Beam position detection method of beam position detector

Abstract

The invention discloses a beam position detection method of a beam position detector. The method comprises the following steps: 1) acquiring an electrode signal at each selected test point in a particle accelerator pipeline by using a beam position detector; 2) performing fitting by using the electrode signals of the test points to obtain a relation function between the beam position and the electrode signals and coefficients under different orders n; 3) fitting according to the sum-difference ratio of each test point in the horizontal direction and the vertical direction and the coefficients under different orders n, and selecting the optimal fitting error or the fitting order nopt corresponding to the fitting error meeting the set condition as the order of the relation function; 4) taking a coefficient corresponding to the order nopt as a coefficient of a nopt order relation function to obtain a specific nopt order relation function; and 5) calculating the electrode signal at the to-be-detected point in the particle accelerator pipeline obtained by the beam position detector by using the nopt order relation function to obtain the beam position at the to-be-detected point.

Description

Technical Field

[0001] The invention belongs to the technical field of accelerators and relates to a beam position detection method of a beam position detector. Background Art

[0002] The beam position monitor (BPM) is one of the most important measuring elements in a particle accelerator. Its main function is to detect the position of the beam (including electron beam and particle beam) when it passes through the pipe. Combined with elements that can adjust the movement trajectory of the beam in the pipe, it can achieve precise control of the beam position, so that the beam does not hit the pipe wall and ensure the normal operation of the accelerator.

[0003] Common BPMs are non-interceptive, using a pickup electrode welded on the pipe to detect the beam position. When the beam passes through the BPM, a voltage signal U of a certain amplitude is generated on the electrode. Figure 1 Schematic diagrams of the pickup electrodes required to measure the beam position in one and two directions are shown respectively. The beam position in one direction can be calculated by using the signals U1 and U2 of the two opposite electrodes, while measuring the beam position in two directions generally requires the signals U1, U2, U3, and U4 of four electrodes.

[0004] Assume that the horizontal and vertical positions of the beam when it passes through the BPM are x beam and beam , then the relationship between the beam position and the BPM electrode signal can be expressed as:

[0005] x beam =f1 (U i ), y beam =f2 (U i ). (1)

[0006] Among them U i represents the signal strength on the i-th electrode, and f1 and f2 represent the functional relationship between the beam position and the signal strength, which is determined by the type and specific design of the BPM. In general, it is a complex polynomial. Taking the simplest two-electrode case as an example, assuming that the radius of the beam pipe is R pipe , the distance between the beam and the electrode is d, and the beam is in the central area of ​​the pipe (x beam ,y beam < <R pipe ), the signal on the electrode is inversely proportional to d. The beam position can be obtained by calculating the difference and sum of the signals of the two electrodes, that is, there is:

[0007]

[0008] Beam position x beam It is proportional to the difference and ratio of the two electrode signals. The proportional coefficient k is also called the sensitivity of BPM. Under non-ideal conditions, such as the difference between the two electrodes or the symmetry of the pipeline, a small offset δ will be caused. If we call the position where the two electrode signals are equal U1=U2 as the electrical center and the ideal dot as the mechanical center, then this offset is the offset of the mechanical center relative to the electrical center, and formula (2) becomes formula (3):

[0009]

[0010] For the processed BPM, determining the functional relationship, i.e., f1 and f2 in formula (1), becomes an important task. For the simplest case, formula (3), only when the sensitivity k and offset δ are measured by the calibration system can the correct beam position be calculated.

