A method for generating a simulation grid of a linear plasma device

Abstract

A method for generating a simulation grid of a linear plasma device, which belongs to the field of numerical simulation of linear plasma devices. This method first requires inputting various parameters of coils and measurement points. By judging the distance between the coils and the measurement points, different calculation methods are selected, and then the magnetic vector potential, magnetic flux, magnetic field strength, etc. of each measurement point are calculated. Then, the information of the grid point coordinates is obtained by using the interpolation method. Next, the above data information is stored in a general file format, and finally, the magnetic field information is displayed through a visualization method. This method has the ability to adaptively calculate the grid and supports flexible adjustment of coil parameters, including current, placement position, etc. The characteristics of the present invention lie in the accurate and efficient calculation method, multi-coil combination simulation, intuitive visualization method, and generation of a general grid, bringing a new technical solution to the field of magnetic field analysis and design of linear devices and numerical simulation, and having significant scientific research and engineering application values.

Description

Technical Field

[0001] The present invention belongs to the field of numerical simulation of linear plasma devices, relates to an advanced electromagnetic field calculation and visualization field, and particularly relates to a method for generating simulation grids suitable for linear plasma devices, which can meet the numerical simulation of linear plasma devices by different programs. Background Art

[0002] Nuclear fusion energy is regarded as the main energy source for humans in the future due to its rich raw materials, cleanliness, safety, etc. As the most likely device to achieve controllable nuclear fusion, Tokamak has become the focus of controlled fusion research worldwide.

[0003] However, there is still a huge gap between the existing Tokamak devices and the steady-state long-pulse discharge required for fusion reactors. At the same time, due to the high cost of the Tokamak's own operation and the limitations of diagnostic means, it is very difficult to deeply carry out research on the divertor plasma physics mechanism and the interaction between plasma and wall materials under different experimental conditions. The linear plasma device is a laboratory device that forms a steady-state plasma beam by constructing a steady-state magnetic field to confine the plasma generated by the plasma source in a vacuum environment, thereby constructing an environment similar to the divertor plasma to carry out research related to divertor physics in the laboratory. Compared with Tokamak devices, the linear plasma device has the advantages of simple geometric structure and low cost. In addition, the interaction between plasma and wall materials (PMI) is one of the most critical issues in the future long-pulse steady-state operation of Tokamaks. However, the complex environment and limitations of diagnostic techniques make it difficult to comprehensively understand the PMI process only through Tokamak experiments, especially under various discharge operation modes. The linear plasma device can also use magnetic fields and plasma sources to generate steady-state plasma beams and construct a Tokamak-like divertor environment, so it is widely used in the research of plasma-wall interaction (PMI) and boundary plasma physics. Many linear plasma devices have been built internationally, such as Pilot-PSI, Magnum-PSI, PSI-2, MAGPIE, PROTO-MPEX, and GyM, to study issues such as PMI and boundary plasma transport behavior. The multi-plasma simulation linear device (MPS-LD) built by Dalian University of Technology has also achieved successful discharges.

[0004] Although the linear plasma device has a simpler structure compared to the tokamak device and its fusion reaction process is relatively more controllable, it still faces challenges such as high experimental costs, long cycles, and the risk of equipment damage. Therefore, for the linear plasma device, it becomes particularly important to conduct numerical simulation research on key physical problems. Numerical simulation can simulate the behavior of plasmas under different parameters and conditions in a virtual environment, optimize experimental designs, reduce the cost of trial and error, and at the same time provide experimental verification support for theories. Through such simulation research, the experiments and theoretical explorations of the linear plasma device can be promoted more economically and efficiently, bringing sustainable progress to the field of fusion research. Internationally, mainstream plasma simulation programs such as SOLPS, BOUT++, UEDGE, EMC3-Eirene, GYRO, etc. are all developed specifically for tokamaks and simulate plasmas based on tokamak simulation grids. However, for linear plasma devices, since the spatial layout and magnetic field configuration are different from those of tokamaks, a method that can generate simulation grids for linear devices becomes particularly important. Thereby, the advantages of simulation software such as BOUT++ and UEDGE can be utilized to simulate the plasma behavior in linear devices. The present invention can combine the parameters of the linear plasma device to quickly, accurately, and completely generate a general grid for the linear device, with high calculation efficiency and strong numerical stability, which is an accurate and high-speed method. Summary of the Invention

[0005] In order to achieve the above object, the present invention provides a general grid generation method, which can calculate information such as magnetic flux and magnetic field strength in the entire device space according to information such as the magnet coil structure, position, thickness, current, etc. of the linear device, and then use the magnetic flux to construct the grid size and store it together with other physical information as a grid file.

