CN104685584B - Method for constructing magnetic resonance image-forming superconducting magnet - Google Patents

Abstract

A kind of method for constructing magnetic resonance image-forming superconducting magnet, including：Determine superconducting wire, running current and feasible current-carrying area；Feasible current-carrying zoning is divided into multiple rectangular mesh, boundary rectangular mesh is rounded, the border in feasible current-carrying area is adjusted and obtains the rectangular mesh number in feasible current-carrying area；Using the center of magnet as origin, a coordinate system is set up, the space coordinate at each rectangular mesh center is obtained；So that with line amount, at least for optimization aim, center field intensity, uniformity of magnetic field and stray magnetic field are constraints, and feasible current-carrying area is planned using integral linear programming algorithm, each integrated distribution region of the initial wire of magnet is obtained；According to influence degree of each integrated distribution region to uniformity of magnetic field, according to the influence degree to uniformity of magnetic field from big to small, with minimum for optimization aim with line amount, center field intensity, uniformity of magnetic field and stray magnetic field are constraints, each integrated distribution region are carried out using integral linear programming algorithm squaring；And obtain the parameter of superconducting magnet coil.

Description

Method for constructing magnetic resonance image-forming superconducting magnet

Technical field

The invention belongs to application superconductor technology field, more particularly to construction magnetic resonance imaging (Magnetic Resonance Imaging, abbreviation MRI) superconducting magnet method.

Background technology

Magnetic resonance imaging (MRI) is the nuclear-magnetism shown using the magnetic core (mainly proton) of organism in magnetic field Resonance characteristics is come the new and high technology that is imaged.Magnetic resonance imaging (MRI) equipment mainly by main magnet, scanning bed, gradient coil, Radio-frequency coil, spectrometer system, switch board, interactive operating desk, computer and image processor etc. are constituted.

Main magnet is the main composition part of MRI machine, for producing homogeneous static magnetic field, decides the image of MRI machine Quality and operating efficiency.Meanwhile, main magnet is also manufacturing cost maximum, operating cost highest part in MRI machine.MRI pairs Intensity, the uniformity and the stability in magnetic field have strict demand, and this three are the most important indexs of main magnet.Come with respect to permanent magnet Say, superconducting magnet can produce intensity, the uniformity and stability all higher magnetic field, so being used to obtain the figure become apparent from Picture.

Detrimental effect can be brought to surrounding environment, such as 10 Gausses due to being distributed in the stray field outside superconducting magnet system The magnetic field of the order of magnitude is possible to cause some electronic equipment cisco unity malfunctions, and the patient with pacemaker is had life Danger, the magnetic field of the 100 Gauss orders of magnitude may can make computer working abnormal, therefore in view of some places to leakage field The limitation of field is, it is necessary to limit the stray magnetic field scope of superconducting magnet.

The magnetic field shielding mode of MRI main magnets includes passive screening and the class of active shield two.When taking passive screening mode, Need to dispose ferromagnetic material around magnet to shield stray field, it is simple in construction, but volume and weight is all very big, and to magnetic field Uniformity can also produce influence.It is general at present to use active shield mode, that is, pass through the logical reversely electricity of outside increase in main coil The shielded coil of stream reduces the stray magnetic field outside magnet, so as to reduce the stray magnetic field scope of magnet.Simultaneously because tradition MRI systems The length of system is longer, and a large amount of clinical trials show that patient's common manifestation in long and narrow space goes out the claustrophobias such as anxiety, uneasiness and showed As, therefore in recent years, short cavity, self-shileding MRI system are designed to a kind of new trend.

The electromagnetic design index of high evenness magnet for magnetic resonant imaging mainly has：

(1) imaging region (Diameter Sensitive Volume, abbreviation DSV), is commonly defined as a diameter of D ball Shape region.

(2) central field B₀, refer to the magnetic induction intensity value at imaging region center point.

(3) uniformity of magnetic field η (peak-to-peak value), computing formula is：

Wherein, Bmax and Bmin are respectively the maximum and minimum value of magnetic induction intensity in DSV.