[0011] For the case where four electrodes measure the beam position in two directions, compared with formula (3), functions f1 and f2 become more complicated. For beams far away from the center of the pipe, the signal and the beam position do not satisfy the strictly proportional relationship, and f1 and f2 become more complicated. However, in general, functions f1 and f2 can be expressed by the following polynomials:

[0012]

[0013] For the case of two electrodes (the voltages of the two electrodes in the horizontal direction are U1 and U2, and the voltages of the two electrodes in the vertical direction are U3 and U4), the difference and ratio between the horizontal and vertical directions are:

[0014]

[0015] For the case of four electrodes, Figure 1 Electrode distribution like in (b):

[0016]

[0017] n is called the function order, and formula (3) is a special case when the order n=1. Figure 1 In (b), the four electrodes are rotated 45° counterclockwise, which is equivalent to the two-electrode case. The horizontal position can be calculated by U1 and U3, and the vertical position can be calculated by U2 and U4.

[0018] The functional relationship between the BPM system signal and the beam position is the basis of its operation. It is determined by the specific design of the BPM system, including the size of the beam pipe, the structure of the pickup electrode, etc. When the measurement accuracy is not high, it can be calculated by simulation software or estimated by analytical formulas. However, the most common method is to build a calibration system to perform actual measurements on the processed BPM detectors, using A i-j,j and B i-j,j The beam position is calculated using the measured value of

[0019] Generally, the calibration system uses an antenna or metal wire passing through the BPM to simulate the beam, changes the position of the antenna in the BPM, and records the signal size of the four electrodes when the antenna (beam) is at different positions. The X in formula (4) can be calculated using the electrode signal and formula (5) or formula (6). raw and Y raw , the grating ruler and other equipment recorded the x in formula (4) beam and beam , and then use the least squares method to calculate the polynomial coefficients A and B.

[0020] Generally, there are two methods to obtain coefficients A and B. One is the experimental measurement method mentioned above, and the other is to use electromagnetic simulation software, such as CST, to simulate the process of repeated experimental measurements. Let us first take the calibration result of an actual processed BPM as an example to illustrate the whole process. As shown in Table 1, it records the U1~U4 of 25 points with an interval of 2mm in a circular BPM with a radius of 11mm in an area of ​​8mm×8mm, and the X calculated using U1~U4. raw and Y raw .

[0021] Table 1 shows the corresponding four electrode signal amplitudes at different positions recorded by the calibration system.

[0022]

[0023]

[0024] Using the data in Table 1, for different orders n, the coefficients AB under different orders are obtained after fitting, and their values ​​are shown in Table 2. For example, when n = 1, according to the coefficients in Table 2, x = 0.0219 + 7.4728 × X raw -0.036×Y raw , the calculation from the four-electrode signal to the horizontal beam position can be completed.

[0025] Table 2 shows the coefficients of the 1st to 4th orders in the x direction obtained using the data in Table 1.

[0026] n＝1 n＝2 n＝3 n＝4 <![CDATA[A 0,0 ]]> 0.0219 0.01591 0.0205 0.0196 <![CDATA[A 1,0 ]]> 7.4728 7.4731 7.8055 7.8056 <![CDATA[A 0,1 ]]> -0.0360 -0.0360 -0.0428 -0.0427 <![CDATA[A 2,0 ]]> / -0.0766 -0.0881 -0.0683 <![CDATA[A 1,1 ]]> / 0.0296 0.0301 0.0392 <![CDATA[A 0,2 ]]> / 0.1191 0.0822 0.0783 <![CDATA[A 3,0 ]]> / / 3.1967 3.1961 <![CDATA[A 2,1 ]]> / / 0.0748 0.0745 <![CDATA[A 1,2 ]]> / / -5.7421 -5.7422 <![CDATA[A 0,3 ]]> / / -0.0086 -0.0091 <![CDATA[A 4,0 ]]> / / / -0.0604 <![CDATA[A 3,1 ]]> / / / -0.0081 <![CDATA[A 2,2 ]]> / / / -0.0205 <![CDATA[A 1,3 ]]> / / / -0.0246 <![CDATA[A 0,4 ]]> / / / 0.0366

[0027] The disadvantages of existing methods for determining the relationship between beam position and signal strength are mainly as follows:

