Method for adjusting a superconducting cyclotron shim coil

Abstract

The present application relates to a kind of superconducting cyclotron pad coil adjustment method, comprising the following steps: setting basic example;On the basis of basic example, integral sliding phase linear equation is established;Linear programming constraint is established: the minimum value λ of integral sliding phase upper limit is obtained;Whether integral sliding phase upper limit satisfies isohronous acceleration requirement is judged;The pad coil arrangement scheme that finally satisfies isohronous acceleration requirement is obtained.The present application is based on Biot-Savart integral method and multi-objective optimization, linear programming method, avoids complex finite element calculation and tedious step-by-step adjustment process, can make superconducting cyclotron pad coil system produce suitable isochronous field, and meet the minimum use of superconducting wire.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of accelerator magnet, and particularly relates to a kind of superconducting cyclotron shim coil adjustment method. BACKGROUND

[0002] The cyclotron can adopt the relative position relationship of shim coil, the selection of excitation current of each group of coils in coil system, to realize the matching of particle cyclotron frequency and high frequency frequency, and the shim of local isochronism. The isochronism is one of the key technical indexes of cyclotron, and good isochronism can ensure that particles obtain relatively high energy gain in the movement process, which is very important for improving the operation efficiency of the accelerator. The methods for adjusting the isochronism of the cyclotron mainly include: 1) shimming isochronous field through magnetic pole shape profile; 2) shimming isochronous field through shim coil. Unlike the traditional cyclotron shim coil, the coil magnetic field in the superconducting accelerator accounts for the main part of the central plane magnetic field, and the shim coil plays a key role in the establishment of the isochronous field, and due to the complex structure, the adjustment scheme thereof must be reasonably designed.

[0003] The difficulty of shimming isochronous field through shim coil lies in that the relationship between each coil current and slip phase is unknown in advance, and it is necessary to try one by one, such as trying in the interval of 0-100,000, 0-200,000, although the number of coil groups is limited, but the numerical interval range is very large, and it may need to be adjusted for countless times, at least dozens of times, or even 100 times to get the desired result, since the number of debugging is uncertain, so the debugging cost is very high. SUMMARY

[0004] In view of the deficiencies of the current superconducting cyclotron shim coil adjustment scheme, the present application proposes a kind of superconducting cyclotron shim coil adjustment method, aiming at solving the problem that the relationship between each coil and slip phase is unknown in the prior art, and it may need to be adjusted for countless times, and the debugging cost is very high.

[0005] The present application proposes the following technical solutions to solve the technical problems:

[0006] A kind of superconducting cyclotron shim coil adjustment method, which is based on a kind of shim coil, the shim coil is composed of a group of peak area and a group of valley area, and is fixed on the same fixed plate by screw and magnetic pole, each group of shim coil is symmetrically distributed up and down, and the position and current size of the shim coil can be adjusted to realize the adjustment of the magnetic field, and the characteristics are as follows: the adjustment method of the shim coil includes the following steps:

[0007] Step one, set the basic example;

[0008] Step two, establish a system of linear equations: on the basis of the basic example, establish an integral slip phase linear equation;

[0009] s = a (0) + A · w # (1) ;

[0010] The vector s in formula (1) represents the slip phase of different radius positions, and the vector a (0) is a constant, the matrix A is a coefficient matrix, and the vector w represents the current of different shim coil groups; wherein, a (0) , A are the results of the basic example, and are known conditions;

[0011] Step three, establishing linear programming constraints:

[0012]

[0013] The formula group (2) represents the constraints that the shim coil current w i needs to meet, wherein is a constant, is an element in the coefficient matrix A, and w i represents the current from the first to the i-th shim coil, I down is the minimum value of the set current, and I up is the maximum value of the current, and n is the number of coil groups arranged along the radius direction of the accelerator. Two coils arranged symmetrically above and below the center plane of the accelerator are a coil group; wherein, and are known conditions after the design phase is completed, and w i and λ are unknown conditions after the design phase is completed;

[0014] Step four, solving the integral slip phase upper limit λ;

[0015] Step five, judging whether λ is less than 20: judging whether the integral slip phase upper limit λ meets the isochronous acceleration requirement, that is, the integral slip phase upper limit λ is less than 20 degrees. If it does not meet the requirement, the current distribution obtained by solving is taken as the basic example, and step one is repeated. If the integral slip phase upper limit λ obtained by iterative calculation meets the requirement, step six is entered;

[0016] Step six, checking the magnetic field: recording the shim coil position distribution and current generated in step five, establishing a finite element calculation model, and checking the result of the integral equation method;

[0017] If the deviation exceeds the threshold value, the result of the finite element calculation is taken as the basic example, and iterative calculation is performed again to obtain a final shim coil arrangement scheme that meets the isochronous acceleration requirement. If the deviation is less than the threshold value, step seven is continued;

[0018] Step seven, outputting the result.

