Method for carrying out magnetic field shimming on full-superconducting cyclotron based on target first harmonic

Abstract

The invention discloses a method for carrying out full-superconducting cyclotron magnetic field shimming based on target first harmonics. Comprising the following steps: determining distribution requirements of target first harmonics; determining a superconducting coil group for generating a target first harmonic; forming the superconducting coil group by a group of coils; the positions and the number of radial measuring points and the total harmonic component number n are determined, and based on Fourier analysis, a first harmonic shimming matrix A based on the unit current adjusting quantity, the total harmonic component n and the total adjusting scheme number m is established; based on Fourier analysis, establishing a target first harmonic amplitude matrix B based on the total harmonic component n; a shimming equation B = AX is listed, X is solved, and X is a matrix of superposition coefficients of the adjustment scheme; according to the invention, magnetic field shimming is carried out by taking one coil group as a unit, and primary harmonics formed by one coil group can better express the distribution shape of the magnetic field, so that a conventional panel shimming method can be better replaced.

Description

Technical Field

[0001] The invention belongs to the technical field of accelerators, and in particular relates to a method for shimming a magnetic field of a full superconducting cyclotron accelerator based on a target first harmonic. Background Art

[0002] An important goal of the development of cyclotron technology is the miniaturization and lightweight of the accelerator. The use of all-superconducting technology has further reduced the weight of the accelerator. Lightweight, coil-based magnetic field regulation methods are important requirements for magnetic field regulation of all-superconducting accelerators. All-superconducting accelerators adopt an iron-coreless design, so it is more convenient to use a coil-based magnetic field regulation method. At present, traditional accelerators with iron cores generally use additional installation devices to control the generation of primary harmonics. Due to the limitations of their coil structure, there is no way to generate primary harmonics only by controlling the current of the existing coils in the structure. Therefore, based on the structural characteristics of all-superconducting accelerators with multiple adjustment coils, a method of generating primary harmonics by adjusting coils has great value in the application of all-superconducting accelerators.

[0003] At present, the first harmonic is generally generated in a non-fully superconducting accelerator (with an iron core) by using a shim strip method. The shim strip needs to be additionally installed on the main magnet of the accelerator, and the shape of the shim strip is adjusted to generate the first harmonic.

[0004] Although non-fully superconducting accelerators can achieve the generation of first harmonics, they are not suitable for the structural characteristics of fully superconducting accelerators. Fully superconducting cyclotron accelerators use coils instead of iron cores. Figure 1a As shown, the coils already occupy a lot of space in the all-superconducting cyclotron, and it is impossible to add additional shims on both sides of each core like in a cyclotron with an iron core.

[0005] The prior art generally adopts a regulation method based on a single coil as a unit for magnetic field shimming of a fully superconducting accelerator. However, a single coil cannot constitute a complete first harmonic, and thus cannot be used to accurately shim the magnetic field of the target first harmonic. Summary of the invention

[0006] In order to solve the problems existing in the prior art, the present invention proposes a method for shimming the magnetic field of a full superconducting cyclotron accelerator based on a target first harmonic, with the purpose of solving the problem that conventional methods for shimming the magnetic field of a full superconducting accelerator generally adopt an adjustment method based on a single coil as a unit. Since a single coil cannot constitute a complete first harmonic, it cannot be used to accurately describe the change of the magnetic field and solve the problem of shimming the target first harmonic magnetic field.

