A tokamak divertor configuration X point identification method
By identifying the X-point of the tokamak divertor configuration through plasma balance calculations and clustering methods, the problem of requiring large-area searches in existing technologies is solved, enabling automated and rapid identification of X-point and O-point coordinates and reducing device dependence.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HEFEI INSTITUTE OF PHYSICAL SCIENCE CHINESE ACADEMY OF SCIENCES
- Filing Date
- 2023-11-22
- Publication Date
- 2026-07-21
AI Technical Summary
Existing technologies require specifying a large area to search for the X point based on the configuration characteristics of the tokamak divertor and the device parameters, resulting in high device dependence. Furthermore, the snowflake or X divertor configuration requires additional specification of the search range inside and outside the vacuum chamber, and there is a lack of a unified automated identification method.
Based on the plasma equilibrium calculation results, clustering methods in unsupervised learning are used to directly identify the X-point coordinates of the tokamak divertor configuration, and gradient expansion techniques are combined to determine the point where the poloidal magnetic field is 0, thus avoiding the need to specify the search area.
It enables automatic and rapid identification of all possible X and O coordinates in a tokamak device without relying on device parameters to set the search area, thus improving identification efficiency and accuracy.
Smart Images
Figure CN117807387B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of plasma control technology, specifically relating to a method for identifying the X-point configuration of a tokamak divertor. Background Technology
[0002] The plasma boundary of a tokamak divertor configuration is defined by the separation surface. The separation surface typically has one or two points where the poloidal magnetic field is zero, known as X-points. Configurations with one X-point above and one below the separation surface are called double-null (DN) configurations; those with only one X-point are called single-null (SN) configurations. In SN configurations, if the X-point is located in the lower divertor region, it is called a lower single-null (LSN) configuration; similarly, if the X-point is located in the upper divertor region, it is called an upper single-null (USN) configuration. Furthermore, in advanced divertor configurations, X-points can also form in the external plasma region in addition to those on the plasma separation surface, such as snowflake divertor configurations and X-divertor configurations. In existing technologies, it is usually necessary to specify one or more large regions based on the characteristics of the divertor configuration and device parameters to search for and identify potential X-points. Within these designated areas, the initial identification point is first found by identifying the point of minimum poloidal magnetic field. Then, the local minimum magnetic field point is obtained near this initial point by using gradient expansion techniques, thus providing the coordinates of point X.
[0003] Existing technologies require specifying one or more large search areas based on the divertor configuration and device parameters (especially the vacuum chamber space range) to find the point where the poloidal magnetic field is zero, i.e., the X point. Furthermore, for snowflake divertors or X-divertor configurations, in addition to the X points existing on the separation surface, configurations where the X point exists inside or outside the vacuum chamber require specifying corresponding search ranges. Different devices require separate settings and adaptations, resulting in significant device dependence. Summary of the Invention
[0004] The purpose of this invention is to provide a method for identifying X-points in the configuration of a tokamak divertor. This method eliminates the need to specify the search area for X-points and instead directly identifies all possible X-point coordinates at once using clustering methods commonly used in unsupervised learning, based on plasma equilibrium calculation results. It can also simultaneously provide the coordinates of the magnetic axis (usually referred to as the O point) where the poloidal magnetic field at the plasma center is zero.
[0005] To achieve the above objectives, this invention proposes a method for identifying the X-point configuration of a tokamak divertor, comprising the following steps:
[0006] S1. First, input the plasma equilibrium calculation results and extract the calculation grid and magnetic flux distribution information on the grid points;
[0007] S2. Calculate the poloidal magnetic field value at the grid points based on the grid information and magnetic flux distribution information in S1;
[0008] S3. Extract grid point information for the first 30-200 minimum magnetic field values based on grid thickness;
[0009] S4. Based on the grid point information of the minimum value in S3, a clustering algorithm is used to divide a specified number of identification regions containing X points.
[0010] S5. Within each of the identification regions defined in S4, find the point where the poloidal magnetic field is 0 using gradient unfolding technology;
[0011] S6. Determine whether the magnetic fields identified within each divided region satisfy the condition that the poloidal magnetic field is 0 (B P →0) condition;
[0012] S7. Based on the judgment result of S6, determine the points (X point or O point) that meet the conditions and whose poloidal magnetic field is 0; if the conditions are not met, they are misjudged points and should be discarded.