[0019] Further, the step one of setting the basic example, the specific process is as follows

[0020] 1) Establish the basic coil system, through the multi-objective optimization algorithm or the method of successive iteration, the magnetic field form that generally meets the requirement of isochronous acceleration is obtained, the differential slip phase Omega (E) = (ω0-ω) / ω is generally required to be less than 1%, ω is the particle cyclotron frequency, and ω0 is the high frequency frequency;

[0021] 2) The magnetic field distribution Delta B i (r, theta) generated by the shim coil at different positions is calculated by using the Biot-Savart integral method, and the excitation current w = (w1, w2... w n ) T ; the results obtained by the example are linearly extrapolated for any current subsequently.

[0022] Further, the step two of establishing the integral slip phase linear equation on the basis of the basic example, the specific process is as follows: a small current increment Delta w = (Delta w1, Delta w2... Delta w n ) T is superimposed on the shim coil current of the basic example, and the current increment with subscript i is non-zero value, and the current increment with subscript of the rest is 0. The linear equation group of the integral slip phase is substituted to obtain a (0) and A; the Delta w is used to solve the matrix A and the constant a0, and the two quantities are unknown before the linear constraint relationship is established.

[0023] Further, under the condition that the shim coil current distribution form is known, the Biot-Savart integral method is used to quickly calculate the magnetic field distribution form of the shim coil, and the integral formula is as follows:

[0024]

[0025] By discretizing the current vector, the magnetic field axial component of the whole plane can be obtained by integral by substituting the position vector of the point (r, theta) into the main concerned cyclotron central plane magnetic field distribution. Wherein, B is the central plane magnetic field, J (r') is the current density at different radii, r is the position vector, and r' is the source vector. By discretizing the current vector, the magnetic field axial component B z (r, theta) of the whole plane can be obtained by integral by substituting the position vector of the point (r, theta) into the main concerned cyclotron central plane magnetic field distribution.

[0026] Further, the arrangement form of the shim coil is that the peak area valley area coil group is staggered distribution, and the most flexible adjustment amount is obtained under the condition of extremely compact; and because of the staggered arrangement form, the magnetic field jump at the joint of the shim coil is compensated, and the modulation degree of the accelerator is improved, and then the axial focusing ability is improved.

[0027] Further, the adjustment amount cannot be too large each time the distribution of the coil current is adjusted, and preferably the step value of the ampere-turns is 2000 or 5000, and the optimal solution is obtained through continuous iteration, and the iteration number is 10-15 times.

[0028] Advantages and effects of the present application

[0029] 1. The present application is based on the Biot-Savart integral method and multi-objective optimization and linear programming method, avoids complex finite element calculation and tedious step-by-step adjustment process, and can make the superconducting cyclotron shim coil system produce a suitable isochronous field and meet the minimization of the amount of superconducting wire.

[0030] 2. The present application establishes a linear relationship between the slip phase s and the coil shim current w, directly solves the coefficient matrix A by using the method of diagonal matrix, then directly establishes the linear relationship, and solves the minimum value of the slip phase by the method of linear programming, without adjusting the current of the shim coil one by one. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 The arrangement form of the shim coil system of the present application;

[0032] Figure 2 The integral slip phase optimization process corresponding to different ampere-turn step lengths of the shim coil system;

[0033] Figure 3 The average field distribution of the shim coil at different positions;

[0034] Figure 4 The flow chart of the adjustment method of the shim coil of the superconducting cyclotron of the present application. DETAILED DESCRIPTION

[0035] The present application will be further explained below in combination with the drawings:

[0036] Design principle of the present application

[0037] Innovative points of the present application: the innovative points are that ① a linear relationship between the slip phase s and the coil shim current w (formula (1)) is established. ② The basic example is used, and the diagonal matrix method is used to directly solve a (0)and A, ③ on the basis of the basic example, the integral slip phase upper limit λ is solved by establishing linear programming constraint conditions (formula group (2)); ④ in this way, the linear relationship is established by adjusting only once, and then the minimum value of the slip phase under the constraint condition can be directly obtained in the constraint interval. The current combination of the coil is determined by adjusting only once. The key point of "adjusting only once" is to use the linear programming method with constraints, instead of adjusting one by one. The establishment of the constraint condition is based on the linear equation formula (1), and the unknown a (0) , A is the method of the basic example.