[0007] The present invention adopts the following technical solutions to solve the technical problems:

[0008] A method for shimming a magnetic field of a fully superconducting cyclotron based on a target first harmonic;

[0009] Its features are:

[0010] Step 1: determine the distribution requirements of the target first harmonic, where the target first harmonic is the target first harmonic that uses a superconducting coil for magnetic field shimming; the superconducting coil is multiple and is arranged along the radial and angular directions of the full superconducting cyclotron;

[0011] Step 2: Determine a superconducting coil group for generating a target first harmonic: a group of coils with the same radial direction and different angular directions in a full superconducting cyclotron accelerator are formed into a superconducting coil group;

[0012] Step 3, obtaining the adjustment scheme of each superconducting coil group and the total number of adjustment schemes m: the adjustment scheme is determined as an adjustment scheme based on the different peak positions of the harmonics of the coil group; assuming that a coil group has 3 coils, any one of the 3 coils is the peak position of the first harmonic, each coil group can generate 3 different adjustment schemes; the total number of adjustment schemes m = the number of coil groups × 3;

[0013] Step 4: Determine the position, number and total harmonic component number n of the radial measurement points. Assume that the number of radial measurement points is k, and each radial measurement point has two harmonic components, sin and cos, so n = 2k;

[0014] Step 5: Based on Fourier analysis, a padding matrix A of the first harmonic based on the unit current regulation amount, the total harmonic component n and the total number of regulation schemes m is established;

[0015] Step 6: Based on Fourier analysis, establish a target first harmonic amplitude matrix B based on the total harmonic component n;

[0016] Step 7: List the padding equation B=AX and solve X, where X is the matrix of the superposition coefficient of the regulation scheme; wherein the element is Xi, Xi corresponds to the superposition coefficient of the current regulation amount in the i-th regulation scheme, and the superposition coefficient is equivalent to regulating several unit currents.

[0017] Further, assuming that a coil group has three coils, each adjustment scheme corresponds to three unit current adjustment amounts I1, I2, and I3, with the unit being ampere (A); I1, I2, and I3 are determined in advance.

[0018] Furthermore, the unit current is adjusted to 1000 ampere turns for each coil, that is, for a coil with x turns, the current adjustment amount is 1000 / x.

[0019] Furthermore, the step 5 is based on Fourier analysis to establish a padding matrix A of the first harmonic based on the unit current regulation amount, the total harmonic component n and the total number of regulation schemes m. The specific process is as follows:

[0020] A. Establish the padding matrix A based on the first harmonic of the unit current

[0021]

[0022] Where n represents the cosine and sin components of the first harmonic at k radial measurement points, and m represents the number of coil adjustment schemes;

[0023] B. Obtain the current adjustment value of each coil group [I1, I2, I3]

[0024] Adjustment Assume that the superposition coefficient of the adjustment scheme corresponding to the i-th coil group is Xi, which is equivalent to adjusting several unit currents. These coefficients can be written as an m-dimensional vector X, written as:

[0025]

[0026] It corresponds to the superposition coefficient of each adjustment scheme of each group of coils in the total adjustment scheme; assuming that the coefficients with subscripts X1, X2, and X3 in formula (2) all correspond to the first group of coils, the total current adjustment amount can be expressed as:

[0027] [I1 I2 I3]=X1[I 11 I 12 I 13 ]+X2[I 21 I 22 I 23 ]+X3[I 31 I 32 I 33 ]#(3)

[0028] [I1, I2, I3] on the left side of the equal sign represents the total current that needs to be adjusted for the three coils in the same group of coils;

[0029] Furthermore, the step six is ​​based on Fourier analysis to establish a target first harmonic amplitude matrix B based on the total harmonic component n, and the specific process is as follows:

[0030] 1) Determine the amplitudes of the two components of the target first harmonic B r,cos ,B r,sin , where r is the corresponding radius measurement point, 1 and 2 are two harmonic components, and the difference can be written as an n-dimensional vector B, whose unit is T.

[0031] 2) The component matrix of the target first harmonic is:

[0032]

[0033] Furthermore, the step 7 lists the shimming equation B=AX and solves X. The specific process is as follows:

[0034] 1) List the shimming equation:

[0035] B=AX#(5)

[0036] 2) Use the solution of the shimming equation to solve the coefficient vector X:

[0037] X=(A T A) -1 A T B#(6)

[0038] Formula (6) is the matrix shift of formula (5). The left side of formula (6) represents the X to be solved, and the right side of the equal sign of formula (6), A T represents the transpose of the A matrix, A T A represents the product of the transpose of matrix A and matrix A. T A) -1 Representative seeking A T The inverse of the A matrix, B represents the component matrix of the target first harmonic, and the product of the matrices on the right (A T A) -1 A T B can calculate X.