[0006] Technical solution of the present invention:

[0007] A method for generating a simulation grid of a linear plasma device. During the entire magnetic field calculation process, first input the geometric parameters of the coil and measurement points and various parameters required for the calculation, including current, grid spacing, etc. Subsequently, by judging the distance between the coil and the measurement points, different calculation methods are selected: for relatively long distances, elliptic integrals are used to calculate the mutual inductance; for relatively short distances, finer grids and mutual inductance calculations are used, combined with the coil current and number of turns, to calculate the magnetic vector potential at each measurement point, and then calculate the magnetic flux according to the magnetic vector potential. Finally, the magnetic field strength is calculated through spatial gradients. Using the interpolation method, the magnetic flux lines are interpolated in the r direction and segmented in the z direction. The calculation results including magnetic field distribution, magnetic flux, magnetic field strength, and coordinate information are finally stored in a general format, such as a.nc file, and the magnetic field information is displayed through a visualization method. The entire calculation process covers the whole process from input to output, and careful handling of each step is required to ensure the accuracy and efficiency of the calculation.

[0008] The described method specifically includes the following steps:

[0009] Step 1: Input the inherent parameters of the coil itself. The inherent parameters include the inner diameter R in of the coil, the outer diameter R out of the coil, the thickness D of the coil, and the number of turns turn of the coil; then input the adjustable parameters of the coil, where the adjustable parameters include the current I0 and the placement position Z of the coil; then input the coordinate parameters, where the coordinate parameters include the coil coordinates (r a , z a ), the measurement point coordinates (r b , z b ), the grid spacing r dim in the r direction, and the grid spacing z dim in the z direction;

[0010] Step 2: Determine the distance between the coil position "a" and the measurement point "b" based on whether the coordinate r b of the measurement point "b" is greater than r a + n×r dim and whether z b is greater than z a + n×z dim ;

[0011] Step 3: If the above judgment is yes, that is, r b is greater than r a + n×r dim and z b is greater than z a + n×z dim , then it is considered that the distance from the coil position "a" to the measurement point "b" is a long distance, and the following equation is used to solve for the mutual inductance:

[0012]

[0013]

[0014] where K(k c ) and E(k c ) are the first and second complete elliptic integral functions respectively, μ0 is the vacuum magnetic permeability; (R0, Z0), that is, (r a , z a ), are the coordinates of the coil, and I0 is the current;

[0015] Step 4: When the judgment in Step 2 is no, that is, r b is less than r a + n×r dim or z b is less than z a + n×zdim , it is necessary to further refine the grid, that is, select d r = r dim / n p , d z = z dim / n p ;

[0016] Step 5: Then it is necessary to further use the coordinates r b of the measurement point "b" to determine whether it is greater than r a –n×r dim and z b to determine whether it is greater than z a –n×z dim to judge whether the distance between the coil position "a" and the measurement point "b" overlaps;

[0017] Step 6: If the judgment result in Step 5 is yes, that is, r b is greater than r a –n×r dim or z b is greater than z a –n×z dim , then continue to calculate using the fine small grid in Step 4 with the following equation:

[0018]

[0019]

[0020] Step 7: If the judgment result in Step 5 is no, that is, r b is less than r a –n×r dim and z b is less than z a –n×z dim , then it is necessary to use the self-inductance of the coil instead of the mutual inductance, and use the following equation:

[0021]

[0022]

[0023]

[0024] L = μ0r c (T1 + T2 + T3)

[0025] where L is the required self-inductance, r c represents the average radius of the coil, and T1, T2, T3 are the three terms in the self-induction formula used to calculate the self-induction of the rectangular coil.