[0038] A method for adjusting a superconducting cyclotron shim coil is shown in Figure 4 , which is based on a shim coil shown in Figure 1 , which is composed of a peak area group and a valley area group, and is fixed on the same fixed plate by screws and magnetic poles. Each group of shim coils is symmetrically distributed above and below, and the adjustment of the position and current size of the shim coil can realize the adjustment of the magnetic field. The characteristics are: the adjustment method of the shim coil comprises the following steps:

[0039] Step one, set the basic example;

[0040] Step two, establish a linear equation group: on the basis of the basic example, establish an integral slip phase linear equation;

[0041] s=a (0) +A·w#(1);

[0042] In formula (1), the vector s represents the slip phase at different radius positions, the vector a (0) is a constant, the matrix A is a coefficient matrix, and the vector w represents the current of different shim coil groups; wherein, a (0) , A is the result of the basic example, which is a known condition;

[0043] Step three, establish linear programming constraint conditions:

[0044]

[0045] Formula group (2) represents the constraint conditions that the shim coil current w i needs to meet, wherein is a constant, is an element in the coefficient matrix A, and w i represents the current of the first to the i-th shim coil, I down is the minimum value of the set current, and I upThe maximum current is n, the number of coil groups arranged along the radial direction of the accelerator, and two coils arranged symmetrically above and below the center plane of the accelerator are a group of coils. And After the design stage is completed, w i , and λ are unknown conditions.

[0046] Supplementary note 1

[0047] The invention is divided into a design stage and a design stage after completion, and the unknown quantities of the two stages are different:

[0048] ① In the design stage, a (0) and A in formula (1) are unknown, and the relationship needs to be established, so the results of the basic example must be used to solve the A matrix of a (0) After the two matrices are solved, the constraint relationship can be established. The solved A of a (0) is equivalent to and

[0049] ② After the design stage is completed, the and in formula group (2) are known conditions, and the current vector w i and the upper limit of the slip phase λ are unknown quantities that can change within the linear constraint conditions of formula group (2), and then the current vector w i is required to find out what value λ gets the minimum value.

[0050] ③ The meaning of formula group (2) is:-λ<s<λ,

[0051] ④ The peak area group is the upper row of the four groups of shim coils in the figure; the valley area group is the lower row of the three groups of shim coils in the figure. Figure 1 Figure 1

[0052] Step four, solve the integral slip phase upper limit λ;

[0053] Step five, judge whether λ is less than 20: judge whether the integral slip phase upper limit λ meets the isochronous acceleration requirement, that is, the integral slip phase upper limit λ is less than 20 degrees; if not, the current distribution obtained by solving is used as a basic example, and step one is repeated; if the integral slip phase upper limit λ obtained by iterative calculation meets the requirement, go to step six.

[0054] ​​Step six, check the magnetic field: record the shim coil position distribution and current generated in step five, establish a finite element calculation model, and check the results of the integral equation method; if the deviation exceeds the threshold value, use the finite element calculation results as the basis example to re-iterate the calculation to obtain the final shim coil layout scheme that meets the isochronous acceleration requirement, if the deviation is less than the threshold value, continue to step seven;

[0055] Step seven, output the results.

[0056] Supplementary note 2

[0057] 1) Since step five is a linear extrapolation of the magnetic field using the integral equation method, it may have some error (which may be within 10 Gauss, which is acceptable.) Therefore, step six is further verified.

[0058] 2) The "threshold value" mentioned above refers to the magnetic field error of the integral equation method and the finite element method. This error is generally within 10 Gauss.

[0059] Supplementary note 3

[0060] 1) As shown in Figure 2 , the horizontal coordinate is the iteration number, and the vertical coordinate is the maximum slip phase. The three curves in the figure represent different step sizes, and it can be seen that the larger the step size, the faster the slip phase decreases.

[0061] 2) Figure 3 There are a total of 5 curves in the figure, of which 4 curves represent the change of the magnetic field of each group of coils at different radii, and the dashed curve is the comprehensive situation of the 4 coil magnetic field curves.

[0062] Further, the setting of the basis example of step one is as follows

[0063] 1) Establish a basic coil system, and through a multi-objective optimization algorithm or a successive iteration method, obtain a magnetic field form that generally meets the isochronous acceleration requirement, with a differential slip phase Ω(E) = (ω0-ω) / ω generally less than 1%, ω is the particle cyclotron frequency, and ω0 is the high frequency.

[0064] 2) Use the Biot-Savart integral method to calculate the magnetic field distribution ΔB i (r, θ) generated by the shim coil at different positions, and record the excitation current w = (w1, w2...w n ) T ; subsequently, the results obtained by the example are linearly extrapolated for any current.