[0039] Furthermore, because the number of radial measurement points k can be any value, and the number of adjustment schemes is m, if the number of elements n in B (n = 2k) is equal to the number of elements in X, formula (6) can obtain a unique solution; if the number of elements n in B is less than the number of elements in X, formula (6) is an overdetermined system of equations, which can be solved by the least squares method; if the number of elements n in B is greater than the number of elements in X, formula (6) is an underdetermined system of equations, which has infinite solutions, but can still be solved by mathematical means to obtain a unique closest solution.

[0040] Advantages and effects of the present invention

[0041] 1. The present invention performs magnetic field shimming with a coil group as a unit, rather than performing magnetic field shimming with a single coil as a unit. A group of coils can form a primary harmonic. Since the primary harmonic formed by a group of coils can better express the distribution shape of the magnetic field, it can better replace the conventional strip shimming method.

[0042] 2. No need to install additional equipment: The existing methods of generating primary harmonics often require the installation of additional equipment, which requires additional labor and equipment costs. The present invention utilizes the design and structural advantages of the all-superconducting accelerator, only adjusts the existing coil current, and uses a program to calculate the adjustment amount, without the need to install additional equipment, thus saving the use cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1a This is the layout diagram of the magnetic field coil of the all-superconducting cyclotron;

[0044] Figure 1b Schematic diagram of the present invention using superconducting coils to perform magnetic field shimming;

[0045] Figure 1c A schematic diagram of magnetic field shimming on both sides of the main magnetic pole using conventional methods;

[0046] Figure 2 A schematic diagram of the magnetic field distribution of a group of coils of the present invention;

[0047] Figure 3 A schematic diagram of radial distribution of the first harmonic generated by the unit current change of the peak coil group used in the present invention;

[0048] Figure 4 A schematic diagram of radial distribution of the first harmonic generated by the unit current change of the valley coil group used in the present invention;

[0049] Figure 5 A schematic diagram of the present invention using a group of coils to adjust the primary harmonic;

[0050] Figure 6 This is a schematic diagram of the circular magnetic field expressed by the first harmonic of the present invention;

[0051] Figure 7 The present invention is a flow chart of a method for performing magnetic field shimming of a full superconducting cyclotron based on a target first harmonic. DETAILED DESCRIPTION

[0052] Design principle of the present invention

[0053] 1. Difficulties in the design of the present invention: One of the difficulties is that the space of the all-superconducting cyclotron is tight. Figure 1a As shown in the figure, there is no iron core, so it is impossible to pad the magnetic field by adding additional padding strips around the iron core like in traditional accelerators. Figure 1c As shown in the figure, the iron core is the main magnetic pole, which has two layers, upper and lower, with four main magnetic pole iron cores in each layer. The magnetic field shimming method is to add shimming strips around each main magnetic pole. The full superconducting cyclotron uses coils instead of iron cores, such as Figure 1aAs shown, the coils have already taken up a lot of space in the all-superconducting cyclotron, and it is impossible to add additional padding strips on both sides of each iron core like the iron core accelerator; Conclusion: The traditional accelerator uses the method of padding, which allows a lot of freedom in design, so it can easily generate the target magnetic field. The shape and position of the existing coils of the all-superconducting accelerator are determined during the physical design of the accelerator, and the only space that can be freely adjusted is the ampere-turns, so it is difficult to adjust the magnetic field by the ampere-turns. The second difficulty is that it is difficult to use a superconducting coil to express the shape of the magnetic field and then pad the magnetic field. As Figure 1b As shown in FIG. 1 , conventional methods all use an independent coil adjustment method, that is, each coil is used as a unit to form a magnetic field adjustment scheme for a full superconducting cyclotron. However, each coil can only express the distribution of half of the magnetic field of the circular coil but cannot express the distribution of the entire magnetic field of the circular coil. Figure 5 As shown, when only one coil is used to adjust the magnetic field, one coil can only adjust the peak value of the sine curve or the positive half cycle of the sine curve, while the negative half cycle is 0. In this way, the circular magnetic field can only be expressed half. Therefore, the difficulty lies in that using one coil to fill the magnetic field is not accurate enough.