[0028] 1. The experimental method has large uncertainty and poor accuracy in beam position measurement. The beam size of modern accelerators is getting smaller and smaller, and the accuracy requirements for beam position measurement are getting higher and higher. In particular, the size of the fourth synchrotron radiation source has reached the micron level, and the orbital stability requirement is sub-micron, which places extremely high demands on the beam position at the light output point. For a collider, the beam position at the collision point is the most critical factor affecting the brightness, and accurate beam position information is also required. There are a large number of BPMs on the accelerator, and it is generally impossible to calibrate hundreds of BPMs one by one. The general method is to select a small number of representatives of a type of BPM for calibration. The coefficients obtained in this way are not suitable for all BPMs. Even if each BPM can be calibrated, the calibration result is greatly affected by accidental factors of installation.

[0029] 2. Even if the coefficient is obtained through calibration, it is related to the calibration range. For example, for a BPM with a pipe radius of 11 mm, the coefficients obtained by calibration within the range of 8 mm × 8 mm and 10 mm × 10 mm are different, which makes the calibration lose the standard. Moreover, there is also the scanning interval (step length x step / y step ) and other parameters increase the uncertainty.

[0030] 3. During calibration, there is another variable, which is the order of fitting n. In the central area of ​​the pipeline, the difference and ratio are linear with the beam position. In the area far from the center, due to nonlinearity, the error of low-order fitting will become larger. In general, in a larger range, the higher the order, the higher the accuracy. In a smaller range, there is little difference, but the higher the order, the greater the amount of calculation, the more computing resources are required, and the longer the delay.

[0031] 4. The analytical formulas all use the derivatives of the difference and ratio at the center of the beam pipe as the beam position changes to determine the position coefficient k. Even when using the CST calculation method, a similar calculation is performed, i.e., the derivatives of the difference and ratio at the center of the pipe as the beam position changes. This method does not conform well to the actual measured values. Summary of the invention

[0032] In view of the problems existing in the prior art, the purpose of the present invention is to provide a beam position detection method of a beam position detector. The present invention is committed to inventing a set of methods that can establish the relationship between the signal for determining the BPM and the beam position, that is, determine the polynomial coefficients in formula (4). In addition, further improvements are made on the traditional method. The complexity of the function can be adjusted according to the accuracy requirements of the accelerator for beam position measurement, and the contradiction between computing resources and measurement accuracy is taken into account. The method can have a wide and high application value on various accelerators and in different debugging stages.

[0033] The technical solution of the present invention is:

[0034] A beam position detection method of a beam position detector, the steps comprising:

[0035] 1) Using the beam position detector to obtain the electrode signal at each selected test point in the particle accelerator pipeline; wherein the signal obtained by the jth electrode of the beam position detector at each test point is U j , j = 1 to 4; U1 and U2 are the electrode signals of two electrodes facing each other in the horizontal direction at the same test point, and U3 and U4 are the electrode signals of two electrodes facing each other in the vertical direction at the same test point on the accelerator; the actual beam position at the i-th test point is (x i ,y i ), i=1~N point , N point is the total number of test points;

[0036] 2) using the electrode signals of each test point to fit the relationship function between the beam position and the electrode signal, and obtaining the coefficients of the relationship function at different orders n;

[0037] 3) According to the sum and difference ratios of the horizontal and vertical directions of each test point and the coefficients under different orders n, the fitting beam position of each test point of the corresponding order is calculated, and the fitting error under the corresponding order is calculated according to the actual beam position and the fitting beam position of each test point under different orders, and the fitting order n corresponding to the optimal fitting error or the fitting error that meets the set conditions is selected. opt as the order of the relationship function;

[0038] 4) Using the order n opt The corresponding coefficient is n opt The coefficient of the order relationship function is used to obtain the specific n opt Order relation function;

[0039] 5) Using n opt The order relationship function calculates the electrode signal at the point to be measured in the particle accelerator pipeline obtained by the beam position detector to obtain the beam position at the point to be measured.