(4) stray magnetic field scope, refers generally to magnet and passes to the area that the 5Gs equipotential lines in produced magnetic field during operating current are surrounded Domain.

The optimization design of magnetic resonance imaging (MRI) superconducting magnet is the basis that magnet makes, and to whole MRI machine Very important effect is played in image quality and production cost control.

The method of conventional construction MRI superconducting magnets can typically be attributed to two major classes, and a class is Direct Search Method, this kind of Method can both be carried out the overall situation preferentially to whole feas ible space, also might be used in the case where not giving magnet coil structure initial value To preselect the operating current and basic loop construction of superconducting magnet, using the structural parameters of magnet as independent variable, imaging region Interior uniformity of magnetic field, stray magnetic field scope, superconducting magnet spatial volume, magnet energy etc. are constraints or object function, are used Nonlinear optimization algorithm such as simulated annealing or genetic algorithm carry out local optima to the structural parameters of superconducting magnet, obtain most Whole magnet structure.But because MRI SUPERCONDUCTING MAGNET DESIGNs are a multi-parameter, the structural optimization problems of multiple target so that such Method is computationally intensive, less efficient, is become apparent when especially variable is more, if the selection of constraints and given initial value are not When rationally, it will be difficult to obtain optimal solution.

The another kind of introducing for being linear programming algorithm for functional based method.First magnet structure is simplified, in superconducting magnet can The rectangular mesh of division rule in row current-carrying area, seeks the equivalent being aligned plan model of MRI SUPERCONDUCTING MAGNET DESIGN problems Solution, obtains the initial current density distribution of the superconducting magnet, is distributed further according to initial current density and determines the basic of magnet coil Structure and location parameter, then using the first quasi-nonlinear optimizing algorithm, obtain final squaring magnet coil structure but by The method that initial current density is distributed to determine magnet basic structure, in the selection of magnet coil number and cross sectional shape still With certain subjective blindness, it is not easy to seek global optimum's result.

And in the final stage of above two method, actual coiling magnet, it is necessary to consider superconducting wire sectional dimension, Coil dimension is subjected to sliding-model control, and position and radius are rounded, round with it is discrete after, uniformity of magnet etc. Index generally has and is decreased obviously, and design result is deviateed optimal solution.

The content of the invention

It is existing for solving it is an object of the invention to provide a kind of method for constructing magnetic resonance image-forming superconducting magnet Magnetic resonance image-forming superconducting magnet method, it is necessary to consider superconducting wire sectional dimension during actual coiling magnet, by coil dimension Carry out sliding-model control, and position and radius rounded, round with it is discrete after, the index such as uniformity of magnet would generally It is decreased obviously, makes the problem of design result deviates optimal solution.

The method for constructing magnetic resonance image-forming superconducting magnet of the present invention, including：Determine superconducting wire, running current with And feasible current-carrying area；Using the center of magnet as origin, a cylindrical-coordinate system (r, z, α) is set up, wherein r is radial distance, and z-axis is Height, α is orientation angles, and magnet axial is z-axis direction；The feasible current-carrying zoning is divided into multiple grids, in feasible current-carrying area The radial direction number of plies of grid and the axial number of turn are rounded respectively, are obtained multiple rectangular mesh, are adjusted the border in feasible current-carrying area simultaneously The rectangular mesh number n in feasible current-carrying area is obtained, the space coordinate for obtaining each rectangular mesh center is (r_i, z_i, α_i)；With with Line amount is at least optimization aim, and center field intensity, uniformity of magnetic field and stray magnetic field are constraints, are calculated using integral linear programming Method is planned feasible current-carrying area, obtains each integrated distribution region of the initial wire of magnet；

According to influence degree of each integrated distribution region to uniformity of magnetic field, according to the influence degree to uniformity of magnetic field From big to small, so that with line amount, at least for optimization aim, center field intensity, uniformity of magnetic field and stray magnetic field are constraints, are utilized Integral linear programming algorithm carries out squaring to each integrated distribution region；And obtain the parameter of superconducting magnet coil.