[0026] T1 represents the product of the radial and axial dimensions and the logarithmic term;

[0027] T2 contains the product of the squares of the radial and axial dimensions and the logarithmic term, T 2a , T 2b , T 2c , T 2d , T 2e , T 2f are its six components respectively, and can be calculated from T 2a =(3βa 2 +γa 2 )α, and calculated;

[0028] T3 is the product of the fourth powers of the radial and axial dimensions and the logarithmic term, T 3a , T 3b , T 3c , T 3d , T 3e are its components respectively,

[0029] that is

[0030]

[0031]

[0032] where α is a logarithmic term, β and γ, etc. are the ratios of the radial and axial dimensions of the rectangular coil to its average radius, u, v, w, w′ are intermediate variables, where u and v are logarithmic terms calculated according to the geometric characteristics of the coil, and w and w′ are the calculated arctangent terms. μ0 is the vacuum permeability;

[0033] Step 8: The mutual inductance of all regions can be calculated through Steps 3, 6 and 7, and the magnetic vector potential of all measurement points is calculated from the mutual inductance:

[0034] A = M × coil current I × number of turns

[0035] Step 9: Calculate the magnetic flux through the magnetic vector potential in Step 8:

[0036] ψ = rA

[0037] where r is the coordinate corresponding to the current grid point;

[0038] Step 10: Calculate the magnetic field strength as follows through the magnetic flux or the magnetic vector potential:

[0039]

[0040]

[0041]

[0042] Among them, N represents the number of groups of coils;

[0043] Step 11: Output and store all magnetic field information;

[0044] Step 12: Extract the isocontours and set the r and z ranges of the grid as well as the corresponding number of grid points;

[0045] Step 13: Use a function to interpolate the horizontal magnetic flux lines and the corresponding z coordinates to obtain the required grid information;

[0046] Step 14: Create a grid file, select the common.nc format, and write the stored magnetic field strength, magnetic flux, and calculated grid point information;

[0047] Step 15: Use the visualization module to read the grid file and display the information.

[0048] Advantages of the present invention: The present invention provides a general grid generation method, which can calculate information such as magnetic flux and magnetic field strength in the entire device space according to the magnet coil structure of the linear device, and then use the magnetic flux to construct the grid size and store it as a grid file together with other physical information. Specifically, it includes:

[0049] (1) High-precision calculation: Through a flexible calculation method, a suitable calculation method is adopted according to the different distances between the coil and the measurement point, so as to ensure high-precision magnetic field calculation results in different situations. (2) Adaptive calculation grid: In response to the change in the distance between the coil and the measurement point, an adaptive calculation grid is adopted, which can not only ensure the calculation accuracy but also improve the calculation efficiency, especially when dealing with the case of a relatively short distance. (3) Considering multiple coils comprehensively: Considering the influence of multiple groups of coils, the magnetic field contributions of each group of coils are combined through an appropriate calculation method to obtain more comprehensive magnetic field information and meet the actual engineering requirements. (5) Flexible grid interpolation: It can be interpolated according to the magnetic flux lines as required, for example, using a non-uniform grid, with a dense grid at the source and target plates and a sparse grid elsewhere. (5) General grid file: The calculation results are stored in a general format (such as a.nc file), which is convenient for subsequent processing and sharing, and at the same time improves the data portability and scalability. (6) Comprehensive output of magnetic field information: Output comprehensive magnetic field information including magnetic field distribution, magnetic flux, and magnetic field strength, providing rich data support for magnetic field design, optimization, and analysis. The present invention has the characteristics of high efficiency, accuracy, and flexibility in the field of linear device simulation, can meet the requirements of magnetic field analysis in complex engineering scenarios, and is an accurate and high-speed simulation grid generation method. Description of the Drawings

[0050] Figure 1It is a schematic diagram of the coil position and the measurement point position.

[0051] Figure 2 It is the calculated magnetic flux diagram.

[0052] Figure 3 It is the calculated magnetic field strength diagram.