[0013] Optionally, the plasma balance calculation results input in S1 specifically include the calculation grid (r,z) and the magnetic flux value ψ(r,z) on the grid points.
[0014] Optionally, the calculation of the grid and the magnetic flux distribution information on the grid points in S1 specifically includes:
[0015] In the plasma equilibrium results, the horizontal grid point coordinate vector rg and the vertical grid point coordinate vector zg are calculated from the grid point information. The magnetic flux distribution in the plasma equilibrium results is usually stored in the two-dimensional array (matrix) variable psirz. After the plasma equilibrium results are input, the three variables, namely the horizontal grid point coordinate vector rg, the vertical grid point coordinate vector zg, and the two-dimensional array (matrix) variable psirz, are directly extracted.
[0016] Optionally, the specific calculation method for the poloidal magnetic field value at the grid points in S2 is as follows:
[0017] After extracting the computational grid coordinates (r, z) and the magnetic flux value ψ(r, z) at the grid points, the horizontal field B at the computational grid points is calculated according to the following formula. r and vertical field B z ;
[0018]
[0019] Based on this, the poloidal magnetic field can be calculated.
[0020] Optionally, S3 specifically involves extracting the grid points with the minimum poloidal magnetic field values from the first 30 to 200 grid points after calculating the poloidal magnetic field values based on the observed plasma configuration.
[0021] Optionally, step S4 specifically includes the following steps:
[0022] S41. Specify the number of clusters K to be divided;
[0023] S42. Randomly initialize K centroids, calculate the distance from the remaining points to the K points, and assign the points to the nearest cluster;
[0024] S43. Calculate the mean of each cluster point and update the mean of each cluster to the new centroid;
[0025] S44. Repeat S42 and S43 until the mean of each cluster no longer changes;
[0026] S45. Output the centroid of each cluster.
[0027] Optionally, step S5 specifically includes the following steps:
[0028] S51. Calculate the grid points of the specified search area and the horizontal field B on the grid points. r Vertical field B z and the polar field B p And the gradient value of the magnetic field;
[0029] S52. Find the grid point with the smallest poloidal magnetic field;
[0030] S53. The horizontal and vertical distances from the point 0 to the point of expansion of the poloidal magnetic field can be calculated using Taylor series expansion.
[0031] S54. Calculate the horizontal and vertical coordinates of the point where the poloidal magnetic field is zero.
[0032] Optionally, the judgment condition in S6 is:
[0033] If there is no polar magnetic field point 0 inside the cluster division region, it is necessary to examine whether the square of the magnetic field gradient angle is close to 1 to confirm whether there is an X point inside the cluster division region.
[0034] Compared with the prior art, the beneficial effects of the present invention are:
[0035] This invention eliminates the need to specify the X-point search region. Instead, it directly uses the plasma equilibrium calculation results and clustering methods commonly used in unsupervised learning to identify and provide the coordinates of all possible X-points at once. It can also simultaneously provide the coordinates of the magnetic axis (usually called the O point) where the poloidal magnetic field at the plasma center is zero. Attached Figure Description
[0036] Figure 1 This is a flowchart of the adaptive X-point recognition method in this invention.
[0037] Figure 2A and Figure 2B These are schematic diagrams of two typical EAST plasma balance calculation grids.
[0038] Figure 3A These are the flux line distribution diagrams and figures for a typical plasma equilibrium result on the EAST tokamak device. Figure 3B This is an isoflux distribution diagram of a typical plasma equilibrium result on the EAST tokamak device.
[0039] Figure 4 This is a typical poloidal magnetic field distribution diagram of EAST plasma equilibrium (a typical distribution diagram of isopolar magnetic field lines of plasma equilibrium results on an EAST tokamak device).
[0040] Figure 5 This is a schematic diagram showing the coordinate distribution of the first 100 minimum poloidal magnetic field points derived from the poloidal magnetic field distribution of a typical configuration of EAST in this invention. The blue lines represent the plasma equilibrium calculation grid, and the red dots are the coordinates of the first 100 minimum poloidal magnetic field points.
