis direction component of magnetic field strength at target point, and grid node current density flow function
Figure 451728DEST_PATH_IMAGE036
Including a first grid node current density flow function
Figure 539770DEST_PATH_IMAGE065
Current density flow function to Mth mesh node
Figure 72383DEST_PATH_IMAGE066
(ii) a The z-axis component of the target point field strength comprises a z-axis component of the first target point field strength
Figure 802441DEST_PATH_IMAGE067
Z-axis component of magnetic field strength to Nth target point
Figure 736899DEST_PATH_IMAGE068
；
Figure 261421DEST_PATH_IMAGE069
Figure 782795DEST_PATH_IMAGE070
For the first mesh node to mth mesh node current density flow function,
Figure 785386DEST_PATH_IMAGE071
，……，
Figure 839930DEST_PATH_IMAGE072
m is the total number of all grid nodes obtained by grid division of cylindrical surfaces of two coils, N is the total number of target points,
Figure 535353DEST_PATH_IMAGE073
the component from the first target point magnetic field intensity in the z-axis direction to the Nth target point magnetic field intensity in the z-axis direction;
step 6, constructing a power consumption constraint function, obtaining a constraint matrix L according to the power consumption constraint function, and solving the grid node current density flow function in the step 5 by utilizing a Tikhonov regularization method
Figure 308137DEST_PATH_IMAGE036
And the z-axis direction component of the magnetic field intensity of the target point to obtain a grid node current density flow function
Figure 848840DEST_PATH_IMAGE036
The specific numerical values of (a);
equation (10) is a typical ill-conditioned system of equations, which is solved in this example using the Tikhonov regularization method,
l is a constraint matrix, and the power consumption constraint function H of the coil is introduced in this example, then:
Figure 757890DEST_PATH_IMAGE074
in formula (12), R1 is the cylindrical surface of the coilThe radius of the bottom surface is greater than the radius of the bottom surface,
Figure 624215DEST_PATH_IMAGE034
for the height of the cylindrical surface of the coil, equation (12) is converted into a current density flow function for the grid node
Figure 618716DEST_PATH_IMAGE057
Is expressed as shown in equation (13):
Figure 963109DEST_PATH_IMAGE075
t is a transpose, a constraint matrix L which can be used in a Tikhonov regularization method is obtained, and a formula (10) is solved according to the constraint matrix L and by adopting the Tikhonov regularization method to obtain a first grid node current density flow function
Figure 992245DEST_PATH_IMAGE065
Current density flow function to Mth grid node
Figure 29471DEST_PATH_IMAGE066
Distribution on the cylindrical surface of the coil.
Step 7, a first grid node current density flow function
Figure 12733DEST_PATH_IMAGE065
Current density flow function to Mth grid node
Figure 160818DEST_PATH_IMAGE066
The equipotential lines distributed on the corresponding cylindrical surface of the coil are arranged in an equipotential value mode to obtain the winding mode of the shim coil, the magnitude of the potential difference current is set to be 20A, and the winding modes of the cylindrical shim coil I and the cylindrical shim coil II on the cylindrical surface of the coil are obtained and are respectively shown in fig. 4 and 5.
Therefore, the invention can control the power consumption of the shimming coil and restrain the magnetic field value of the shimming coil on a target point. The cylindrical shimming coil designed by the method can effectively eliminate the uneven magnetic field components of each order of the main magnetic field introduced in the manufacturing process of the cylindrical magnet system.
Finally, it should be noted that: the above embodiment is exemplified by the 2 nd order axial shim coil and is not limited to the 2 nd order shim coil, and the above embodiment is only used for illustrating the technical solution of the present invention and is not limited thereto, although the present invention is described in detail with reference to the preferred embodiments, those skilled in the art should understand that: modifications and equivalents may be made to the invention without departing from the spirit and scope of the invention.