[0053] Figure 4 It is the 68×64 grid diagram generated by this method.

[0054] Figure 5 It is the method flow chart of the present invention. Specific Embodiments

[0055] To make the technical problems solved by the present invention, the technical solutions adopted and the achieved technical effects clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. The specific embodiments described herein are only used to explain the present invention, rather than limiting the present invention. Additionally, it should be pointed out that for the convenience of clear description, only the parts related to the present invention rather than all the content are shown in the accompanying drawings.

[0056] In the process of magnetic field calculation, first, the geometric parameters of the coil and the measurement point and various parameters required for the calculation are input, including current, grid spacing, etc. Then, by judging the distance between the coil position and the measurement point, such as Figure 1 , different calculation methods are selected. Taking the third coil as an example, when the measurement point is at (r,z), it is considered that the distance from the coil is relatively far at this time, and the elliptic integral is used to calculate the mutual inductance; when the measurement point is at (r 1 ,z 1 ), it is considered that the distance is relatively close at this time, and a finer grid is used to calculate the mutual inductance; for the overlapping part of the two positions, that is, at (r 2 ,z 2 ), the calculated self-inductance is used instead. Combining the coil current and the number of turns, the magnetic vector potential of each measurement point is calculated, and then the magnetic flux is calculated according to the magnetic vector potential, as shown in Figure 2 . Finally, the magnetic field strength is obtained by calculating the spatial gradient as shown in Figure 3 . Using the interpolation method, the magnetic flux lines are interpolated in the r direction and segmented in the z direction to obtain the grid point information as shown in Figure 4 . Finally, the calculation results including the magnetic field distribution, magnetic flux, magnetic field strength, and coordinate information are stored in a general format, such as a.nc file, and the magnetic field information is displayed through a visualization method. The overall flow chart is as shown in Figure 5 .

[0057] A method for generating a simulation grid of a linear plasma device, the specific steps are as follows:

[0058] Step 1: It is necessary to input the parameters inherent in the coil itself. Generally, these parameters will not change. Here, taking the parameters of the MPS-LD device with 11 coils as an example, such as the inner diameter R of the coil in = 0.3m, 0.3m, 0.3m, 0.3m, 0.3m, 0.3m, 0.3m, 0.3m, 0.4m, 0.4m, 0.4m; the outer diameter R of the coil out = 0.6m, 0.6m, 0.6m, 0.6m, 0.6m, 0.6m, 0.6m, 0.6m, 0.665m, 0.665m, 0.665m; the thickness D of the coil = 0.08m, 0.08m, 0.08m, 0.08m, 0.08m, 0.08m, 0.08m, 0.08m, 0.135m, 0.135m, 0.135m; the number of turns turn of the coil = 162, 162, 162, 162, 162, 162, 162, 162, 200, 200, 200. Then input the adjustable parameters of the coil, such as the current I = 550A, 550A, 550A, 538A, 538A, 538A, 516A, 516A, 625A, 613A, 625A; the placement position Z of the coil = 0m, 0.264m, 0.598m, 0.982m, 1.316m, 1.700m, 2.034m, 2.418m, 2.798m, 3.296m and 3.703m; these are adjustable. Then input the parameters regarding the coordinates, such as the coil coordinates, such as the coil coordinates (r a , z a ), where r a = (R in + R out ) / 2 and z a = Z + D / 2. The coordinates of the measurement point (r b , z b ), and its range is 0m < r b < 0.5m and 0m < z b < 4.5m, the grid spacing r dim in the r direction = 0.01m, the grid spacing z dim in the z direction = 0.01m. Here, the coordinates of the measurement point can be divided into three cases such as Figure 1 .

[0059] Step 2: According to whether the coordinate r b of the measurement point "b" is greater than r a + n × r dim , and whether z b is greater than z a + n × z dim , to judge the distance between the coil position "a" and the measurement point "b", which helps to calculate the mutual inductance near the coil position more accurately.

