JPH05326197A - Method of arranging magnet - Google Patents

Abstract

PURPOSE:To determine an optimum magnet arrangement in a practical time by operating the magnet strength in a determined position on the basis of the mutual relation between a magnet in this position and a magnet within a determined distance around it by means of simulated annealing method. CONSTITUTION:A magnet position can be realized, for example, by an arithmetic device A. In the arithmetic device A, a central arithmetic processing unit 2 operates it by the use of simulated annealing method on the basis of the data inputted by an input device 1. In the operation by the device 2, a setting circuit 3 automatically or manually sets the magnet number around to consider the effect to a magnetic field calculated position. According to the magnet number set by the circuit 3, the device 2 conducts the operation. A memory circuit 4 stores the operating condition and result. A comparing circuit 5 compares the condition in the previous operation stored in the circuit 4 with the condition in the following operation, and when the conditions are coincident to each other, the previous operation result is applied to the following operation. An output device 6 outputs the operation result by the device 2.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a magnet arrangement method,
More specifically, the present invention relates to a method for arranging magnets used for an undulator of a synchrotron radiation device.

[0002]

2. Description of the Related Art A synchrotron radiation device used in almost all fields of basic science in recent years emits light by changing the moving direction of electrons by its powerful magnet (undulator magnet). FIG. 5 is a flowchart showing an arrangement procedure in an example of a conventional magnet arrangement method,
FIG. 6 is a flowchart showing a transition candidate creation algorithm, FIG. 7 is a schematic diagram showing an arrangement example of undulator magnets,
FIG. 8 is a schematic diagram showing a seat for a magnet, and FIG. 9 is an explanatory diagram showing the relationship between the magnet and the spatial position. As shown in FIG. 7, the undulator magnet has permanent magnets arranged in two rows in parallel. However, the magnetic force of each magnet is not uniform in size and direction as shown by the arrow in the figure, and there are variations in each. In order to exert the performance of the undulator magnet, the magnetic field at the positions P1 to P (2 * L) +1 between the magnets in FIG. It is necessary to arrange the magnets optimally. Conventionally, a method has been used in which the magnetic field of the undulator magnet is actually measured manually and the magnets are rearranged by trial and error. However, this method requires time and effort for rearranging, and trial and error until the optimum arrangement is not possible. Therefore, a method is possible in which the optimal placement is obtained in advance by a computer and the actual magnets are arranged based on this result. As one of such optimization methods, there is known a magnet arrangement optimization method by a simulated annealing method Simulated Annealing Algorithum (hereinafter abbreviated as SA) that imitates the principle of metal annealing. Hereinafter, an example in which the conventional magnet arrangement method by SA is applied to the arrangement of undulator magnets will be described in order of steps S1, S2, ... With reference to FIG. 5, FIG. 6, FIG. 8 and FIG.
As shown in FIG. 5, in the conventional SA, the initial temperature T ₀ is first set (S1). The initial temperature T ₀ is an initial value of the temperature T, which is a kind of parameter for performing the convergence calculation by SA, and is a value sufficient to cause a change in the arrangement of magnets (magnet array) depending on the metal to be annealed. And need to. Next, consider a magnet seat as shown in FIG. Randomly select one each from the left, right, up and down directions, and end magnets for this seat, and pack from the top of the seat. By doing this, one magnet array xx (magnet array) can be formed. A so-called transition candidate xx ', which is a new array, is randomly selected and generated from the neighborhood Sxx of the array xx (an array group in which only one magnet is different from the array xx) (S2). The algorithm for creating the transition candidate xx 'is to randomly replace two magnets as shown in FIG. 6 (S10 to S1).
5). Here, for example, in the case of an undulator magnet, the magnets forming each magnet row include the following three types of magnets. (1) Terminal magnets (4) (2) Horizontal magnets (4 x number of cycles) (3) Vertical magnets (4 x number of cycles-2) In addition, one cycle consists of 4 upper and 4 lower, total 8 Composed of magnets. When the relationship between the magnet j and the position Pi in the space is expressed as shown in FIG. 9, the magnetic force My in the vertical direction and the magnetic force M in the horizontal direction of the magnet j are shown.
Magnetic field (magnetic field strength) B created by x at position Pi in the r and θ directions
r and Bθ are represented by the following equations. Br (My) = (My / 4π) × (2cos θy / r ³ ) ... (1a) Br (Mx) = (Mx / 4π) × (2cos θx / r ³ ) ... (1b) Bθ (My) = (My / 4π) × (2sin θy / r ³ ) ... (1c) Bθ (Mx) = (Mx / 4π) × (2cos θx / r ³ ) ... (1d) Further, the X component of the magnetic field by all the magnets at the position Pi,
The Y component is represented by the following formula.