[0065] Supplementary note 4

[0066] 1) In the basic example above, w is the initial value of each group of coils. The integral phase slip corresponding to this initial value is very large, which is unacceptable. Therefore, the integral phase slip needs to be optimized based on this.

[0067] 2) The differential sliding phase Ω(E) is only an initial value. There is a corresponding relationship between the integral sliding phase and the differential sliding phase. When the differential sliding phase is less than a certain value, the integral sliding phase may be relatively large. Therefore, it is necessary to integrate from the differential sliding phase to obtain the integral sliding phase.

[0068] Furthermore, in step two, based on the basic calculation example, an integral sliding linear equation is established. The specific process is as follows: A small current increment Δw = (Δw1, Δw2…Δw) is superimposed on the padding coil current in the basic calculation example. n ) T We sequentially set the current increment at index i to a non-zero value, and the current increments at the other indices to zero. Substituting these values ​​into the linear equations of the integral sliding phase, we obtain a. (0) And A; the Δw is used to solve for matrix A and constant a0, which are unknown before the linear constraint relationship is established.

[0069] Supplementary note 5

[0070] 1) The phrase "sequentially make the current increment at index i non-zero, and the remaining index components zero" means that the current increment of the current coil is non-zero, while the current increments of other coils (the current increments are zero, not that the currents are zero) are zero. For example, in the basic calculation example, each coil has an initial current. To calculate A, an increment is added to this current, such as 1000. Then, the increment current of each coil is increased sequentially to calculate A.

[0071] 2) For a given radius, if there are 7 adjusting coils, then the equation will have 8 unknowns. Therefore, 8 equations are needed to solve for these 8 unknowns. So we need to assume that the current increment is a small value, and then add the case where the current increment is all 0. This will form 8 equations, and these 8 equations can solve for the 8 unknowns.

[0072] Furthermore, given the known current distribution of the padding coil, the Biot-Savart integration method is used to quickly calculate the magnetic field distribution of the padding coil. The integration formula is as follows:

[0073]

[0074] By discretizing the current vector, the axial components of the magnetic field in the entire plane can be obtained by integrating the position vector of point (r, θ) into the magnetic field distribution in the central plane of the cyclotron of main interest.

[0075] Where B is the magnetic field of the center plane, J(r') is the current density of different radius, r is the position vector, and r' is the source vector. By discretizing the current vector, the magnetic field axial component B(r,θ) of the whole plane can be obtained by integrating the position vector of the point (r,θ) into the main concerned cyclotron center plane magnetic field distribution z (r,θ).

[0076] Further, the arrangement of the shim coils is staggered distribution of the peak and valley coil groups, and the most flexible adjustment amount is obtained under the extremely compact condition; and due to the staggered arrangement, the magnetic field jump at the joint of the shim coils is compensated, and the modulation degree of the accelerator is improved, and the axial focusing ability is further improved.

[0077] Further, the adjustment amount of the coil current distribution cannot be too large each time, and the ampere-turn step value is preferably 2000 or 5000, and the optimal solution is obtained by continuous iteration, and the iteration number is 10-15 times.

[0078] Embodiment one

[0079] A proton superconducting cyclotron is designed, a straight edge fan magnetic pole is used, 4 pairs of shim coils are arranged in the peak area, and 3 pairs of shim coils are staggered arranged in the valley area. The position and current of the shim coils are designed by using the Biot-Savart integral method and the linear programming method. The magnetic field distribution of the shim coils in the peak area is obtained by calculation as shown in Figure 3 .

[0080] Based on the calculated distribution of the shim coils, the linear extrapolation is performed to establish a linear programming equation, and the simplex method is used to solve the optimal current combination. Without using the shim coils, the maximum value of the particle differential slip phase is 1.5%, and by reasonably designing the shim coils, the maximum value can be reduced to 1‰, which meets the isochronous acceleration requirement.

[0081] Figure 2 The change of the upper limit of the integral slip phase of the accelerator at different radii after each iteration under different step lengths is shown. It can be seen that the integral slip phase is continuously reduced, and the adjustment of the current of the shim coils is automatically completed.

[0082] The specific embodiments are only an explanation of the present application, and are not a limitation of the present application. Those skilled in the art can make modifications to the embodiments without creative contribution after reading the specification, and the modifications are protected by the patent law as long as they are within the scope of the claims.