[0041] Figure 6 for Figure 5 The diagram shows the distribution of four clusters obtained by selecting 100 points with minimum poloidal magnetic fields under a typical configuration of EAST. These are the identification regions for four possible points with a poloidal magnetic field of 0.
[0042] Figure 7 The diagram shows the correct point where the poloidal magnetic field is zero, determined by whether the condition of zero poloidal magnetic field is met.
[0043] Figure 8 This is a schematic diagram showing the identification results of all points where the poloidal magnetic field is 0 in the EAST dual-zero divertor configuration.
[0044] Figure 9 A schematic diagram showing the identification results of all points where the poloidal magnetic field is 0 for the single-zero divertor configuration of EAST.
[0045] Figure 10 This is a schematic diagram showing the identification results of all poloidal magnetic fields being zero in the configuration of the EAST quasi-snowflake divertor. Detailed Implementation
[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0047] Please see Figure 1 A method for identifying the X-point configuration of a tokamak divertor includes the following steps:
[0048] S1. First, input the plasma equilibrium calculation results and extract the calculation grid and magnetic flux distribution information on the grid points;
[0049] Please see Figure 2A , Figure 2B , Figure 3A as well as Figure 3B The input plasma equilibrium results typically include the computational grid (r,z) and the magnetic flux values ψ(r,z) at its grid points. Based on the plasma equilibrium results, the computational grid and magnetic flux information can be extracted. For example... Figure 2A , Figure 2B The diagram shows two typical EAST plasma balance calculation grids. Figure 2A , Figure 2B The schematic diagram shows a 17×17 grid, but in actual calculations, different grid distributions such as 65×65, 129×129, or 257×257 can be used. The subdivision range is usually determined based on the configuration under study, such as... Figure 2A The defined ranges are: R: 0.5m~2.9m; Z: -2m~1.2m. Figure 2B The division range is: R: 1.2m~2.6m; Z: -1.2m~1.2m. Figure 3A The rectangle formed by the thick black lines represents the grid boundary for plasma equilibrium calculations. Based on the isomagnetic flux distribution map, it can be observed manually that there may be as many as five X points within this plasma equilibrium calculation grid region. Figure 3B The rectangle formed by the thick black lines represents the grid boundary for plasma equilibrium calculation. Based on the isomagnetic flux distribution map, it can be observed manually that there may be one point X within this plasma equilibrium calculation grid region.
[0050] In the plasma equilibrium results, the horizontal grid point coordinate vector rg and the vertical grid point coordinate vector zg are calculated from the grid point information. The magnetic flux distribution in the plasma equilibrium results is usually stored in the two-dimensional array (matrix) variable psirz. After the plasma equilibrium results are input, the three variables, namely the horizontal grid point coordinate vector rg, the vertical grid point coordinate vector zg, and the two-dimensional array (matrix) variable psirz, are directly extracted.
[0051] S2. Calculate the poloidal magnetic field value at the grid points based on the grid information and magnetic flux distribution information in S1;
[0052] Please see Figure 4 After extracting the computational grid coordinates (r,z) and the magnetic flux value ψ(r,z) at the grid points, the horizontal field B at the computational grid points is calculated according to the following formula. r and vertical field B z ;
[0053]
[0054] Based on this, the poloidal magnetic field can be calculated. The numbers marked on the isotropic magnetic field lines represent the magnetic field values of those lines, measured in Tesla. Based on the distribution of the isotropic magnetic field, it can be observed that there are two possible points with a poloidal magnetic field zero within the plasma equilibrium calculation grid (indicated by the dashed arrows): point X is located near the bottom of the grid, and point O is located in the center.
[0055] S3. Extract the grid point information of the first 30 to 200 minimum magnetic field values based on the grid size (e.g., 65×65, 129×129 and 257×257);
[0056] Please see Figure 5 Based on the observed plasma configuration, after calculating the poloidal magnetic field values of the grid points, the grid points with the minimum poloidal magnetic field values from the first 30 to 200 are extracted.
[0057] S4. Based on the grid point information of the minimum value in S3, a clustering algorithm is used to divide a specified number of identification regions containing X points.