[0054] 2. Innovation of the present invention: The innovation lies in using a group of coils (a group of coils with the same radius) to shim the magnetic field, rather than using a single coil as a unit to shim the magnetic field (the conventional method uses a single coil as a unit to shim the magnetic field, rather than using a coil group as a unit to shim the magnetic field). A group of coils can better express the distribution shape of the first harmonic than a single coil, and can also replace the conventional strip shim method. The details are as follows:

[0055] First, the present invention uses a group of coils (3 coils) to perform magnetic field padding as shown in the following formula (3). Although there are three adjustment schemes on the right side of the equal sign, these three adjustment schemes are three adjustment schemes formed when the peak values ​​of a group of coils are located at different coils. However, three adjustment schemes and one scheme using three coils for adjustment are two different concepts. Three schemes do not mean that each scheme uses only one coil, but that each scheme uses three coils.

[0056] [I1 I2 I3]=X1[I 11 I 12 I 13 ]+X2[I 21 I 22 I 23 ]+X3[I 31 I 32 I 33 ]#(3) Second, the principle of using three coils to fill the magnetic field is as follows Figure 5As shown, ① the first coil is used to adjust the curve of the upper half of the sine curve, and the last two coils form the curve of the negative half. Although the more coils there are, the smoother the sine curve will be, the original intention of the present invention is not to add additional coils. ② The relationship between the magnetic field and the first harmonic (sine curve) is as follows Figure 2 , Figure 6 As shown, the direction of the magnetic field is a clockwise circular curve, with the upper half from left to right and the lower half from right to left. The upper half is equivalent to the upper half of the sine curve, and the lower half is equivalent to the lower half of the sine curve. Since three coils (discrete mode) can basically express a sine curve, and one coil can only express the upper half of the sine curve, it is more accurate to use three coils to fill the first harmonic than to use one coil to fill the first harmonic.

[0057] Based on the above principle, the present invention designs a method for shimming the magnetic field of a full superconducting cyclotron based on the target first harmonic, such as Figure 7 As shown;

[0058] Its features are:

[0059] Step 1: determine the distribution requirements of the target first harmonic, where the target first harmonic is the target first harmonic that uses a superconducting coil for magnetic field shimming; the superconducting coil is multiple and is arranged along the radial and angular directions of the full superconducting cyclotron;

[0060] Supplementary Note 1:

[0061] like Figure 1a , 1b As shown, the coil to be adjusted in the present invention refers to the shimming coil. The superconducting coil includes the outermost annular coil, 3 or 4 magnetic pole coils in the annular coil, and shimming coils in the 3 or 4 magnetic pole coils. The shimming coils are divided into the inner and outer parts of the magnetic pole. There are 4 shimming coils in the magnetic pole and 3 shimming coils outside the magnetic pole. The 3 shimming coils outside the magnetic pole and the 4 shimming coils in the magnetic pole are not on the same radius. According to the radius, there are 7 shimming coils in the radial direction. Since there are 3 magnetic pole coils in this embodiment, there are 21 shimming coils available for adjustment in this embodiment.

[0062] Step 2: Determine a superconducting coil group for generating a target first harmonic: a group of coils with the same radial direction and different angular directions in a full superconducting cyclotron accelerator are formed into a superconducting coil group;

[0063] Supplementary Note 2:

[0064] like Figure 1bAs shown, the invention is creative in that the magnetic field is compensated by a coil group. The coil group is a group of coils with the same radius, and there are 7 groups in total. Because the three coils in the coil group can form a first harmonic, and the error of a single coil in expressing the first harmonic is large, although it is a discrete expression, if it is adjusted in units of a single coil, the magnetic field error will increase.