[0040] Furthermore, a root mean square error is used as the fitting error.

[0041] Furthermore, the width of the particle accelerator pipeline is x range , long range The test points are selected from the area, and the total number of test points Among them, x step is the scanning step length along the width direction of the particle accelerator pipe, y step is the scanning step length along the length of the particle accelerator pipe.

[0042] The advantages of the present invention are as follows:

[0043] The present invention analyzes the parameters that affect the calibration results through measured data, and converges the calibration results by determining the experimental setting parameters, so as to facilitate the unified comparison of BPMs installed on different accelerators and enable the comparison of the simulation calculation method with the experimental method.

[0044] Its advantages are:

[0045] 1. Provide unified standards for the process of experimental calibration coefficients, which can improve calibration accuracy, improve efficiency and reduce accidental errors.

[0046] 2. Different calibration methods can be selected according to different accuracy requirements; different calibration methods can also be used according to different periods of beam adjustment.

[0047] 3. Provide a unique method for situations where you want a larger calibration range, higher calibration accuracy, and at the same time want to save computing resources and reduce latency.

[0048] 4. A method for simulating and calculating the relationship between the signal and the beam position is provided, so that the experimental data can be compared with the calculated data. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is a schematic diagram of the beam position detector calculating the beam position;

[0050] (a) is a diagram of the BPM structure in which two pickup electrodes are used to measure the beam position in one direction; (b) is a diagram of the BPM structure in which four pickup electrodes are used to measure the beam position in two directions.

[0051] Figure 2 It is the fitting effect diagram when the order n is 1-6;

[0052] (a) The fitting effect diagram of 4mm×4mm with a step size of 2mm and an order n of 1-6.

[0053] (b) The fitting effect diagram of 12mm×12mm with a step size of 0.25mm and an order n of 1-6.

[0054] Figure 3 The distribution diagram of fitting error when n takes different values;

[0055] (a) is the fitting error distribution diagram when n=1, (b) is the fitting error distribution diagram when n=3, and (c) is the fitting error distribution diagram when n=5.

[0056] Figure 4 It is the fitting error when n=1-6.

[0057] Figure 5 It is the fitting error diagram in different scanning ranges;

[0058] (a) Variation of errors of different orders with scanning range, (b) Variation of total number of points with scanning range.

[0059] Figure 6 Fitting error diagram for different orders of changing scanning step size;

[0060] (a) is the fitting error and the number of fitting points when n=1, and (b) is the fitting error at different orders.

[0061] Figure 7 The present invention is a flow chart of the method.

[0062] Figure 8 For the first type of BPM n=1-8, the simplified front and back fitting errors;

[0063] (a) is the horizontal direction and (b) is the vertical direction.

[0064] Fig. 9 For the first BPM n=1, 3, 5, 7 (x fit -x fit simplify ,y fit -y fit simplify ) of the dot matrix, where N point =2401.

[0065] Fig.10 For the second BPM n=1-8, the simplified front and back fitting errors;

[0066] (a) Horizontal direction (b) Vertical direction.

[0067] Fig.11 For the third BPM n=1, 3, 5, 7 (x fit simplify -x fit ,y fitsimplify -y fit ) of the dot matrix, where N point =1089.

[0068] Fig.12 For the third type of BPM n=1-8, the simplified front and back fitting errors;

[0069] (a) Horizontal direction, (b) vertical direction.

[0070] Fig.13 For the third BPM n=1, 3, 5, 7 (x fit simplify -x fit ,y fit simplify -y fit ) of the dot matrix, where N point =5329. DETAILED DESCRIPTION

[0071] The present invention is further described in detail below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention but not to limit the scope of the present invention.