[Equation 1] The magnetic field is calculated by the above equations (1a) to (1d) and equations (2a) to (2d) (S3). Next, the desired magnetic field is defined, for example, as a magnetic field that minimizes the following evaluation function E, and the evaluation function before and after the transition, which is a change of magnet between the array xx and the transition candidate xx ′, is performed. The change Δ of E is calculated (S4).

[Equation 2] Based on the change Δ of the evaluation function, it is determined whether the transition candidate xx ′ is accepted or rejected (S5). Such transition is repeated until the equilibrium condition at the temperature T is achieved (S6). When the equilibrium condition is achieved (until the end condition is satisfied (S7)), the temperature T is updated (S8),
Repeat steps S2 to S8. In this way, when the temperature T is gradually lowered and the termination condition is satisfied, the evaluation function E is minimized and the optimum magnet arrangement is obtained. As the initial temperature T ₀ setting method, the equilibrium condition determination condition at each temperature, the temperature T update method, and the termination condition determination condition, for example, an annealing schedule such as Kirkpatrick, Huang is used.

[0003]

In the magnet placement method by the conventional simulated annealing method as described above, in the magnet placement problem of the undulator, since the number of repeated calculations for obtaining the optimum placement is enormous, the calculation is performed. It was not practical in terms of time. SUMMARY OF THE INVENTION It is an object of the present invention to improve a magnet placement method and to provide a magnet placement method capable of obtaining an optimum magnet placement in a practical time in order to solve the problems in the conventional art. It is a thing.

[0004]

In order to achieve the above object, the present invention calculates the magnetic field strength at a predetermined position by rearranging the arrangement of the magnets when deciding the arrangement of a plurality of magnets forming a magnet array. Then, at least in each of the above recombination, an evaluation function for evaluating the magnetic field strength is obtained from the magnetic field strength, and in the magnet arrangement method for determining the optimum arrangement of the magnets from the evaluation function by using a simulated annealing method, It is configured as a magnet arrangement method characterized in that the magnetic field strength at a predetermined position is calculated based on the mutual relationship between the magnet at that position and the magnets within a predetermined distance around it. When determining the arrangement of a plurality of magnets forming the magnet array, the arrangement of the magnets is rearranged to calculate the magnetic field strength at a predetermined position, and at least an evaluation function for evaluating the magnetic field strength is calculated for each rearrangement. Obtained from the above magnetic field strength,
In the magnet arrangement method for determining the optimum arrangement of the magnets from the above evaluation function by using the simulated annealing method, if the mutual relationship between the magnets is equal between one magnet position and another magnet position, the above is present. It is a magnet arranging method characterized in that the calculation of the magnetic field strength for the magnet at the position is applied to the magnet at the other position. Furthermore, when determining the arrangement of a plurality of magnets forming the magnet array, the arrangement of the magnets is rearranged to calculate the magnetic field strength at a predetermined position, and an evaluation function for evaluating the magnetic field strength at least for each rearrangement is calculated. In the magnet placement method for determining the optimum placement of the magnets from the evaluation function by using the simulated annealing method, the magnetic field strength at the predetermined position is set to the magnet at the predetermined position and a predetermined distance around the magnet. If the mutual relationship between magnets is the same between one magnet position and another magnet position, the calculation of the magnetic field strength for the magnet at the above-mentioned position is performed as described above. It is a magnet arranging method characterized in that the magnet at the position is used.

[0005]

According to the present invention, the arrangement of a plurality of magnets forming a magnet array is rearranged to calculate the magnetic field strength at a predetermined position, and an evaluation function for evaluating the magnetic field strength is calculated at least for each rearrangement. When determining the optimum arrangement of the magnets from the above-mentioned evaluation function using the simulated annealing method, the magnetic field strength at the predetermined position is limited to the magnet at that position and the magnets within a predetermined distance around the position. It is calculated based on the mutual relationship of. Further, when the mutual relationship between the magnets is equal between a certain magnet position and another magnet position, the calculation of the magnetic field strength for the magnet at the certain position is applied to the magnet at the other position. As a result, the calculation time is greatly reduced, and the optimum magnet arrangement can be obtained in a practical time.

[0006]