Claims (4)

1. A design method of a cylindrical shimming coil is characterized by comprising the following steps:
step 1, firstly, carrying out grid division on a coil cylindrical surface where a cylindrical shimming coil is located to obtain each grid node;
step 2, selecting a target point on the target spherical surface;
step 3, establishing a current density flow function of the grid node
Figure 946222DEST_PATH_IMAGE001
And finite difference relationship of grid node current density;
step 4, setting the magnetic field intensity of a target point;
step 5, establishing a grid node current density flow function
Figure 812546DEST_PATH_IMAGE002
And the z-axis direction component of the magnetic field strength of the target point;
step 6, constructing a power consumption constraint function H, obtaining a constraint matrix L according to the power consumption constraint function H, and solving the grid node current density flow function in the step 5 by utilizing a Tikhonov regularization method
Figure 807047DEST_PATH_IMAGE002
And the z-axis component of the magnetic field strength of the target pointProgram group to obtain current density flow function of grid node
Figure 417020DEST_PATH_IMAGE002
The specific numerical values of (a);
Figure 446156DEST_PATH_IMAGE003
wherein R1 is the bottom surface radius of the coil cylindrical surface,
Figure 217803DEST_PATH_IMAGE004
is the height of the cylindrical surface of the coil,
Figure 965179DEST_PATH_IMAGE005
the grid current density is the angular direction around the circumference,
Figure 113264DEST_PATH_IMAGE006
is the grid current density in the z-axis direction, zs is the z-axis height variable of the grid node,
Figure 996906DEST_PATH_IMAGE007
is the azimuthal variation of the axial dividing line,
and 7, arranging the distributed equipotential lines of the current density flow function of each grid node on the corresponding coil cylindrical surface in an equal difference mode to obtain the winding mode of the shimming coil.
2. The method for designing a cylindrical shim coil according to claim 1, wherein in the step 1:
selecting one of axial dividing lines of the cylindrical surface of the coil where the cylindrical shimming coil is positioned as a starting axial dividing line, numbering each axial dividing line in a clockwise or reverse time mode, and indicating the number of the axial dividing line by i;
and selecting one end to the other end of the cylindrical surface of the coil where the cylindrical shimming coil is positioned to number each circumferential division circle of the cylindrical surface of the coil where the cylindrical shimming coil is positioned, wherein the number of the circumferential division circle is represented by j.
3. The method as claimed in claim 2, wherein in step 3, the grid node current density comprises a grid current density in an angular direction around the circumference
Figure 939454DEST_PATH_IMAGE005
And z-axis grid current density
Figure 410012DEST_PATH_IMAGE006
Grid current density in angular directions around the circumference
Figure 361788DEST_PATH_IMAGE005
And z-axis grid current density
Figure 99936DEST_PATH_IMAGE006
The relationship between them is:
Figure 478965DEST_PATH_IMAGE008
in the above formula, the first and second carbon atoms are,
Figure 935354DEST_PATH_IMAGE009
as a mesh node
Figure 690821DEST_PATH_IMAGE010
The grid current density is at an angular orientation around the circumference,
Figure 549055DEST_PATH_IMAGE011
as a mesh node
Figure 98985DEST_PATH_IMAGE012
The grid current density in the direction of the z axis,
Figure 777091DEST_PATH_IMAGE013
as a mesh node
Figure 70669DEST_PATH_IMAGE014
The radius of the cylindrical surface of the coil on which the coil is located,
Figure 284875DEST_PATH_IMAGE015
is the angular difference between the azimuths of adjacent axial divisions of the cylindrical surfaces of the coils,
Figure 5707DEST_PATH_IMAGE016
the spacing between circles is divided for adjacent circumferential directions of the cylindrical surfaces of the coils,
Figure 171109DEST_PATH_IMAGE017
representing the current density flow function at the grid node (i, j),
Figure 268378DEST_PATH_IMAGE018
representing the current density flow function at the grid node (i +1, j),
Figure 835625DEST_PATH_IMAGE019
representing the current density flow function at the grid node (i, j + 1).
4. The method for designing a cylindrical shim coil according to claim 3, wherein the step 5 comprises the following steps:
step 5.1, establishing the component of the target point magnetic field intensity in the z-axis direction
Figure 727358DEST_PATH_IMAGE020
Discrete equations of the governing equation of (1);
Figure 114477DEST_PATH_IMAGE021
in the above formula, zs is the z-axis height variable of the mesh node,f = 1，2…N，
Figure 15437DEST_PATH_IMAGE022
is as followsfCoordinate values of the target points under the rectangular coordinate system,
Figure 437191DEST_PATH_IMAGE023
step 5.2, according to the component of the magnetic field intensity of the target point in the z-axis direction
Figure 765404DEST_PATH_IMAGE024
The discrete equation of the control equation of (1) and the current density flow function of the grid node
Figure 639819DEST_PATH_IMAGE002
And z-axis direction component of the magnetic field strength at the target point:
Figure 580356DEST_PATH_IMAGE025
Figure 856616DEST_PATH_IMAGE026
for the first mesh node to mth mesh node current density flow function,
Figure 355731DEST_PATH_IMAGE027
，……，
Figure 717442DEST_PATH_IMAGE028
m is the total number of all grid nodes obtained by grid division of the cylindrical surface of the coil, N is the total number of target points,
Figure 960204DEST_PATH_IMAGE029
the z-axis direction components of the magnetic field strengths of the first target point to the Nth target point.
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