Adjusting method for shimming coil of superconducting cyclotron

Abstract

The invention relates to a method for adjusting a shimming coil of a superconducting cyclotron. The method comprises the following steps of: setting a basic example; establishing an integral sliding-phase linear equation on the basis of the basic example; establishing a linear programming constraint; solving to obtain a minimum value lambda of the upper bound of the integral sliding phase; judging whether the integral sliding phase upper bound meets the isochronous acceleration requirement or not; and a shimming coil arrangement scheme which finally meets the isochronous acceleration requirement is obtained. According to the method, on the basis of the Biot-Savart integral method and the multi-objective optimization and linear programming method, complex finite element calculation and a tedious step-by-step adjustment process are avoided, a superconducting cyclotron shimming coil system can generate a proper isochronous field, and the requirement for minimizing the using amount of superconducting wires is met.

Description

Technical Field

[0001] The invention belongs to the field of accelerator magnets, and in particular relates to a method for adjusting a shimming coil of a superconducting cyclotron accelerator. Background Art

[0002] The cyclotron accelerator can achieve the matching of particle cyclotron frequency and high-frequency frequency and the shimming of local isochronism by adjusting the relative position relationship of the shimming coils and the selection of the excitation current of each group of coils in the coil system. Isochronism is one of the key technical indicators of the cyclotron accelerator. Good isochronism can ensure that particles obtain relatively high energy gain during movement, which is very important for improving the operating efficiency of the accelerator. The main methods for adjusting isochronism of the cyclotron accelerator are: 1) shimming the isochronous field through the shape contour of the magnetic pole; 2) shimming the isochronous field through shimming coils. Unlike the traditional shimming coils of the cyclotron, the coil magnetic field in the superconducting accelerator occupies the main part of the central plane magnetic field. The shimming coil plays a key role in the establishment of the isochronous field, and due to its complex structure, its adjustment scheme must be reasonably designed.

[0003] The difficulty of shimming the equal time field by shimming coils is that the relationship between each coil current and the sliding phase is unknown in advance, and it is necessary to try one number and one coil at a time, such as trying in the range of 0 to 100,000 or 0 to 200,000. Although the number of coil groups is limited, the range of the digital interval is very large, and it may take countless adjustments, at least dozens or even 100 times to get the desired result. Since the number of debugging times is uncertain, the debugging cost is very high. Summary of the invention

[0004] In view of the shortcomings of the current superconducting cyclotron shim coil adjustment scheme, the present invention proposes a superconducting cyclotron shim coil adjustment method, aiming to solve the problem in the prior art that the relationship between each coil and the sliding phase is unknown, and it may be necessary to adjust countless times, resulting in high debugging costs.

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

[0006] A method for adjusting a shimming coil of a superconducting cyclotron accelerator is based on a shimming coil, the shimming coil is composed of a group of peak areas and a group of valley areas, and is fixed to the same fixing plate with a magnetic pole by screws. Each group of shimming coils is symmetrically distributed up and down. The magnetic field can be adjusted by adjusting the position of the shimming coil and the current size. The method is characterized in that the shimming coil adjustment method comprises the following steps:

[0007] Step 1: Set up the basic example;

[0008] Step 2: Establish a linear equation system: Based on the basic example, establish the integral sliding phase linear equation;

[0009] s=a (0) +A·w#(1);

[0010] In formula (1), vector s represents the sliding phase at different radial positions, and vector a (0) is a constant, the matrix A is a coefficient matrix, and the vector w represents the current of different shimming coil groups; where a (0) , A is the result of the basic example and is a known condition;

[0011] Step 3: Establish linear programming constraints:

[0012]

[0013] Formula group (2) represents the shimming coil current w i The constraints that need to be satisfied are is a constant, is the element in the coefficient matrix A, w i represents the current from the 1st to the i-th shimming coil, I down is the minimum current setting, I up is the maximum current, n is the number of coil groups arranged along the radius of the accelerator, and two coils arranged symmetrically up and down with the accelerator center plane as the boundary are a group of coils; where, and After the design phase is completed, it is a known condition. i ,λ is an unknown condition after the design phase is completed;