Embodiments of the present invention will be described below with reference to the accompanying drawings for the understanding of the present invention. The following embodiments are examples of embodying the present invention and are not of the nature to limit the technical scope of the present invention. Here, FIG. 1 is a flowchart showing an arrangement procedure by a magnet arrangement method according to an embodiment of the present invention, FIG. 2 is a block diagram showing a schematic configuration of an arithmetic unit A for realizing the magnet arrangement method, and FIG. FIG. 4 is a table showing a calculation result by the device A, and FIG. 4 is a graph showing a calculation result by the device A. Further, the same reference numerals are used for the elements common to the flowchart showing the arrangement procedure in the example of the conventional magnet arrangement method shown in FIG. The magnet arranging method according to the present invention is basically optimal by performing a so-called transition in which a simulated annealing method (hereinafter abbreviated as SA) is used to rearrange the arrangement of magnets (magnet row) in the metal to be annealed. It is the same as the conventional example in that the arrangement is obtained. However, the conventional example has a magnetic field strength at a predetermined position (hereinafter abbreviated as magnetic field).
Is calculated under the influence of all the magnets, the present invention limits the magnetic field at a predetermined position to the influence of the magnets within a predetermined distance around the magnetic field and calculates the previous calculation. This is different from the conventional example in that the result is used for the next calculation result. In the present embodiment, parts different from the conventional example will be mainly described, and the same parts as the conventional example are as described above, and thus detailed description thereof will be omitted. An arrangement procedure by the magnet arrangement method according to this embodiment will be described below in the order of steps S1, S2, ... With reference to FIG. As shown in FIG. 1, in the present embodiment, the initial temperature T ₀ is first set in the same procedure as the conventional example (S1), one magnet array xx is generated, and transition candidates are randomly selected from the vicinity Sxx. x
x'is selected and generated (S2). Next, we calculate the magnetic field, and pay attention to the following two points. That is, when the transition candidate xx ′ is generated as shown in FIG. 6, only two magnets are replaced at most in the previous magnet arrangement xx and the next transition candidate xx ′. That is, it is understood that the magnetic fields Br and Bθ do not have to be calculated each time, only the exchanged magnets and the positions affected by them are calculated, and the other calculation results can be used. In this case, the calculation amount is theoretically reduced to (2 × number of magnets) / (number of positions × number of magnets). That is, 1 / in cycle 5
6, it becomes 1/21 in 20 cycles. From the equations (1a) to (1d), the magnet j shown in FIG.
The magnetic fields Br and Bθ at the position Pi of the
Since it is proportional to the third power of the distance r between i, it is possible to ignore the influence of magnets that are far apart. In other words, the magnetic field calculation for a certain position does not calculate for all the magnets, and even if the calculation is performed only for the N magnets around the affected area, the calculation result hardly changes. As a result, the calculation amount is reduced to (N × number of positions) / (number of magnets × number of positions). For example, if N = 18, 3 / with a cycle of 5 compared to the conventional example.
7, with a period of 20 becomes 10/81. On the other hand, the calculation amount for the evaluation function calculation in the conventional example that does not use these methods is the number of magnets × the number of positions (proportional to the number of magnets), and increases with the square of the number of magnets. On the other hand, in the above-described calculation method, the calculation amount increases only at most in proportion to the number of magnets, which is particularly advantageous when the number of magnets is large. The data shown below is 1000 in cycle 5.
A comparison of the time for calculating the time evaluation function using a computer with about 5 Mips shows that the theoretical calculation amount decreases (1
/ 6 × 3/7 = 1/14). Calculation of evaluation function according to conventional example: A = 22 minutes 40 seconds (13
60 seconds) Calculation of evaluation function by the above: B = 1 minute 38 seconds (
(98 seconds) A / B = 13.5 Therefore, when calculating the magnetic field, only the influence of N magnets is calculated around the magnetic field calculation position (S3a). The number of magnets N is set automatically based on the magnetic force of each magnet or manually. If the mutual relationship between the magnets is the same between one magnet position and another magnet position among these calculation results, the magnetic field calculation result for the magnet at a certain magnet position is used for the magnet at another position. That is, the mutual relationship between the magnets and the calculation result are stored, and if there is the same mutual relationship at the time of the next calculation, the previous calculation result is used (S3).
b). Next, the change Δ of the evaluation function is calculated (S4), the acceptance judgment (S5), the equilibrium condition judgment (S6), the end condition judgment (S7), and the temperature update (S) in the same procedure as the conventional example.
8) is sequentially performed, and steps S2 to S8 are repeated. In this way, when the temperature T is gradually lowered and the termination condition is satisfied, the evaluation function E is minimized and the optimum magnet arrangement is obtained.