[0058] Please see Figure 6 The algorithm uses a clustering algorithm based on the coordinates of the first 100 specified minimum poloidal magnetic field points to divide the possible regions where the poloidal magnetic field is zero. It then clusters the selected minimum poloidal magnetic field point samples into K classes with the same variance, minimizing the sum of squares within each cluster. This algorithm divides a set of N data samples (such as the 100 minimum poloidal magnetic field point samples in this example) into K (such as 4 in this example) disjoint clusters C. j Each is calculated using the mean μ of the samples within that cluster. j The formula for (often referred to as the "centroid" of a cluster) minimizes the sum of squared errors within each cluster, as follows:
[0059]
[0060] 1) Specify the number of clusters K to be divided;
[0061] 2) Randomly initialize K centroids, calculate the distances from the remaining points to the K points, and assign each point to the nearest cluster;
[0062] 3) Calculate the mean of each cluster point and update the mean of each cluster to the new centroid;
[0063] 4) Repeat steps 2) and 3) until the mean of each cluster no longer changes;
[0064] 5) Output the centroid of each cluster.
[0065] S5. Within each of the identification regions defined in S4, find the point where the poloidal magnetic field is 0 using gradient unfolding technology;
[0066] Gradient unfolding is a traditional method for finding the point where the poloidal magnetic field is zero in tokamak divertors. In this patent, within the K clustered identification regions, a small region centered on the point of minimum magnetic field within each cluster, with a horizontal and vertical distance of 2 grid points (the grid spacing calculated from the plasma equilibrium results described in S1), is re-identified and searched for the point where the poloidal magnetic field is zero by dividing it into a finer grid (default 100 grid points). The horizontal and vertical field values for each grid point can also be calculated within this grid. The main identification steps are as follows:
[0067] 1) Calculate the grid points of the specified search area and the horizontal field B on the grid points. r Vertical field B z and the polar field B p And the gradient value of the magnetic field, i.e. and
[0068] 2) Find the grid point with the smallest poloidal magnetic field (this point is called the expansion point, and its coordinates are r). expansion and z expansion Its horizontal and vertical field values are denoted as B. rexpansion and B zexpansion );
[0069] 3) The horizontal and vertical distances from the point of origin to the expansion point of the poloidal magnetic field can be calculated using Taylor series expansion, which requires the following formula:
[0070]
[0071] B in z =B r The distances δr and δz from the point where the poloidal magnetic field is zero to the expansion point are obtained by solving for δr and δz. The matrix calculation method is as follows:
[0072]
[0073] Its solution can be expressed as:
[0074]
[0075] in:
[0076]
[0077] 4) The horizontal and vertical coordinates of the point where the poloidal magnetic field is zero are:
[0078]
[0079] S6. Determine whether the magnetic fields identified within each divided region satisfy the condition that the poloidal magnetic field is 0 (B P →0) condition;
[0080] The method for identifying the zero point of the poloidal magnetic field is to find it through Taylor series expansion within each clustered region. The zero point of the poloidal magnetic field found using this technique needs to be sufficiently close to the expansion point. If there is no zero point of the poloidal magnetic field within the clustered region, the gradient of the magnetic field is usually parallel or antiparallel.
[0081]
[0082] Right now:
[0083] D exp =0;
[0084] Therefore, it is impossible to find a point where the polar magnetic field is 0.
[0085] Meanwhile, examining whether the square of the magnetic field gradient angle is close to 1 can further confirm whether there is an X point inside the cluster division region.
[0086]
[0087] S7. Based on the judgment result of S6, determine the points (X point or O point) that meet the conditions and whose poloidal magnetic field is 0; if the conditions are not met, they are misjudged points and should be discarded. Figure 7 As shown, clusters 1 and 4 have a poloidal field of 0, denoted by x; clusters 2 and 3 have no poloidal magnetic field of 0.
[0088] If it is necessary to determine whether the identified poloidal magnetic field is point X or point O, the distance between the store and the center of the given computational grid can be used to determine whether it is point O, and then the coordinates of all X points can be obtained.
[0089] Furthermore, the plasma balance calculation results input in S1 specifically include the calculation grid (r,z) and the magnetic flux value ψ(r,z) at the grid points.