[0072] 1.1. Basic Methods

[0073] In order to determine the coefficients, as mentioned before, it is necessary to use a certain range of signals (U1~U4) and beam positions (x beam ,y beam ), use the signal (U1~U4) to calculate the difference and ratio X in the two directions raw and Y raw , where X raw is the horizontal difference and ratio, Y raw is the vertical difference and ratio; then the coefficients are fitted using the least squares method, which are the values ​​in Table 2. Different orders n give different coefficients. The beam position can be calculated using the difference and ratio and the coefficient using formula (4). The beam positions calculated using different orders n and coefficients are as follows: Figure 2 (a). Table 1 and Figure 2 The number of points used for calculation in (2) is only 25. In actual practice, the number of points and the range used will be larger. Figure 2 (b) shows the fitting effect in the range of 12mm×12mm with a step size of 0.25mm. In order to evaluate the fitting situation, the fitting error is generally defined as:

[0074]

[0075] Where (x i ,y i ) represents the beam position at the i-th point, The beam position at the i-th point calculated by fitting functions f1 and f2 is shown in the following figure. The typical distribution within the range of 12 mm × 12 mm is as follows: Figure 3 As shown, the differences between the results of n=2 and n=1, the results of n=4 and n=3, and the results of n=6 and n=5 are very small. When n=1, the maximum error is as high as 1mm, and when n=5, the maximum value does not exceed 100μm.

[0076] from Figure 3 It can be seen that the position errors calculated by different orders are different. The higher the order, the smaller the error and the smaller the value of the Z axis. In order to measure the fitting effect, a fitting root mean square (root-mean-square RMS) error is introduced:

[0077]

[0078] Where N point is the total number of points recorded by the scan, x fit is the position calculated by using the coefficients and differences and ratios according to formula (4), x is the actual position, and the errors when n = 1 to 6 are as follows: Figure 4 shown.

[0079] 1.2. Parameters related to results

[0080] 1.1 above describes the method of determining the coefficients through experiments. The following discusses the parameters that affect the results one by one.

[0081] 1.2.1. Scanning range

[0082] According to the previous description, the difference between the horizontal and vertical results of the circular pipe is very small. In addition, the difference between the fitting results of two adjacent odd and even orders is also negligible. For a circular pipe with a radius of 11 mm, when the interval is fixed at 0.25 mm, the fitting errors in different scanning ranges are as follows: Figure 5 shown.

[0083] In this patent, the calibration range is generally a square, that is, x range =y range Under this condition, the total number of points within the scanning range satisfies:

[0084]

[0085] like Figure 5 As shown, the higher the fitting order, the smaller the fitting error, but there must be enough fitting points. Figure 5 In, that is, N point When it is greater than 81, the error is mainly affected by the fitting order rather than accidental error.

[0086] 1.2.2. Scanning step length

[0087] If the scanning range is kept as a square with a side length of 12 mm, that is, x range =6mm unchanged, changing the scanning step size, the fitting errors of different orders are as follows Figure 6 As shown, it can be seen that no matter what the order is, the error becomes smaller as the step size becomes smaller and the number of points increases, but once the number of points exceeds a certain number, such as Figure 6 The error changes are very small.

[0088] Based on the above analysis, we conclude that it is necessary to ensure that there are enough points when fitting, that is, to reduce accidental errors. In addition, in order to ensure sufficient fitting accuracy, especially when the beam changes in a large range, high-order coefficients are needed to calculate the beam position.

[0089] 1.2.3. High-level computing

[0090] As mentioned before, compared with the linear calculation method, i.e., coefficients with n=1, higher-order coefficients have higher accuracy and smaller fitting errors, but the amount of calculation will also increase. Specifically, for the order n, the number of coefficients in the horizontal and vertical directions is N. coefficient With n satisfying:

[0091]

[0092] Columns 1-3 in Table 3 list the order n, the number of coefficients in the horizontal / vertical direction, and the complete calculation formula. Figure 3 It can be seen that for the calculation of the second order, although there are 6 coefficients to be calculated, the fitting error is the same as that for the calculation of the 3 coefficients of the first order, that is, the effect is the same as when n=1. For n=4, the calculation effect of 15 coefficients is equal to 10 coefficients, and the same is true for n=6 and n=8. In addition, it can be seen from Table 2 that the absolute values ​​of most coefficients are much less than 1. Using the same rule, we can further simplify the formulas. The number of simplified coefficients N simplify The formula is shown in Table 3, which can greatly simplify the calculation and save resources.