When the present invention optimizes design to magnet, so that internal layer magnet coil at least can be made certainly for optimization aim with line amount Trend internal compression, can make outer coil automatic to external compression, by integral linear programming by constraints of stray magnetic field Obtained current-carrying rectangular mesh can form distributed areas in more close line set, can be met the complete of design requirement Office's optimal solution, design result is integer layer and circle, efficiently avoid the round-off error in usual method.

Brief description of the drawings

Fig. 1 show the schematic diagram of the embodiment of method one of magnetic resonance imaging construction superconducting magnet of the present invention；

Fig. 2 is feasible current-carrying area schematic diagram；

Fig. 3 show regional distribution chart in initial line set；

Fig. 4 be it is squaring after magnet structure schematic diagram；

Fig. 5 is the uniformity distribution in imaging area magnetic field；

Fig. 6 show the 5Gs patterns of equipotentials of magnet stray magnetic field.

Embodiment

Fig. 1 show the schematic diagram of the embodiment of method one of magnetic resonance imaging construction superconducting magnet of the present invention, such as Fig. 1 institutes Show：

Step 1, estimation magnet coil feasible current-carrying area maximum magnitude, including the minimum inside radius in feasible current-carrying area with And maximum outer radius, required according to Magnetic Field Design, the maximum magnetic induction in space constraint and feasible current-carrying area, determine superconduction Wire rod simultaneously determines running current Iop；

Step 2, using the center of magnet as origin, a cylindrical-coordinate system (r, z, α) is set up, wherein r is radial distance, z-axis For height, α is orientation angles, and magnet axial is z-axis direction；According to the size of selected superconducting wire, feasible current-carrying zoning is divided into Multiple grids, make the size in section of the physical dimension equal to selected superconducting wire of each grid, to grid in feasible current-carrying area The radial direction number of plies and the axial number of turn rounded respectively, form multiple rectangular mesh, and accordingly adjust each feasible current-carrying area Border, and obtain the rectangular mesh number n in the feasible current-carrying area of the magnet coil and the space seat at each rectangular mesh center It is designated as (r_i, z_i, α_i)。

Step 3, so that with line amount, at least for optimization aim, center field intensity, uniformity of magnetic field and stray magnetic field are constraints, Feasible current-carrying area is planned using integral linear programming algorithm, each integrated distribution region of the initial wire of magnet is obtained, If distributed areas are difficult to carry out the squaring of next step in the wire integrated distribution or line set of the design requirement that is not being met, Then return to step 1；

Wherein step 3 is specifically as follows：

The contribution to each magnetic field axial component for investigating point when each rectangular mesh passes to running current Iop is calculated, and often The length of superconducting wire contained by individual rectangular mesh：

Rectangular mesh under running current Iop can be equivalent to the electric current loop positioned at rectangular mesh center, its electricity Flow for I=Iop, i.e., by the current equivalence for having cross-sectional sizes in rectangular mesh into the plain conductor in rectangular mesh center, And the wire cross-section area is zero, logical electric current is running current Iop.Then electric current loop is investigating point coordinates (r_j, z_j) place's generation Magnetic field z is to component：

Wherein,

μ₀=4 π × 10^-7Tm/A (tesla's rice/ampere)

Introduce factor e_i=-1,0,1, obtain B_{Zi, j}=e_ia_ijI, the formula represents to work as e_iThe rectangular mesh is void when=0, i.e., To magnetic field without contribution；Work as e_iThe rectangular mesh is real when=1 or -1, is positive or negative to field contribution, superconducting magnet is corresponded to respectively Positive coil and reverse winding；

Then the magnetic field of each investigation point is：

The length of superconducting wire can be calculated by following formula contained by each rectangular mesh：

L_i=2 | e_i|πr_i

Magnet is then expressed as with line amount：

N is the rectangular mesh number in feasible current-carrying area, and I is equal to running current Iop.