[0060] Step 3: If the above judgment is yes, that is, r b is greater than r a + n×r dim , z b is greater than z a + n×z dim , then it is considered that the distance from the coil position "a" to the measurement point "b" is a long distance, and the following equation is used to solve the mutual inductance:

[0061]

[0062]

[0063] where: K(k c ) and E(k c ) are the complete elliptic integral functions of the first and second kinds respectively, and μ0 is the vacuum permeability; (R0, Z0), that is, (r a , z a ) are the coordinates of the coil, where R0 = (R in + R out ) / 2, and I0 is the total current;

[0064] Step 4: If the judgment in Step 2 is no, that is, r b is less than r a + n×r dim , z b is less than z a + n×z dim , it is necessary to further refine the grid, that is, select d r = r dim / n p , d z = z dim / n p ;

[0065] Step 5: Then it is necessary to further use the criterion of whether the coordinate r b of the measurement point "b" is greater than r a – n×r dim , and whether z b is greater than z a – n×z dim to judge whether the distance between the coil position "a" and the measurement point "b" overlaps.

[0066] Step 6: If the judgment result in Step 5 is yes, that is, r b is greater than r a – n×r dim or z b is greater than z a – n×z dim, then continue to calculate using the fine small grid in Step 4 with the following equation:

[0067]

[0068]

[0069] Step 7: If the judgment result in Step 5 is no, that is, r b is less than r a – n × r dim and z b is less than z a – n × z dim , then the self - inductance of the coil needs to be used instead of the mutual inductance, and the following equation is adopted:

[0070]

[0071]

[0072]

[0073] L = μ0r c (T1 + T2 + T3)

[0074] where L is the required self - inductance, r c represents the average radius of the coil, and T1, T2, T3 are two terms in the self - induction formula used to calculate the self - induction of a rectangular coil. T1 represents the product of the radial and axial dimensions and the logarithmic term; T2 contains the product of the squares of the radial and axial dimensions and the logarithmic term, T 2a , T 2b , T 2c , T 2d , T 2e , T 2f are its six components respectively, and can be calculated from T 2a =(3βa 2 + γa 2 ); T3 is the product of the fourth powers of the radial and axial dimensions and the logarithmic term, and T 3a , T 3b , T 3c , T 3d , T 3e are its components respectively, that is

[0075] Here, α is a logarithmic term, β, γ, etc. are the ratios of the radial and axial dimensions of the rectangular coil to its average radius, u, v, w, w′ are intermediate variables, where u and v are logarithmic terms calculated based on the geometric characteristics of the coil, and w and w′ are the calculated arctangent terms. μ0 is the magnetic permeability of vacuum.

[0076] Step 8: Through Steps 3, 6, and 7, the mutual inductance of all regions can be obtained. Calculate the magnetic vector potential at all measurement points from the mutual inductance:

[0077] A = I × coil current × number of turns

[0078] Step 9: Calculate the magnetic flux from the magnetic vector potential in Step 8, and the result is as Figure 2 follows:

[0079] ψ = rA

[0080] Here, r is the r corresponding to the current grid point

[0081] Step 10: Calculate the magnetic field strength from the magnetic flux in Step 9 or the magnetic vector potential in Step 8. The equation used is:

[0082]

[0083]

[0084]

[0085] Here, 11 represents 11 groups of coils, which can be adjusted according to the actual situation. The obtained result is as Figure 3 shown.

[0086] Step 11: Output and store all magnetic field information

[0087] Step 12: Extract the contour lines and set the r, z ranges and the corresponding number of grid points of the grid. Here, the number of grid points in the r direction is 64, the range is 0 m < r < 0.2 m, the number of grid points in the z direction is 68, and the range is 0 m < z < 3.5 m.

[0088] Step 13: Perform non-uniform linear interpolation on the horizontal magnetic flux lines and the corresponding z coordinates to obtain the grid point coordinate information, as Figure 4 shown.

[0089] Step 14: Create a grid file, select the common.nc format, and write the stored magnetic field strength, magnetic flux, and the calculated grid point information into it.

[0090] Step 15: Use the visualization module to read the grid file and display the information. The overall flow chart is as Figure 5 shown.