[0065] Step 3, obtaining the adjustment scheme of each superconducting coil group and the total number of adjustment schemes m: the adjustment scheme is determined as an adjustment scheme based on the different peak positions of the harmonics of the coil group; assuming that a coil group has 3 coils, any one of the 3 coils is the peak position of the first harmonic, each coil group can generate 3 different adjustment schemes; the total number of adjustment schemes m = the number of coil groups × 3;

[0066] Supplementary Note 3:

[0067] One adjustment scheme of the present invention does not mean that only one coil is used for adjustment, but one adjustment scheme uses three coils for adjustment. A group of coils has three adjustment schemes, which means that the positions of the peaks are different, but each scheme is inseparable from the other two coils besides the peak coil.

[0068] Step 4: Determine the position, number and total harmonic component number n of the radial measurement points. Assume that the number of radial measurement points is k, and each radial measurement point has two harmonic components, sin and cos, so n = 2k;

[0069] Supplementary Note 4:

[0070] A. The position of the radial measurement point can be arbitrary and does not represent the position of the coil.

[0071] B. Use two harmonic components, sin and cos, to represent the position of the magnetic field, just like using X and Y to represent the position of a point on a plane coordinate system.

[0072] Step 5: Based on Fourier analysis, a padding matrix A of the first harmonic based on the unit current regulation amount, the total harmonic component n and the total number of regulation schemes m is established;

[0073] The specific process is as follows:

[0074] A. Establish the padding matrix A based on the first harmonic of the unit current

[0075]

[0076] Where n represents the cosine and sin components of the first harmonic at k radial measurement points, and m represents the number of coil adjustment schemes;

[0077] Supplementary Note 5:

[0078] Figure 3 The peak value of the first harmonic generated by the peak coil group is distributed radially; Figure 4 The peak value of the first harmonic generated by the valley coil group is distributed radially; there are three coils in the valley, so there are three curves; these two figures describe the distribution of the peak value of the first harmonic generated by the coil group in the radial direction, and intuitively show part of the content in the matrix A. Because A describes the distribution of the first harmonic generated by a regulation scheme.

[0079] B. Obtain the current adjustment value of each coil group [I1, I2, I3]

[0080] Assume that a coil group has three coils, and each adjustment scheme corresponds to three unit current adjustment quantities I1, I2, and I3, in ampere (A); I1, I2, and I3 are determined in advance.

[0081] The unit current is adjusted to 1000 ampere turns for each coil, that is, for a coil with x turns, the current adjustment amount is 1000 / x.

[0082] Adjustment: Let the superposition coefficient of the adjustment scheme corresponding to the i-th coil group be X i ,X i Equivalent to adjusting several unit currents, these coefficients can be written as an m-dimensional vector X, written as:

[0083]

[0084] It corresponds to the superposition coefficient of each adjustment scheme of each group of coils in the total adjustment scheme; assuming that the coefficients with subscripts X1, X2, and X3 in formula (2) all correspond to the first group of coils, the total current adjustment amount can be expressed as:

[0085] [I1 I2 I3]=X1[I 11 I 12 I 13 ]+X2[I 21 I 22 I 23 ]+X3[I 31 I 32 I 33 ]#(3)

[0086] [I1, I2, I3] on the left side of the equal sign represents the total current that needs to be adjusted for the three coils in the same group of coils;

[0087] Supplementary Note 6:

[0088] A. X1, X2, and X3 in formula (3) are unknown numbers, not known numbers;

[0089] B. I1, I2, and I3 in formula (3) are known numbers;

[0090] Step 6: Based on Fourier analysis, establish a target first harmonic amplitude matrix B based on the total harmonic component n;

[0091] The specific process is as follows:

[0092] 1) Determine the amplitudes of the two components of the target first harmonic B r,cos ,B r,sin , where r is the corresponding radius measurement point, 1 and 2 are two harmonic components, and the difference can be written as an n-dimensional vector B, whose unit is T.