Wherein, in the present invention, the minimum inside radius in the feasible current-carrying area of magnet coil is by reserved room temperature aperture, Dewar structure With the limitation of magnet skeleton, reserved a certain amount is needed during design；The maximum outer radius and the axial length of magnet of magnet coil The problems such as by magnet volume, Dewar weight, Consumer's Experience, is limited, and they also influence whether the field quality of magnet, so that The reasonability, practicality and economy of final optimization pass result are had influence on, so rationally to be limited the two variables；

When optimizing design to magnet using this method, so that internal layer magnet wire at least can be made for optimization aim with line amount Circle internally compresses automatically, can make outer coil automatic to external compression by constraints of stray magnetic field, by integer linear Plan that obtained current-carrying rectangular mesh can form distributed areas in more close line set, to carry out next step to magnet Optimization.

Step 5, according to influence degree of each integrated distribution region to uniformity of magnetic field, according to the shadow to uniformity of magnetic field From big to small, with minimum for optimization aim with line amount, center field intensity, uniformity of magnetic field and stray magnetic field are constraint bar to the degree of sound Part, it is squaring to each integrated distribution region progress using integral linear programming algorithm, to obtain with the minimum magnet structure of line amount；

Wherein, squaring is that each integrated distribution region is planned using integral linear programming algorithm.It is each to concentrate Distributed areas can be to the decision procedure of the influence degree of uniformity of magnetic field：Process -1-0-1 integral linear programmings are investigated to obtain The initial line set of magnet in distributed areas, each integrated distribution region of each separation to the influence degree of uniformity of magnetic field, Find influence degree most strong one, it is constant then to fix other integrated distribution regions, and rectangle is carried out to the integrated distribution region Change；It is met after the result of condition, then it is squaring using same method progress to next integrated distribution region；It is squaring At the end of, the final cross section parameter of superconducting magnet coil is obtained, the optimization design of magnet is completed；

A kind of more excellent selection is to consider the initial each integrated distribution region of wire of gained, each integrated distribution region Shape carries out rectangle to each integrated distribution region in order close to the degree and its influence degree to uniformity of magnetic field of rectangle Change, to obtain with the minimum magnet structure of line amount：

Judge whether not yet to carry out each integrated distribution region of the initial wire of the squaring magnet, if complete Into then execution step obtains the cross section parameter of superconducting magnet coil, otherwise returns squaring to each integrated distribution region progress The step of；

It is to the algorithm of realizing that each integrated distribution region carries out squaring step：

Each integrated distribution region under the running current is subjected to rectangular mesh division again, divided according to each concentrate Cloth region determines the new feasible current-carrying area in the feasible current-carrying area, and the radial direction number of plies to grid in new feasible current-carrying area and axial direction The number of turn is rounded respectively, and the border in the new feasible current-carrying area of adjustment simultaneously obtains the space coordinate at each rectangular mesh center and newly may be used Total rectangular mesh number n1 in row current-carrying area, the electric current positioned at rectangular mesh center is equivalent to by the plurality of rectangular mesh Ring, the electric current of the electric current loop is equal to the running current, and electric current loop is investigating point coordinates (r_j, z_j, α_j) place produce magnetic field axial direction z Component is：

B_{Zi, j}=e_ia_ijI

Wherein,

μ 0=4 π × 10^-7Tm/A, (2)

Factor e_iFor -1,0 or 1, work as e_iWhen=0 the integrated distribution region to magnetic field without contribution；Work as e_iConcentration point when=1 Cloth region is to field contribution for just, the positive coil of correspondence superconducting magnet works as e_iThe integrated distribution region is to magnetic field tribute when=- 1 It is negative to offer, the reverse winding of correspondence superconducting magnet；

Then the magnetic field z of each investigation point is to component：

The length of superconducting wire is calculated by following formula contained by each integrated distribution region：

L_i=2 | e_i|πr_i (7)

Magnet is then expressed as with line total amount：

Wherein, n1 is total grid number in new feasible current-carrying area, and I is equal to the running current.

Step 6, whether judge the parameter of final design Project Realization and can meet JC (B) characteristic of superconducting wire, if Meet then optimization to terminate, return to step 1 if being unsatisfactory for.