[0014] Step 4: solve the upper bound λ of the integral sliding phase;

[0015] Step 5, judging whether λ is less than 20: judging whether the integral sliding phase upper bound λ meets the isochronous acceleration requirement, which means that the integral sliding phase upper bound λ is less than 20 degrees; if not, the current distribution obtained by the solution is used as the basic calculation example, and step 1 is repeated. If the integral sliding phase upper bound λ obtained by iterative calculation meets the requirement, proceed to step 6;

[0016] Step 6: Check the magnetic field: record the position distribution and current of the shimming coil generated in step 5, establish a finite element calculation model, and check the results of the integral equation method;

[0017] If the deviation exceeds the threshold, the result of the finite element calculation is used as the basic calculation example, and the iterative calculation is repeated to obtain the shimming coil arrangement scheme that finally meets the isochronous acceleration requirements; if the deviation is less than the threshold, continue to step seven;

[0018] Step 7: Output the results.

[0019] Furthermore, the step 1 of setting up the basic example is as follows:

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

[0021] 2) Using the Biot-Savart integration method, calculate the magnetic field distribution ΔB generated by the shimming coils at different positions i (r, θ), and record the excitation current w = (w1, w2...w n ) T ; Subsequently, the results obtained by this example are used to perform linear extrapolation for any current.

[0022] Furthermore, in step 2, based on the basic example, an integral sliding phase linear equation is established. The specific process is as follows: a small current increment Δw=(Δw1, Δw2…Δw n ) T , let the current increments with subscript i be non-zero values, and the current increments of the other subscripts be 0. Substituting into the linear equations of the integral sliding phase, we can get a (0) and A; the Δw is used to solve the matrix A and the constant a0, which are unknown before the linear constraint relationship is established.

[0023] Furthermore, under the condition that the current distribution form of the shimming coil is known, the Biot-Savart integration method is used to quickly calculate the magnetic field distribution form of the shimming coil. The integration formula is as follows:

[0024]

[0025] By discretizing the current vector, the axial component of the magnetic field in the entire plane can be obtained by substituting the position vector of the point (r, θ) into the central plane magnetic field distribution of the cyclotron accelerator, which is the main concern. 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 of the magnetic field in the entire plane can be obtained by substituting the position vector of the point (r, θ) into the central plane magnetic field distribution of the cyclotron accelerator, which is the main concern. z (r,θ);

[0026] Furthermore, the shimming coils are arranged in a staggered manner with peak and valley coil groups, so as to obtain the most flexible adjustment possible under extremely compact conditions; and due to the staggered arrangement, the magnetic field jump at the junction of the shimming coils can be compensated, and at the same time the modulation degree of the accelerator can be improved, thereby improving the axial focusing capability.

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

[0028] Advantages and effects of the present invention

[0029] 1. The present invention is based on the Biot-Savart integration method, multi-objective optimization and linear programming method, avoiding complex finite element calculations and cumbersome step-by-step adjustment processes, and can enable the superconducting cyclotron shim coil system to generate a suitable isochronal field and minimize the use of superconducting wires.

[0030] 2. The present invention establishes a linear relationship between the phase sliding s and the coil padding current w, uses a diagonal matrix method to directly solve the coefficient matrix A, and then directly establishes the linear relationship. The minimum value of the phase sliding is obtained by a linear programming method, without adjusting the current of the padding coil one by one. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 The arrangement form of the shimming coil system of the present invention;

[0032] Figure 2 The integral sliding phase optimization process corresponding to different ampere-turns step lengths of the shimming coil system;

[0033] Figure 3 is the average field distribution of shimming coils at different positions;

[0034] Figure 4 The present invention is a flow chart of a method for adjusting a superconducting cyclotron shimming coil. DETAILED DESCRIPTION

[0035] The present invention is further explained below in conjunction with the accompanying drawings:

[0036] Design principle of the present invention

[0037] The innovation of the present invention is that ① the linear relationship between the sliding phase s and the coil shim current w is established (Formula (1)). ② the basic calculation example is used to directly solve a using the diagonal matrix method. (0)and the matrix of A. ③ On the basis of the basic example, by establishing the linear programming constraint conditions (formula group (2)), the upper limit λ of the integral sliding phase is obtained. ④ In this way, the linear relationship is established only once, and then in this constraint interval, the minimum value of the sliding phase under this constraint condition can be directly obtained. The current combination of the coil is determined by only one adjustment. The key point of "only one adjustment" is to use a linear programming method with constraints instead of adjusting one number at a time. The establishment of constraints is based on the linear equation group formula (1), and solving the unknown number a in formula (1) (0) , Method A is the method of basic example.

[0038] A method for adjusting a superconducting cyclotron shim coil Figure 4 As shown, the method is based on a shimming coil such as Figure 1 As shown, the shimming coils are composed of a group of peak areas and a group of valley areas, which are fixed to the same fixing plate with the magnetic poles by screws. Each group of shimming coils is symmetrically distributed up and down. The magnetic field can be regulated by adjusting the position of the shimming coils and the current size. The shimming coil regulation method includes the following steps:

[0039] Step 1: Set up the basic example;

[0040] Step 2: Establish a linear equation system: Based on the basic example, establish the integral sliding phase linear equation;

[0041] s=a (0) +A·w#(1);

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

[0043] Step 3: Establish linear programming constraints:

[0044]

[0045] Formula group (2) represents the shimming coil current w i The constraints that need to be satisfied are is a constant, is the element in the coefficient matrix A, w i represents the current from the 1st to the i-th shimming coil, I down is the minimum current setting, I upis the maximum current, n is the number of coil groups arranged along the radius of the accelerator, and two coils arranged symmetrically up and down with the accelerator center plane as the boundary are a group of coils; where, and After the design phase is completed, it is a known condition. i ,λ is an unknown condition after the design phase is completed;

[0046] Supplementary Note 1

[0047] The present invention is divided into a design phase and a post-design phase. The unknown quantities in these two phases are different:

[0048] ① Design stage, a in formula (1) (0) and A are unknown. To establish this relationship, we must use the results of the basic example to solve a (0) The matrix A of A. After these two matrices are solved, the constraint relationship can be established. (0) A is equivalent to the formula group (2) and

[0049] ② After the design phase is completed, the formula group (2) and Given the known conditions, the coil current vector w is padded i and the upper limit λ of the phase slip are unknown quantities and can be varied within the linear constraints satisfying the equation group (2). Then, we need to solve the current vector w i Under what value does λ get the minimum value?

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

[0051] ④ The peak area group is Figure 1 There are 4 groups of shimming coils in the upper middle row; one group in the valley area is Figure 1 The three groups of shimming coils in the lower middle row;

[0052] Step 4: solve the upper bound λ of the integral sliding phase;

[0053] Step 5, judging whether λ is less than 20: judging whether the integral sliding phase upper bound λ meets the isochronous acceleration requirement, which means that the integral sliding phase upper bound λ is less than 20 degrees; if not, the current distribution obtained by the solution is used as the basic calculation example, and step 1 is repeated. If the integral sliding phase upper bound λ obtained by iterative calculation meets the requirement, proceed to step 6;

[0054] Step 6, check the magnetic field: record the position distribution and current of the shimming coil generated in step 5, establish a finite element calculation model, and check the results of the integral equation method; if the deviation exceeds the threshold, use the result of the finite element calculation as the basic example, re-iterate the calculation, and finally obtain the shimming coil arrangement scheme that meets the isochronous acceleration requirements; if the deviation is less than the threshold, continue to step 7;

[0055] Step 7: Output the results.

[0056] Supplementary Note 2

[0057] 1) Since step five uses the integral equation method to perform linear extrapolation of the magnetic field, there may be a certain error between it and the finite element method (maybe within 10 Gauss, which is acceptable). Therefore, step six is ​​needed for further verification.

[0058] 2) The above “threshold” refers to the magnetic field error of the integral equation method and the finite element magnetic field calculation. This error is generally within 10 gauss.