[0093] 2) The component matrix of the target first harmonic is:

[0094]

[0095] Supplementary Note 7:

[0096] A. In formula (6), B is the amplitude of the target first harmonic, that is, the amplitude of the target magnetic field shimming to be achieved, which is a known number;

[0097] B. n=2k, k is a radial measurement point, and each radial measurement point has two amplitudes, the amplitude of sin and con.

[0098] Step 7: List the padding equation B=AX and solve X, where X is the matrix of the superposition coefficient of the regulation scheme; wherein the element is Xi, Xi corresponds to the superposition coefficient of the current regulation amount in the i-th regulation scheme, and the superposition coefficient is equivalent to regulating several unit currents.

[0099] The specific process is as follows:

[0100] 1) List the shimming equation:

[0101] B=AX#(5)

[0102] 2) Use the solution of the shimming equation to solve the coefficient vector X:

[0103] X=(A T A) -1 A T B#(6)

[0104] Formula (6) is the matrix shift of formula (5). The left side of formula (6) represents the X to be solved, and the right side of the equal sign of formula (6), A T represents the transpose of the A matrix, A T A represents the product of the transpose of matrix A and matrix A. T A) -1 Representative seeking A T The inverse of the A matrix, B represents the component matrix of the target first harmonic, and the product of the matrices on the right (A TA) -1 A T B can calculate X.

[0105] Because the number of radial measurement points k can be any value, and the number of adjustment schemes is m, if the number of elements n in B (n = 2k) is equal to the number of elements in X, formula (6) can obtain a unique solution; if the number of elements n in B is less than the number of elements in X, formula (6) is an overdetermined system of equations and can be solved by the least squares method; if the number of elements n in B is greater than the number of elements in X, formula (6) is an underdetermined system of equations and has infinite solutions, but the only closest solution can still be solved by mathematical means.

[0106] It should be emphasized that the above specific embodiments are merely explanations of the present invention, and they are not limitations of the present invention. After reading this specification, those skilled in the art can make modifications to the above embodiments without any creative contribution as needed, but as long as they are within the scope of the claims of the present invention, they are protected by patent law.

Claims

1. A method for shimming the magnetic field of a fully superconducting cyclotron based on a target first harmonic; Features: Step 1: determine the distribution requirements of the target first harmonic, where the target first harmonic is the target first harmonic that uses a superconducting coil for magnetic field shimming; the superconducting coil is multiple and is arranged along the radial and angular directions of the full superconducting cyclotron; Step 2: Determine a superconducting coil group for generating a target first harmonic: a group of coils with the same radial direction and different angular directions in a full superconducting cyclotron accelerator are formed into a superconducting coil group; Step 3, obtaining the adjustment scheme of each superconducting coil group and the total number of adjustment schemes m: the adjustment scheme is determined as an adjustment scheme based on the different peak positions of the harmonics of the coil group; assuming that a coil group has 3 coils, any one of the 3 coils is the peak position of the first harmonic, each coil group can generate 3 different adjustment schemes; the total number of adjustment schemes m = the number of coil groups × 3; Step 4: Determine the position, number and total harmonic component number n of the radial measurement points. Assume that the number of radial measurement points is k, and each radial measurement point has two harmonic components, sin and cos, so n = 2k; Step 5: Based on Fourier analysis, a padding matrix A of the first harmonic based on the unit current regulation amount, the total harmonic component n and the total number of regulation schemes m is established; Step 6: Based on Fourier analysis, establish a target first harmonic amplitude matrix B based on the total harmonic component n; Step 7: List the padding equation B=AX and solve X, where X is the matrix of the superposition coefficient of the regulation scheme; wherein the element is Xi, Xi corresponds to the superposition coefficient of the current regulation amount in the i-th regulation scheme, and the superposition coefficient is equivalent to regulating several unit currents.