Step 7, output parameter and associated arguments are calculated, including：Magnetic of the structure chart, magnetic field of output winding in homogeneity range Field distribution and the scope of equipotential line, the maximum field in magnet current-carrying area and 5 gaussian lines.

Below in conjunction with the accompanying drawings 1 and foregoing construction magnetic resonance image-forming superconducting magnet method, to further illustrate this hair Bright principle and specific embodiment.

As shown in figure 1, its basic step can be as follows：

Step 1. sets the feasible current-carrying of short cavity self-shileding superconducting magnet coil according to Magnetic Field Design requirement and space constraint Area, selects suitable superconducting wire and determines running current Iop.

Fig. 2 is feasible current-carrying area schematic diagram.Magnet is symmetrical on Z axis, and symmetrical on Z=0 planes, so shown in Fig. 2 Part is 1/4 section in feasible current-carrying area.The feasible current-carrying area inside radius R of magnet coil₁=0.5m, outer radius R₂=0.92m, Length L=0.645m.The sectional dimension of superconducting wire used is 1.80 × 1.20mm², running current is 400A.

Feasible current-carrying zoning is divided into multiple rectangular mesh by step 2..

According to the size of selected superconducting wire, feasible current-carrying zoning is divided into multiple rectangular mesh, makes the several of rectangular mesh What size is equal to selected superconducting wire size, and the border in feasible current-carrying area is rounded and accordingly adjusted to rectangular mesh, magnet is obtained The rectangular mesh number n in the feasible current-carrying area of coil, it is then determined that the space coordinate at each rectangular mesh center.

Step 3. calculates contribution and contained superconducting wire length of each rectangular mesh to magnetic field.

Each rectangular mesh is equivalent to the electric current loop of position at its center, its running current is I=Iop, each should The space coordinate at rectangular mesh center is (r_i, z_i, α_i), calculate each electric current loop and investigate point (r in each magnetic field_j, z_j, α_j) produce Magnetic field z to component.

Superconducting wire length contained by each rectangular mesh is then calculated by following formula：

L_i=2 π r_i

Wherein, then can be long by superconducting wire contained by each rectangular mesh if it is considered that quadrant is symmetrical on Z=0 planes Degree is then calculated by following formula：

L_i=4 π r_i

Step 4. use -1-0-1 integral linear programmings method optimizes calculating to the wire integrated distribution of magnet.

So that at least with line amount as optimization aim, central field, imaging area uniformity of magnetic field and stray magnetic field scope etc. are constraint Condition, optimizes calculating, Fig. 3 is shown initially using -1-0-1 integral linear programmings method to the wire integrated distribution of magnet Regional distribution chart in line set, wherein, it is forward direction coil, i.e. factor e that black box 1,2,3 and 4 bodies, which represent electric current,₁, e₂, e₃And e₄ For 1, it is reverse winding, factor e that white framework 5,6 and 7, which represents electric current,₅、e₆And e₇For -1.

Step 5. is squaring to the progress of wire concentrated area, obtains the final optimization pass result of magnet.

Fig. 4 be it is squaring after magnet structure schematic diagram, wherein, it is positive line that black box 1,2,3 and 4 bodies, which represent electric current, Circle, i.e. factor e₁, e₂, e₃And e₄For 1, it is reverse winding, factor e that white framework 5,6 and 7, which represents electric current,₅、e₆And e₇For -1.

Magnet length is 1.29m, and superconducting wire overall length used is 63.6km, and table 1 designs the line completed for the implementation case Enclose parameter.

Table 1

Step 6, whether judge the parameter of final design Project Realization and can meet JC (B) characteristic of superconducting wire, if Meet then optimization to terminate, return to step 1 if being unsatisfactory for.