[0093] Table 3 shows the beam position calculation formula before and after optimization. For convenience, U is used instead of X. raw , V replaces Y raw

[0094]

[0095] By observing, we can conclude that when calculating the horizontal / vertical position, only the X raw / Y rawThe odd-order terms of the beam position contribute to its position calculation. We analyze the data within the range of ±6mm and the spacing of 0.25mm. The difference between the beam position calculated by the simplified formula and the beam position before simplification is within 10 -5 mm, while X of 1, 3, 5 and 7 orders error The difference between -9 mm, 1.6×10 -7 mm,6.7×10 -7 mm, 1.4×10 -6 mm. For extreme cases, such as the above ±4 mm range, the data with a spacing of 2 mm is analyzed, and the difference between the positions is on the order of 0.01 mm. error The difference between them is 1.0×10 -3 mm, 3.5×10 -3 mm,3.6×10 -3 mm, 3.6×10 -3 mm, it can be seen that the influence of the simplified formula on the position calculation is almost negligible.

[0096] 1.3. Basic process

[0097] In order to obtain the beam position through different types of beam position detectors, the specific process is as follows Figure 7 As shown, the steps include:

[0098] Step 1: Determine the possible position range of the beam in the detector. If the beam position of the accelerator varies greatly at different times, several different ranges can be determined and the position calculation algorithm can be determined one by one. In special cases, such as when the beam in the injection area or the extraction area passes through the beam position detector, it is eccentric and not in the center of the pipeline. The algorithm (the polynomial coefficients mentioned later) is for a specific range.

[0099] Step 2: Through experiments or theoretical calculations, obtain the different beam positions (x i ,y i ) The signal strength U of all electrodes of the beam position detector j , where i = 1 to N point , N point is the total number of test points, j is 1 to 4; N point The typical value is selected between 100 and 10000.

[0100] Step 3: Through U j The sum and difference ratio X of the horizontal direction of the i-th test point is obtained by using formula (5) or formula (6): raw The difference and ratio Y between i and the vertical directionraw i, where i=1~N point .

[0101] Step 4: Use the beam position (x i ,y i ) and the corresponding sum-difference ratio (X raw i,Y raw i), combined with formula (4) to fit the relationship between the beam position and the electrode signal, the function f1 and f2, can also be obtained at different orders n coefficient A p-q,q and B p-q,q .

[0102] Step 5: According to the sum and difference ratio (X raw i,Y raw i) and coefficient A p-q,q and B p-q,q The beam fitting position of the i-th test point can be calculated Then the fitting error is obtained, and the appropriate fitting order n is selected according to the fitting error. opt If the calculated error does not meet the position calculation requirements, try increasing Npoint and n to repeat steps 2 to 5.

[0103] Step 6: If there are enough resources to perform the n-order position calculation in step 5, directly use the coefficients of the corresponding order to perform the position calculation. If there are not enough resources or the time overhead is not enough, try to use the simplified n-order formula in Table 3 to perform the position calculation and obtain the simplified formula At the same time, check whether the simplified error meets the requirements. If it does, the simplified formula and corresponding coefficients can be used to calculate the position.

[0104] 1.4. Specific application of the present invention in engineering

[0105] The present invention is to calculate the beam position using the signal of the beam position detector. Taking a typical calibration system as an example, the motion platform moves with the antenna simulating the beam, with a repeatability of 1μm and a minimum step of 0.5μm, and can achieve two-dimensional motion in the lateral x and y directions. We calibrated three different BPMs of the high-energy light source HEPS, and the radius of the button electrode was 4mm. The first BPM pipe is circular with a radius of 11mm; the second BPM pipe is elliptical, with horizontal and vertical radii of 18mm and 15mm respectively; the third BPM pipe is elliptical, with horizontal and vertical radii of 18mm and 26mm respectively.