2. The method for shimming a full superconducting cyclotron magnetic field based on a target first harmonic according to claim 1, characterized in that: Assume that a coil group has three coils, and each adjustment scheme corresponds to three unit current adjustment quantities I1, I2, and I3, in ampere (A); I1, I2, and I3 are determined in advance.

3. According to the method for shimming the magnetic field of a fully superconducting cyclotron accelerator based on the target first harmonic in claim 2, the unit current is adjusted by 1000 ampere-turns for each coil, that is, for a coil with x turns, the current adjustment amount is 1000 / x.

4. The method for performing magnetic field shimming using superconducting coils in a fully superconducting cyclotron according to claim 1, characterized in that: The step 5 is based on Fourier analysis to establish a padding matrix A of the first harmonic based on the unit current regulation amount, the total harmonic component n and the total number of regulation schemes m. The specific process is as follows: A. Establish the padding matrix A based on the first harmonic of the unit current Where n represents the cosine and sin components of the first harmonic at k radial measurement points, and m represents the number of coil adjustment schemes; B. Obtain the current adjustment value of each coil group [I1, I2, I3] Adjustment Assume that the superposition coefficient of the adjustment scheme corresponding to the i-th coil group is Xi, which is equivalent to adjusting several unit currents. These coefficients can be written as an m-dimensional vector X, written as: It corresponds to the superposition coefficient of each adjustment scheme of each group of coils in the total adjustment scheme; assuming that the coefficients with subscripts X1, X2, and X3 in formula (2) all correspond to the first group of coils, the total current adjustment amount can be expressed as: [I1 I2 I3]=X1[I 11 I 12 I 13 ]+X2[I 21 I 22 I 23 ]+X3[I 31 I 32 I 33 ]#(3) [I1, I2, I3] on the left side of the equal sign represents the total current that needs to be adjusted for the three coils in the same group of coils.

5. The method for shimming a magnetic field of a full superconducting cyclotron based on a target first harmonic according to claim 1, characterized in that: The step six is ​​based on Fourier analysis to establish a target first harmonic amplitude matrix B based on the total harmonic component n. The specific process is as follows: 1) Determine the amplitudes of the two components of the target first harmonic B r，cos , B r，sin , where r is the corresponding radius measurement point, 1 and 2 are two harmonic components, and the difference can be written as an n-dimensional vector B, whose unit is T. 2) The component matrix of the target first harmonic is:

6. The method for performing magnetic field shimming of a full superconducting cyclotron based on a target first harmonic according to claim 1, characterized in that: The step 7 lists the shimming equation B=AX and solves X. The specific process is as follows: 1) List the shimming equation: B=AX#(5) 2) Use the solution of the shimming equation to solve the coefficient vector X: X=(A T A) -1 A T B#(6) Formula (6) is the matrix shift of formula (5). The left side of formula (6) represents the X to be solved, and the right side of the equal sign of formula (6) is A T represents the transpose of the A matrix, A T A represents the product of the transpose of matrix A and matrix A. T A) -1 Representative seeking A T The inverse of the A matrix, B represents the component matrix of the target first harmonic, and the product of the matrices on the right (A T A) -1 A T B can calculate X.

7. The method for shimming a magnetic field of a full superconducting cyclotron based on a target first harmonic according to claim 6, characterized in that: Because the number of radial measurement points k can be any value, and the number of adjustment schemes is m, if the number of elements n in B (n = 2k) is equal to the number of elements in X, formula (6) can obtain a unique solution; if the number of elements n in B is less than the number of elements in X, formula (6) is an overdetermined system of equations and can be solved by the least squares method; if the number of elements n in B is greater than the number of elements in X, formula (6) is an underdetermined system of equations and has infinite solutions, but the only closest solution can still be solved by mathematical means.

Images