Fig. 5 is the magnet center B0=1.5T of gained in the uniformity distribution in imaging area magnetic field, the present embodiment, and magnet is carried Flow area maximum field Bmax=6.07T, imaging area uniformity of magnetic field distribution as shown in figure 5, unit be rice (m), can see Go out, in a diameter of 50cm spheric region, meet the design objective that the uniformity is less than 10ppm.It is illustrated in figure 6 magnet spuious The 5Gs patterns of equipotentials of field, unit is rice (m), and distance of the 5Gs equipotential lines away from magnet center, radially less than 3.5m, is axially less than 4m。

Step 7. output parameter simultaneously calculates associated arguments, including：Magnetic of the structure chart, magnetic field of output winding in homogeneity range Field distribution and the scope of equipotential line, the maximum field in magnet current-carrying area and 5 gaussian lines.

The method that the present invention is used to construct magnetic resonance image-forming superconducting magnet passes through the feasible current-carrying Division magnet coil Grid, the physical dimension of grid is selected ribbon dimension, is considered with line amount, magnetic induction intensity, uniformity of magnetic field, stray magnetic field The indexs such as scope, area distribution in the initial line set of magnet coil are obtained using -1-0-1 integral linear programming algorithms, then press Certain order carries out distributed areas in the initial line set of magnet squaring to obtain final optimization pass result.It is above-mentioned to be used to construct magnetic The method of resonance image-forming superconducting magnet can not only carry out traditional MRI SUPERCONDUCTING MAGNET DESIGNs, be also applied for internal layer and be distributed with instead To the short cavity MRI SUPERCONDUCTING MAGNET DESIGNs, asymmetric solenoid coil system and open biplane coil system of current coil MRI SUPERCONDUCTING MAGNET DESIGNs etc., in addition, can flexibly be set according to the foundation of specific design coordinate system and symmetric relation Put, for example, for above-mentioned MRI SUPERCONDUCTING MAGNET DESIGNs if unsymmetric structure, then coordinate system is not required on Z=0 planes pair Claim.The above embodiment of the present invention is by taking -1-0-1 integral linear programming algorithms as an example, can also actually to use such as 0-1 integer lines Property planning algorithm etc., because realization principle is similar to the above embodiments, those skilled in the art refer to above-described embodiment realization, Therefore will not be described here.

In summary, it is interior can at least be made for optimization aim with line amount when optimizing design to magnet in the present invention Layer magnet coil internally compresses automatically, can make outer coil automatic to external compression by constraints of stray magnetic field, pass through The current-carrying rectangular mesh that integral linear programming is obtained can form distributed areas in more close line set, can be met The globally optimal solution of design requirement, design result is integer layer and circle, efficiently avoid the round-off error in usual method.

Although exemplary embodiment describing the present invention with reference to several, it is to be understood that, term used is explanation and shown Example property and nonrestrictive term.Due to the present invention can be embodied in a variety of forms without departing from the present invention spirit or Essence, it should therefore be appreciated that above-described embodiment is not limited to any foregoing details, and the essence that should be limited in appended claims Widely explained in god and scope, therefore the whole changes fallen into claim or its equivalent scope and remodeling all should be appended Claim is covered.

Claims (9)

1. a kind of method for constructing magnetic resonance image-forming superconducting magnet, it is characterised in that including：

Determine superconducting wire, running current and feasible current-carrying area；

Using the center of magnet as origin, a cylindrical-coordinate system (r, z, α) is set up, wherein r is radial distance, and z-axis is height, and α is side Parallactic angle degree, magnet axial is z-axis direction, the feasible current-carrying zoning is divided into multiple grids, to the footpath of grid in feasible current-carrying area Rounded respectively to the number of plies and the axial number of turn, obtain multiple rectangular mesh, adjusted the border in feasible current-carrying area and obtain feasible The rectangular mesh number n in current-carrying area, the space coordinate for obtaining each rectangular mesh center is (r_i,z_i, α_i)；

So that with line amount, at least for optimization aim, center field intensity, uniformity of magnetic field and stray magnetic field are constraints, utilize -1-0-1 Integral linear programming algorithm is planned feasible current-carrying area, obtains each integrated distribution region of the initial wire of magnet；

According to influence degree of each integrated distribution region to uniformity of magnetic field, according to the influence degree to uniformity of magnetic field from big To small, so that with line amount, at least for optimization aim, center field intensity, uniformity of magnetic field and stray magnetic field are constraints, utilize -1-0- 1 integral linear programming algorithm carries out squaring to each integrated distribution region；And obtain the parameter of superconducting magnet coil.