[0059] Supplementary Note 3

[0060] 1) If Figure 2 As shown, the horizontal axis is the number of iterations, and the vertical axis is the maximum sliding phase. The three curves in the figure represent different step sizes. It can be seen that the larger the step size, the faster the sliding phase decreases.

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

[0062] Furthermore, the step 1 of setting up the basic example is as follows:

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

[0064] 2) Using the Biot-Savart integration method, calculate the magnetic field distribution ΔB generated by the shimming coils at different positions i (r, θ), and record the excitation current w = (w1, w2...w n ) T ; Subsequently, the results obtained by this example are used to perform linear extrapolation for any current.

[0065] Supplementary Note 4

[0066] 1) In the above basic calculation example, w is the initial value of each group of coils. The integral sliding phase corresponding to this initial value is very large and unacceptable. Therefore, the integral sliding phase should be optimized on this basis;

[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 the differential sliding phase to obtain the integral sliding phase.

[0068] Furthermore, in step 2, based on the basic example, an integral sliding phase linear equation is established. The specific process is as follows: a small current increment Δw=(Δw1, Δw2…Δw n ) T , let the current increments with subscript i be non-zero values, and the current increments of the other subscripts be 0. Substituting into the linear equations of the integral sliding phase, we can get a (0) and A; the Δw is used to solve the matrix A and the constant a0, which are unknown before the linear constraint relationship is established.

[0069] Supplementary Note 5

[0070] 1) The above “let the current increments with subscript i be non-zero values ​​in turn, and the other subscript components be 0” means that the current increment of the current coil is non-zero and the current increments of other coils are zero (the current increment is zero, not the current is zero). For example, in the basic calculation example, each coil has an initial current. In order to calculate A, an increment is added to this current, such as 1000. Then the incremental current of each coil is increased in turn to calculate A.

[0071] 2) For a certain radius, if there are 7 adjustment coils, then the equation has 8 unknowns. So 8 equations are needed to solve these 8 unknowns. So we need to set the current increment to a small value, and add the current increment to 0, so that 8 equations are formed, and 8 equations can solve these 8 unknowns.

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

[0073]

[0074] By discretizing the current vector, the axial component of the magnetic field in the entire plane can be obtained by integrating the position vector of the point (r, θ) in the cyclotron center plane magnetic field distribution of main concern;

[0075] Where B is the magnetic field in the center 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 of the magnetic field in the center plane of the cyclotron accelerator, which is of primary concern, can be obtained by integrating the position vector of the point (r,θ). z (r,θ).

[0076] Furthermore, the shimming coils are arranged in a staggered manner with peak and valley coil groups, so as to obtain the most flexible adjustment possible under extremely compact conditions; and due to the staggered arrangement, the magnetic field jump at the junction of the shimming coils can be compensated, and at the same time the modulation degree of the accelerator can be improved, thereby improving the axial focusing capability.

[0077] Furthermore, each time the coil current distribution is adjusted, the adjustment amount cannot be too large, and the ampere-turn step value can be 2000 or 5000. The optimal solution is obtained through continuous iteration, and the number of iterations is 10 to 15 times.

[0078] Embodiment 1

[0079] A proton superconducting cyclotron is designed. Straight-edge fan poles are used. Four pairs of shimming coils are arranged in the peak area, and three pairs of shimming coils are arranged alternately in the valley area. The position and current of the shimming coils are designed using the Biot-Savart integration method and linear programming method. The magnetic field distribution of the shimming coils in the peak area is obtained by calculation as follows: Figure 3 As shown:

[0080] Based on the calculated distribution of shimming coils, linear extrapolation is performed to establish a linear programming equation, and the simplex method is used to solve the optimal current combination. When the shimming coils are not used, the maximum value of the differential slip of the particles is 1.5%. By reasonably designing the shimming coils, it can be reduced to 1‰, meeting the isochronous acceleration requirements.