Claims

1. A method for adjusting a padding coil in a superconducting cyclotron accelerator, the method being based on a padding coil consisting of a peak region group and a valley region group, fixed to the same fixed plate by screws and magnetic poles, with each group of padding coils symmetrically distributed vertically. The magnetic field can be adjusted by changing the position and current magnitude of the padding coils, characterized in that: The adjustment method for the padding coil includes the following steps: Step 1: Set up the basic calculation example; Step 2: Establish a system of linear equations: Based on the basic example, establish the integral sliding linear equations; s=a (0) +A·w# (1) In Formula 1, vector s represents the sliding phase at different radii, and vector a (0) A is a constant, matrix A is a coefficient matrix, and vector w represents the current of different padding coil groups; where a (0) A is the result of the basic example, which is a known condition; Step 3: Establish linear programming constraints: Formula group (2) represents the padding coil current w i The constraints that need to be satisfied, among which It is a constant. w is an element in coefficient matrix A. i I represents the current from the first to the i-th padding coil. down To set the minimum current, I up is the maximum current; n is the number of coil groups arranged along the radial direction of the accelerator, where two coils arranged symmetrically above and below the accelerator's central plane constitute a coil group; where, and After the design phase is completed, the known conditions are w. i λ is an unknown condition after the design phase is completed; Step 4: Solve for the upper bound λ of the integral sliding phase; Step 5: Determine if λ is less than 20: Determine if the upper bound of the integral sliding phase λ meets the isochronous acceleration requirement. Meeting the isochronous acceleration requirement means that the upper bound of the integral sliding phase λ is less than 20 degrees. If it does not meet the requirement, use the current distribution obtained by the solution as the basic example and repeat Step 1. If the upper bound of the integral sliding phase λ obtained by the iterative calculation meets the requirement, proceed to Step 6. Step Six: Verify the magnetic field: Record the position distribution and current of the padding coils generated in Step Five, establish a finite element calculation model, and verify the results of the integral equation method; if the deviation exceeds the threshold, use the finite element calculation results as the basic example and re-perform iterative calculation to obtain the final padding coil arrangement scheme that meets the isochronous acceleration requirements; if the deviation is less than the threshold, continue to Step Seven. Step 7: Output the results.

2. The method for adjusting the padding coil of a superconducting cyclotron accelerator according to claim 1, characterized in that: The specific process for setting up the basic calculation example in step one is as follows: 1) Establish a basic coil system, and obtain a magnetic field form that roughly meets the requirements of isochronous acceleration through multi-objective optimization algorithm or successive iteration method. The differential sliding phase Ω(E)=(ω0-ω) / ω is generally required to be less than 1%, where ω is the particle cyclotron frequency and ω0 is the high-frequency frequency. 2) The magnetic field distribution B generated by the padding coils at different positions is calculated using the Biot-Savart integration method. i (r, θ), and record the excitation current used w = (w1, w2...w n ) T The results obtained from this example are then used for linear extrapolation for any current.

3. The method for adjusting the padding coil of a superconducting cyclotron accelerator according to claim 1, characterized in that: Step two involves establishing an integral sliding phase linear equation based on the basic calculation example. The specific method is as follows: A small current increment Δw = (Δw1, Δw2...Δw) is superimposed on the padding coil current in the basic calculation example. n ) T Let the current increment at index i be non-zero, and the current increment at the other indices be 0. Substitute these values ​​into the linear equations of the integral sliding phase and solve to obtain a. (0) And A; the Δw is used to solve for matrix A and constant a0, which are unknown before the linear constraint relationship is established.

4. The method for adjusting the padding coil of a superconducting cyclotron accelerator according to claim 1, characterized in that: Given the current distribution of the padding coil, the magnetic field distribution of the padding coil can be quickly calculated using the Biot-Savart integration method. The integration formula is as follows: Where B is the magnetic field in the central plane, J(r′) is the current density at different radii, r is the position vector, and r′ is the source vector; by discretizing the current vector, the axial component B of the magnetic field in the entire plane can be obtained by substituting the position vector of point (r, θ) into the magnetic field distribution in the central plane of the cyclotron of main interest. z (r, θ).

5. The method for adjusting the padding coil of a superconducting cyclotron accelerator according to claim 1, characterized in that: The padding coils are arranged in an alternating pattern of peak and valley coil groups, which allows for the most flexible adjustment range under extremely compact conditions. Furthermore, due to the alternating arrangement, the magnetic field jumps at the junctions of the padding coils are compensated for, and the modulation degree of the accelerator can be improved, thereby enhancing the axial focusing capability.

6. The method for adjusting the padding coil of a superconducting cyclotron accelerator according to claim 1, characterized in that: Each time the distribution of the coil current is adjusted, the adjustment amount should not be too large. The step value of ampere-turns can be 2000 or 5000. The optimal solution is obtained through continuous iteration, with the number of iterations being 10 to 15.

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