2. the method as described in claim 1, it is characterised in that the feasible current-carrying area is symmetrical on Z axis, and on Z=0 planes Symmetrically.

3. the method as described in claim 1, it is characterised in that with minimum for optimization aim, center field intensity, magnetic field with line amount The uniformity and stray magnetic field are constraints, and feasible current-carrying area is planned using integral linear programming algorithm, realizes that algorithm is：

The plurality of rectangular mesh is equivalent to the electric current loop positioned at rectangular mesh center, the electric current of the electric current loop is equal to the fortune Row electric current, electric current loop is investigating point coordinates (r_j,z_j,α_j) the axial z-component in magnetic field that produces of place is：

B_zi,j=e_ia_ijI

Wherein,

$a_{ij}=\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}\frac{1}{{\[{(r_i+r_j)}^2+{(z_j-z_i)}^2\]}^{\frac{1}{2}}}\×\{K\left(k\right)-\[\frac{{r_j}^2-{r_i}^2+{(z_j-z_i)}^2}{{\left(r_j-r_i\right)}^2+{(z_j-z_i)}^2}\]E\left(k\right)\},---\left(1\right)$

μ₀=4 π × 10^-7Tm/A, (2)

$k={\[\frac{4r_i{r}_j}{{(r_i+r_j)}^2+{(z_j-z_i)}^2}\]}^{\frac{1}{2}},---\left(3\right)$

$K\left(k\right)=\underset{0}{\overset{\mathrm{\π}/2}{\∫}}\frac{d\mathrm{\α}}{\sqrt{1-k^2{\sin }^2\mathrm{\α}}},---\left(4\right)$

$E\left(k\right)=\underset{0}{\overset{\mathrm{\π}/2}{\∫}}\sqrt{1-k^2{\sin }^2\mathrm{\α}}d\mathrm{\α},---\left(5\right)$

Factor e_iFor -1,0 or 1, work as e_iWhen=0 the rectangular mesh to magnetic field without contribution；Work as e_iThe rectangular mesh is to magnetic field when=1 Contribute as just, the positive coil of correspondence superconducting magnet works as e_iThe rectangular mesh is negative, correspondence superconducting magnetic to field contribution when=- 1 The reverse winding of body；

Then the magnetic field z of each investigation point is to component：

$B_{zj}=\underset{i=1}{\overset{n}{\Σ}}{e}_i{a}_{ij}I---\left(6\right)$

The length of superconducting wire is calculated by following formula contained by each rectangular mesh：

L_i=2 | e_i|πr_i (7)

Magnet is then expressed as with line total amount：

$L=2\mathrm{\π}\underset{i=1}{\overset{n}{\Σ}}\left|e_i\right|r_i---\left(8\right)$

Wherein, n is the rectangular mesh number in feasible current-carrying area, and I is equal to the running current, and (4) formula is the first ellptic integral, (5) formula For the second ellptic integral.

4. the method as described in claim 1, it is characterised in that using integral linear programming algorithm to each integrated distribution region Planning is carried out to specifically include：

Squaring step is carried out to each integrated distribution region, including：Calculate the magnetic obtained by the integral linear programming Each integrated distribution region of the initial wire of body is to the influence degree of uniformity of magnetic field, and it is most strong one to find influence degree, so After to fix other integrated distribution regions constant, the integrated distribution region is carried out squaring；

Judge whether not yet to carry out each integrated distribution region of the initial wire of the squaring magnet, if completed, The cross section parameter that step obtains superconducting magnet coil is performed, otherwise returns and squaring step is carried out to each integrated distribution region Suddenly.