[0090] Taking the divertor configuration of the EAST device as an example, Figures 8-10 The results show the identification of points with a poloidal magnetic field of 0 (including points X and O) in EAST's double-zero divertor configuration, lower-single-zero divertor configuration, and quasi-snowflake divertor configuration. The results demonstrate that the identification method implemented in this patent can simultaneously identify points with a poloidal magnetic field of 0 at different locations for different configurations.
[0091] In summary, this invention no longer requires specifying the search area for X points. Instead, it directly uses the plasma equilibrium calculation results and clustering methods commonly used in unsupervised learning to identify and provide the coordinates of all possible X points at once. It can also simultaneously provide the coordinates of the magnetic axis (usually called the O point) where the poloidal magnetic field at the plasma center is zero. For the tokamak plasma divertor configuration, it automatically searches and identifies all possible X points (including the O point at the magnetic axis) in the entire computational grid area without specifying the search area based on the divertor configuration.
[0092] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A method for identifying the X-point configuration of a tokamak divertor, characterized in that, The methods and steps include the following: S1. First, input the plasma equilibrium calculation results and extract the calculation grid and magnetic flux distribution information on the grid points; The specific information regarding the calculation grid and magnetic flux distribution at grid points in S1 is as follows: In the plasma equilibrium results, the horizontal grid point coordinate vector is calculated from the grid point information. and vertical grid point coordinate vector The magnetic flux distribution in plasma equilibrium results is typically stored in a two-dimensional array. In the process, after the plasma equilibrium results are input, the horizontal grid point coordinate vectors are directly extracted. Vertical grid point coordinate vector and two-dimensional array variables Information on three variables; S2. Calculate the poloidal magnetic field value at the grid points based on the grid information and magnetic flux distribution information in S1; S3. Extract grid point information for the first 30-200 minimum magnetic field values based on grid thickness; S4. Based on the grid point information of the minimum value in S3, a clustering algorithm is used to divide a specified number of identification regions containing X points. S5. Within each of the identification regions defined in S4, find the point where the poloidal magnetic field is 0 using gradient unfolding technology; S5 specifically includes the following steps: S51. Calculate the grid points of the specified search area and the horizontal field on the grid points. Vertical field and poloidal field And the gradient value of the magnetic field; S52. Find the grid point with the smallest poloidal magnetic field; S53. The horizontal and vertical distances from the point 0 to the point of expansion of the poloidal magnetic field can be calculated using Taylor series expansion. S54. Calculate the horizontal and vertical coordinates of the point where the poloidal magnetic field is zero; S6. Determine whether the magnetic fields identified within each divided region meet the condition that the poloidal magnetic field is 0. S7. Based on the judgment result of S6, the points that meet the conditions are identified as points with a poloidal magnetic field of 0; if the conditions are not met, they are misjudged points and should be discarded. The judgment condition in S6 is: If there is no polar magnetic field point 0 inside the cluster division region, it is necessary to examine whether the square of the magnetic field gradient angle is close to 1 to confirm whether there is an X point inside the cluster division region.
2. The method for identifying the X-point configuration of a tokamak divertor according to claim 1, characterized in that, The plasma balance calculation results input in S1 specifically include the calculation grid. and the magnetic flux values at its grid points .
3. The method for identifying the X-point configuration of a tokamak divertor according to claim 1, characterized in that, The specific calculation method for the poloidal magnetic field value at the grid points in S2 is as follows: Extracting the computational grid coordinates and the magnetic flux value at the grid points Then, the horizontal field on the computational grid points is calculated according to the following formula. and vertical field ; ； Based on this, the poloidal magnetic field can be calculated. .
4. The method for identifying the X-point configuration of a tokamak divertor according to claim 1, characterized in that, Specifically, S3 involves extracting the grid points with the minimum poloidal magnetic field values from the first 30 to 200 grid points after calculating the poloidal magnetic field values based on the observed plasma configuration.
5. The method for identifying the X-point configuration of a tokamak divertor according to claim 1, characterized in that, S4 specifically includes the following steps: S41. Specify the number of clusters to be created. ; S42, Random Initialization Given a centroid, calculate the remaining points to... The distance between points is used to assign each point to the nearest cluster. S43. Calculate the mean of each cluster point and update the mean of each cluster to the new centroid; S44. Repeat S42 and S43 until the mean of each cluster no longer changes; S45. Output the centroid of each cluster.