[0106] The first BPM calibration results with a step size of 0.25 mm in a range of 12×12 mm are as follows: Figure 8As shown, the fitting errors of the first order without simplification and after simplification are 544μm and 546μm respectively, 73μm and 87μm respectively for the third order, 25μm and 54μm respectively for the fifth order, and 16μm and 50μm respectively for the seventh order. fit and fit The value of changes in the order of 10μm. For 1, 3, 5 and 7 orders (x fit simplify -x fit ,y fit simplify -y fit )Draw a picture like Fig. 9 shown.

[0107] The second BPM calibration effect with a step size of 0.5mm in the range of 16×16mm is as follows Fig.10 and Fig.11 The third BPM calibration effect with a step size of 0.25mm in the range of 18×18mm is shown in Fig.12 and Fig.13 As shown, it can be seen from these results that the simplified formula has little effect on the error of beam position calculation.

[0108] The simplified 1st, 3rd, 5th and 7th order calculation formulas in the present invention reduce the amount of calculation by 66%, 70%, 71% and 72% respectively compared with the complete 1st, 3rd, 5th and 7th order formulas.

[0109] The simplified calculation formula in the present invention can reduce the error caused by accidental factors in the experimental calibration process. For the simplified polynomial coefficients, since their own values ​​are small, they are greatly affected by the BPM installation accuracy, etc., while the remaining polynomial coefficients after simplification have larger values ​​themselves and are less affected by the installation.

[0110] The invention has a wide application range and can be applied to the beam position calculation of different beam detectors of various accelerators.

[0111] Although the specific embodiments of the present invention are disclosed for the purpose of illustration, the purpose is to help understand the content of the present invention and implement it accordingly, those skilled in the art will understand that various substitutions, changes and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the present invention should not be limited to the content disclosed in the best embodiment, and the scope of the present invention is subject to the scope defined in the claims.

Claims

1. A beam position detection method of a beam position detector, the steps comprising: 1) Using the beam position detector to obtain the electrode signal at each selected test point in the particle accelerator pipeline; wherein the signal obtained by the jth electrode of the beam position detector at each test point is U j , j = 1 to 4; U1 and U2 are the electrode signals of two electrodes facing each other in the horizontal direction at the same test point, and U3 and U4 are the electrode signals of two electrodes facing each other in the vertical direction at the same test point on the accelerator; the actual beam position at the i-th test point is (x i ,y i ), i=1~N point , N point is the total number of test points; 2) using the electrode signals of each test point to fit the relationship function between the beam position and the electrode signal, and obtaining the coefficients of the relationship function at different orders n; 3) According to the sum and difference ratios of the horizontal and vertical directions of each test point and the coefficients under different orders n, the fitting beam position of each test point of the corresponding order is calculated, and the fitting error under the corresponding order is calculated according to the actual beam position and the fitting beam position of each test point under different orders, and the fitting order n corresponding to the optimal fitting error or the fitting error that meets the set conditions is selected. opt as the order of the relationship function; 4) Using the order n opt The corresponding coefficient is n opt The coefficient of the order relationship function is used to obtain the specific n opt Order relation function; 5) Using n opt The order relationship function calculates the electrode signal at the point to be measured in the particle accelerator pipeline obtained by the beam position detector to obtain the beam position at the point to be measured.

2. The method according to claim 1, characterized in that The root mean square error is used as the fitting error.

3. The method according to claim 1, characterized in that Width x on particle accelerator pipe range , long range The test points are selected from the area, and the total number of test points Among them, x step is the scanning step length along the width direction of the particle accelerator pipe, y step is the scanning step length along the length of the particle accelerator pipe.

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