5. method as claimed in claim 4, it is characterised in that the reality of squaring step is carried out to each integrated distribution region Now algorithm is：

Each integrated distribution region under the running current is subjected to rectangular mesh division again, according to each areal concentration Domain determines the new feasible current-carrying area in the feasible current-carrying area, and to the radial direction number of plies and the axial number of turn of grid in new feasible current-carrying area Rounded respectively, the border in the new feasible current-carrying area of adjustment and the space coordinate and new feasible load for obtaining each rectangular mesh center Total rectangular mesh number n1 in area is flowed, the plurality of rectangular mesh is equivalent to the electric current loop positioned at rectangular mesh center, should The electric current of electric current loop is equal to the running current, and electric current loop is investigating point coordinates (r_j,z_j,α_j) the axial z-component in magnetic field that produces of place For：

B_zi,j=e_ia_ijI

Wherein,

$a_{ij}=\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}\frac{1}{{\[{(r_i+r_j)}^2+{(z_j-z_i)}^2\]}^{\frac{1}{2}}}\×\{K\left(k\right)-\[\frac{{r_j}^2-{r_i}^2+{(z_j-z_i)}^2}{{(r_j-r_i)}^2+{(z_j-z_i)}^2}\]E\left(k\right)\},---\left(1\right)$

μ₀=4 π × 10^-7Tm/A, (2)

$k={\[\frac{4r_i{r}_j}{{(r_i+r_j)}^2{(z_j-z_i)}^2}\]}^{\frac{1}{2}},---\left(3\right)$

$K\left(k\right)=\underset{0}{\overset{\mathrm{\π}/2}{\∫}}\frac{d\mathrm{\α}}{\sqrt{1-k^2{\sin }^2\mathrm{\α}}},---\left(4\right)$

$E\left(k\right)=\underset{0}{\overset{\mathrm{\π}/2}{\∫}}\sqrt{1-k^2{\sin }^2\mathrm{\α}}d\mathrm{\α},---\left(5\right)$

Factor e_iFor -1,0 or 1, work as e_iWhen=0 the integrated distribution region to magnetic field without contribution；Work as e_iAreal concentration when=1 Domain is to field contribution for just, the positive coil of correspondence superconducting magnet works as e_iThe integrated distribution region is to field contribution when=- 1 It is negative, the reverse winding of correspondence superconducting magnet；

Then the magnetic field z of each investigation point is to component：

$B_{zj}=\underset{i=1}{\overset{n1}{\Σ}}{e}_i{a}_{ij}I---\left(6\right)$

The length of superconducting wire is calculated by following formula contained by each integrated distribution region：

L_i=2 | e_i|πr_i (7)

Magnet is then expressed as with line total amount：

$L=2\mathrm{\π}\underset{i=1}{\overset{n1}{\Σ}}\left|e_i\right|r_i---\left(8\right)$

Wherein, n1 is total grid number in the new feasible current-carrying area, and I is equal to the running current.

6. the method as described in claim 1, it is characterised in that also wrapped after the final cross section parameter for obtaining superconducting magnet coil Include, whether can Project Realization and meet the characteristic of superconducting wire, design and complete if meeting if judging the parameter of final design, if It is unsatisfactory for, the step of returning to determination superconducting wire, running current and feasible current-carrying area, and adjusts superconducting wire, running current And feasible current-carrying area.

7. method as claimed in claim 4, it is characterised in that the cross section parameter includes：The structure chart of output winding, magnetic field exist The scope of Distribution of Magnetic Field and equipotential line, the maximum field in magnet current-carrying area and 5 gaussian lines in homogeneity range.

8. the method as described in claim 1, it is characterised in that if the wire integrated distribution for the design requirement that is not being met or Distributed areas are difficult to carry out the squaring of next step in line set, then return and determine superconducting wire, running current and feasible load The step of flowing area, and adjust superconducting wire, running current and feasible current-carrying area.

9. the method as described in claim 1, it is characterised in that the method for construction magnetic resonance image-forming superconducting magnet is applied to internal layer The short cavity MRI SUPERCONDUCTING MAGNET DESIGNs and asymmetric solenoid coil system and open double flat of reverse current coil is distributed with The MRI SUPERCONDUCTING MAGNET DESIGNs of planar coil system.