[0081] Figure 2 The changes in the upper bounds of the integral sliding phase at different radii of the accelerator after each iteration under different step sizes are shown. It can be seen that the integral sliding phase continues to decrease, thereby automatically completing the adjustment of the shimming coil current.

[0082] This specific embodiment is merely an explanation of the present invention and is not a limitation of the present invention. After reading this specification, those skilled in the art may make non-creative modifications to the present embodiment as needed. However, as long as they are within the scope of the claims of the invention, they are protected by the patent law.

Claims

1. A method for adjusting a superconducting cyclotron shimming coil, the method is based on a shimming coil, the shimming coil is composed of a group of peak areas and a group of valley areas, and is fixed to the same fixing plate with a magnetic pole by screws, each group of shimming coils is symmetrically distributed up and down, and the magnetic field can be adjusted by adjusting the position of the shimming coil and the current size, and the method is characterized in that: The adjustment method of the shimming coil comprises the following steps: Step 1: Set up the basic example; Step 2: Establish a linear equation system: Based on the basic example, establish the integral sliding phase linear equation; s=a (0) +A·w# (1) In formula 1, vector s represents the sliding phase at different radial positions, and vector a (0) is a constant, the matrix A is a coefficient matrix, and the vector w represents the current of different shimming coil groups; where a (0) , A is the result of the basic example and is a known condition; Step 3: Establish linear programming constraints: Formula group (2) represents the shimming coil current w i The constraints that need to be satisfied are is a constant, is the element in the coefficient matrix A, w i represents the current from the 1st to the i-th shimming coil, I down is the minimum current setting, I up is the maximum current; n is the number of coil groups arranged along the radius of the accelerator, and two coils arranged symmetrically up and down with the accelerator center plane as the boundary are a group of coils; where, and After the design phase is completed, it is a known condition. i ,λ is an unknown condition after the design phase is completed; Step 4: solve the upper bound λ of the integral sliding phase; Step 5, judging whether λ is less than 20: judging whether the integral sliding phase upper bound λ meets the isochronous acceleration requirement, which means that the integral sliding phase upper bound λ is less than 20 degrees; if not, the current distribution obtained by the solution is used as the basic calculation example, and step 1 is repeated. If the integral sliding phase upper bound λ obtained by iterative calculation meets the requirement, proceed to step 6; Step 6, check the magnetic field: record the position distribution and current of the shimming coil generated in step 5, establish a finite element calculation model, and check the results of the integral equation method; if the deviation exceeds the threshold, use the result of the finite element calculation as the basic example, re-iterate the calculation, and finally obtain the shimming coil arrangement scheme that meets the isochronous acceleration requirements; if the deviation is less than the threshold, continue to step 7; Step 7: Output the results.

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

3. The method for adjusting a superconducting cyclotron shimming coil according to claim 1, characterized in that: The second step is to establish an integral sliding phase linear equation based on the basic example. The specific method is as follows: superimpose a small current increment Δw=(Δw1, Δw2...Δw n ) T , let the current increment with subscript i be non-zero value, and the current increment with other subscripts be 0. Substitute it into the linear equation system of integral sliding phase and solve it to get a (0) and A; the Δw is used to solve the matrix A and the constant a0, which are unknown before the linear constraint relationship is established.

4. The method for adjusting a superconducting cyclotron shimming coil according to claim 1, characterized in that: Under the condition that the current distribution form of the shimming coil is known, the Biot-Savart integration method is used to quickly calculate the magnetic field distribution form of the shimming coil. The integration formula is as follows: Where B is the magnetic field in the center 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 of the magnetic field in the center plane of the cyclotron accelerator, which is of main concern, can be obtained by integrating the position vector of the point (r, θ): z (r, θ). .

5. The method for adjusting a superconducting cyclotron shimming coil according to claim 1, characterized in that: The shimming coils are arranged in a staggered manner with peak and valley coil groups, so as to obtain the most flexible adjustment possible under extremely compact conditions; and due to the staggered arrangement, the magnetic field jumps at the junctions of the shimming coils can be compensated, and at the same time the modulation degree of the accelerator can be improved, thereby improving the axial focusing capability.

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

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