[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: modifications made to the technical solutions described in the foregoing embodiments, or equivalent replacements of some or all of the technical features therein, do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for generating a simulation grid for a linear plasma device, characterized in that: The method specifically comprises the following steps: Step 1: Input the inherent parameters of the coil, including the inner diameter R of the coil in , coil outer diameter R out , coil thickness D, coil turns turn; then enter the coil adjustable parameters, adjustable parameters include current I0 and coil placement Z; then enter the coordinate parameters, coordinate parameters include coil coordinates (r a ,z a ), measuring point coordinates (r b ,z b ), grid spacing in r direction r dim , grid spacing z in z direction dim ; Step 2: Based on the coordinates r of the measured point "b" b Is it greater than r a +n×r dim and z b Is it greater than z a +n×z dim , to determine the distance between the coil position "a" and the measuring point "b"; Step 3: If the above judgment is yes, that is, r b Greater than r a +n×r dim And z b Greater than z a +n×z dim , then the distance from coil position "a" to measurement point "b" is considered to be a long distance, and the following equation is used to solve the mutual inductance: Among them, K(k c ) and E(k c ) are the first and second complete elliptic integral functions, μ0 is the vacuum permeability; (R0, Z0) is (r a ,z a ) are the coordinates of the coil, I0 is the current; Step 4: When the judgment of step 2 is no, that is, r b Less than r a +n×r dim or b Less than z a +n×z dim , we need to further refine the grid, that is, select d r =r dim / n p , d z =z dim / n p ; Step 5: Then you need to further use the coordinates r of the measurement point "b" b Is it greater than r a –n×r dim and z b Is it greater than z a –n×z dim To determine whether the distance between coil position "a" and measurement point "b" overlaps; Step 6: If the result of step 5 is yes, then r b Greater than r a –n×r dim or b Is it greater than z a –n×z dim , then use the fine grid in step 4 to continue calculating using the following equation: Step 7: If the result of step 5 is no, that is, r b Less than r a –n×r dim And z b Less than z a –n×z dim , you need to use the self-inductance of the coil instead of the mutual inductance, using the equation: <h2 style=";text-align:left;direction:ltr">L=μ0r<h2 style=";text-align:left;direction:ltr"> c <h2 style=";text-align:left;direction:ltr"> (T1+T2+T3) Where L is the required self-inductance, r c represents the average radius of the coil, T1, T2, T3 are three terms in the self-inductance formula, which are used to calculate the self-inductance of a rectangular coil; T1 represents the product of the radial and axial dimensions and the logarithmic term; T2 contains the product of the square of the radial and axial dimensions and the logarithmic term, T 2a , T 2b , T 2c , T 2d , T 2e , T 2f They are its six components, which can be expressed by T 2a =(3βa 2 +γa 2 )α, Calculated; T3 is the product of the radial and axial dimensions raised to the fourth power and the logarithmic term, T 3a , T 3b , T 3c , T 3d , T 3e are their components, namely Among them, α is a logarithmic term, β and γ are the ratios of the radial and axial dimensions of the rectangular coil to its average radius, u, v, w, w′ are intermediate variables, among which u and v are logarithmic terms calculated based on the geometric characteristics of the coil, and w and w′ are calculated inverse tangent terms; μ0 is the vacuum permeability; Step 8: Through steps 3, 6 and 7, the mutual inductance of all areas can be calculated, and the magnetic loss potential of all measurement points can be calculated by the mutual inductance: A=M×coil current I×number of turns Step 9: Calculate the magnetic flux using the magnetic potential loss in step 8: ψ=rA Among them, r is the coordinate corresponding to the current grid point; Step 10: Calculate the magnetic field strength through magnetic flux or magnetic potential loss as follows: Where N represents the number of coil groups; Step 11: Output and store all magnetic field information; Step 12: Extract the contour lines and set the r, z range of the grid and the corresponding number of grids; Step 13: Use the function to interpolate the horizontal magnetic flux lines and the corresponding z coordinates to obtain the desired grid information; Step 14: Create a grid file, select the general .nc format, and write the stored magnetic field intensity, magnetic flux and calculated grid point information; Step 15: Use the visualization module to read the grid file and display the information.

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