This magnet arranging method can be realized by an arithmetic unit A as shown in FIG. 2, for example. The arithmetic unit A is an input device 1 for inputting data such as the magnitude and direction of the magnetic force of each magnet, and SA based on the data input by the input device 1.
And a setting circuit 3 for automatically or manually setting the number of magnets around which the influence on the magnetic field calculation position should be taken into consideration in the calculation by the central processing unit 2; The central processing unit 2 calculates the number of magnets set by the circuit 3, and stores a calculation condition and a result of the calculation, and a storage circuit 4 stores a previous calculation condition stored in the storage circuit 4 at the time of the next calculation. If the conditions are compared with each other and the conditions are matched, the comparison circuit 5 that uses the previous calculation result for the next calculation and the output device 6 for outputting the calculation result by the central processing unit 2 are included. The results calculated by this device A are shown in FIGS. That is, as shown in FIG. 3, an improvement rate of 34% was obtained for the entire evaluation function. At this time, C8 was 28% and C9 was 70%. FIG. 4 shows the transition of the evaluation function. According to the present embodiment, the number of repetitions until the end of calculation is 222,653, and the calculation time by the central processing unit 2 (75Mips) is about 1 hour and 37 minutes, both of which are in the practical range. As mentioned above,
According to the present embodiment, the calculation time can be significantly shortened as compared with the conventional example, so that the optimum magnet arrangement can be obtained in a practical time. As a result, the optimum design of the undulator magnet and the like can be performed in a short time, and the performance of the synchrotron radiation device using the undulator magnet and the like can be improved. In the arithmetic unit A of the above embodiment, the setting circuit 3, the memory circuit 4, and the comparison circuit 5 are provided independently of the central arithmetic processing unit 2, but in actual use, each circuit 3, 4, 5 is used. There is no problem even if a part or all of the above is included in the central processing unit 2. In the above embodiment, the undulator magnets of the synchrotron device are arranged. However, in actual use, the magnets may be applied to other magnet arrangements (eg, wiggler magnet arrangements) without any problem.

[0008]

Since the magnet arrangement method according to the present invention is configured as described above, the calculation time is greatly shortened as compared with the conventional example, and the optimum magnet arrangement can be obtained in a practical time. it can. As a result, the optimum design of the undulator magnet and the like can be performed in a short time, and the performance of the synchrotron radiation device using the undulator magnet and the like can be improved.

[Brief description of drawings]

FIG. 1 is a flowchart showing an arrangement procedure by a magnet arrangement method according to an embodiment of the present invention.

FIG. 2 is a block diagram showing a schematic configuration of an arithmetic unit A for realizing a magnet arrangement method.

FIG. 3 is a list showing calculation results by the calculation device A.

FIG. 4 is a graph showing a calculation result by the calculation device A.

FIG. 5 is a flowchart showing an arrangement procedure in an example of a conventional magnet arrangement method.

FIG. 6 is a flowchart showing a transition candidate creation algorithm.

FIG. 7 is a schematic diagram showing an arrangement example of undulator magnets.

FIG. 8 is a schematic diagram showing a seat for a magnet.

FIG. 9 is an explanatory diagram showing a relationship between a magnet and a spatial position.

[Explanation of symbols]

 A ... Arithmetic device 1 ... Input device 2 ... Central arithmetic processing unit 3 ... Setting circuit 4 ... Memory circuit 5 ... Comparison circuit 6 ... Output device

 ─────────────────────────────────────────────────── ─── Continued Front Page (72) Inventor Osamu Morioka 1-3-18 Wakihamacho, Chuo-ku, Kobe City Kobe Steel, Ltd. Kobe Head Office

Claims (3)

[Claims] 1. When determining the arrangement of a plurality of magnets constituting a magnet row, the arrangement of the magnets is rearranged to calculate the magnetic field strength at a predetermined position, and the magnetic field strength is evaluated at least for each rearrangement. In a magnet placement method in which an evaluation function is obtained from the magnetic field strength and the optimum placement of the magnets is determined from the evaluation function using a simulated annealing method, the magnetic field strength at the predetermined position is determined by measuring the magnetic field strength at the predetermined position and the magnet around the position. A magnet arranging method, wherein calculation is performed based on a mutual relationship with a magnet within a predetermined distance. 2. When determining the arrangement of a plurality of magnets forming a magnet row, the arrangement of the magnets is rearranged to calculate the magnetic field strength at a predetermined position, and the magnetic field strength is evaluated at least for each rearrangement. In a magnet placement method in which an evaluation function is obtained from the magnetic field strength and the optimum placement of the magnets is determined from the above evaluation function by using a simulated annealing method, the mutual interaction between magnets between a magnet position and another magnet position is determined. If the relations are equal, the method of arranging magnets is characterized in that the calculation of the magnetic field strength of the magnet at the certain position is applied to the magnet at the other position. 3. When determining the arrangement of a plurality of magnets constituting a magnet array, the arrangement of the magnets is rearranged to calculate the magnetic field strength at a predetermined position, and the magnetic field strength is evaluated at least for each rearrangement. In a magnet placement method in which an evaluation function is obtained from the magnetic field strength and the optimum placement of the magnets is determined from the evaluation function using a simulated annealing method, the magnetic field strength at the predetermined position is determined by measuring the magnetic field strength at the predetermined position and the magnet around the position. Calculation is performed based on the mutual relationship with the magnets within a predetermined distance, and when the mutual relationship between the magnets is equal between one magnet position and another magnet position, the calculation of the magnetic field strength for the magnet at the certain position is performed. A method for arranging magnets, wherein the magnets at different positions are used.