A boundary plasma simulation method under a unit magnetic surface coordinate system

Abstract

The application discloses a boundary plasma simulation method under a unit magnetic surface coordinate system and belongs to the technical field of magnetic confinement tokamak boundary plasma simulation. Firstly, a physical model is expressed by using a unit magnetic surface coordinate system, physical quantity and geometric effect are separated by using unitized base vectors, and singularity near an X point is avoided; secondly, a toroidal Fourier series representation is combined with difference along a magnetic field line, problem dimension is reduced, and numerical dissipation is reduced; thirdly, a generalized finite difference method and a transformed coordinate system are adopted to process the X point and adjacent points, and the X point can be directly contained in a grid; finally, a grid screening method is used to pre-calculate geometric quantities and difference coefficients under high-density grids, and the calculation precision of geometric effect is improved. The application can accurately simulate the influence of the X point on the stability of the boundary plasma, significantly reduces the consumption of computing resources, and improves the simulation efficiency and accuracy.

Description

Technical Field

[0001] This invention belongs to the field of boundary plasma simulation technology of magnetically confined tokamak, and particularly relates to a method for simulating boundary plasma in a unit magnetic surface coordinate system. Background Technology

[0002] Modern tokamaks primarily operate in a divertor configuration. The core magnetic field of a divertor-configured tokamak consists of nested closed magnetic surfaces, with an open magnetic surface outside the interface. A special point on the interface, where the poloidal magnetic field is zero, is called the X-point. When simulating the boundary plasma of a divertor-configured tokamak, the simulation region needs to span the interface; therefore, the handling of the X-point and the interface must be carefully considered.

[0003] The main international framework for simulating boundary plasmas is BOUT++, which uses a field-line coordinate system to represent operators. However, due to singularities in the field-line coordinate system at the plasma interface and point X, BOUT++ must avoid these singularities by avoiding the plasma interface and point X, and cannot use a mesh containing X and the interface to simulate divertor configuration boundary plasmas. This method cannot accurately account for the significant influence of the interface and point X on plasma physics, particularly the stabilizing effect of point X on the boundary plasma. Furthermore, BOUT++ simplifies the operators, ignoring the effect of the partial derivatives along the magnetic field lines in the second-order operators. This approximation may not be applicable near point X, because the magnetic field near point X is very close to circumferential, and the connection length between adjacent points (the length of the magnetic field line connecting the two points) can vary significantly even with a low rate of change along the field lines, and cannot be ignored as in other locations. These issues lead to non-physical results near point X when using BOUT++ to simulate boundary plasmas. On the other hand, BOUT++ uses a three-dimensional mesh to simulate tokamak plasma, which does not make good use of the circumferential symmetry of the plasma in the tokamak. This makes it difficult to specifically consider the interactions between certain circumferential modes, such as when studying a circumferential mode number concentrated in a certain range. When instability occurs, if a resonant magnetic perturbation of n=1 is introduced, all [variables] must be continuously considered in BOUT. And at this time, among them Some of these are wasteful of computational resources. Furthermore, the inefficiency is even more pronounced when performing linear simulations.

[0004] There are also some boundary plasma fluid simulation programs suitable for tokamaks, such as JOREK and CLT, but they mainly simulate defined plasma fluid equations and cannot freely change the simulation content, so they cannot be called simulation frameworks. Furthermore, although they can solve the X-point simulation problem, they do not use a magnetic coordinate system, which may introduce significant numerical dissipation, and requires high-density meshing in the pole direction to handle simulations with large circumferential moduli. Their main drawback is the lack of a magnetic coordinate system and differential calculations along the magnetic field direction, as this does not take advantage of the strong anisotropy along the magnetic field direction in tokamas. Summary of the Invention

[0005] To address the above technical problems, this invention provides a method for simulating boundary plasma in a unit magnetic surface coordinate system. The specific technical solution is as follows:

[0006] A method for simulating boundary plasma in a unit magnetic surface coordinate system includes the following steps:

[0007] Step 1: Express the physical model using operators in the unit magnetic surface coordinate system: Define the unit magnetic surface coordinate system based on the tokamak magnetic field configuration. The unit magnetic surface coordinate system has three basis vectors, where the first basis vector is perpendicular to the magnetic surface and outwards, the third basis vector is the magnetic field direction, and the second basis vector is the cross product of the third basis vector and the first basis vector. Using the unit magnetic surface coordinate system, tensor differential operators are combined and expressed using basic directional derivative differential operators, and geometric quantities are calculated to describe the geometric effects of the magnetic field configuration, thereby avoiding singularities near point X and achieving separation of physical quantities and geometric effects.

[0008] Step 2: Combine the circumferential coordinates processed by Fourier series with the difference along the magnetic field line for numerical discretization: divide the grid on the circumferential section of the tokamak, perform Fourier decomposition on the circumferential coordinates to obtain the Fourier coefficients of each circumferential modulus, derive the expression of the difference operator using the coordinates along the magnetic field line, construct the transformation matrix connecting the basic operator and the partial derivatives, express the basic differential operator in the coordinate system along the magnetic field line, and use finite difference discretization for the radial and parallel directions, and Fourier series discretization for the circumferential direction, thereby achieving low-dissipation difference along the magnetic field line direction in the conventional region;

[0009] Step 3: Process point X and its neighboring points using the generalized finite difference method and a transformed coordinate system: Addressing the inapplicability of the method in Step 2 near point X due to infinite phase translation angles, for point X, the difference along the magnetic field lines is directly obtained using the third basis vector of the unit magnetic surface coordinate system. For neighboring points of point X, the difference operator is directly expressed in the magnetic surface coordinate system without phase translation along the magnetic field lines, and the generalized finite difference method is used to determine the difference scheme, thereby establishing a numerical scheme suitable for singular points in point X and its surrounding region; and...

[0010] Step 4: Pre-calculate geometric quantities and difference coefficients using a mesh selection method: Pre-calculate the geometric quantities and partial derivative coefficients required in steps 1 to 3 using a mesh density higher than that required for the simulation, and select a suitable mesh density for the simulation calculation, thereby improving the calculation accuracy of geometric effects without affecting the calculation efficiency.

[0011] The present invention has the following beneficial effects:

[0012] (1) In the simulation framework of this invention, by selecting the unit magnetic surface coordinate system, the singularity of the field line coordinate system near point X is avoided, and a complete set of coordinates can be used to describe the entire simulation region. At the same time, the normalized basis vectors allow physical quantities and geometric effects to be independent, avoiding the coupling between physical quantities and geometry caused by the change in the length of the basis vectors in general coordinate systems. In addition, the selection of the unit magnetic surface coordinate system also allows us to construct its basic operators in different ways in different regions, which can better fit the physical properties at different locations.

[0013] (2) In the framework of this invention, the coupling of field line difference and circumferential Fourier representation allows the use of very few poloidal grids in the simulation, while only the influence of the circumferential modulus that needs to be considered can be taken into account, saving the n modulus that needs to be considered in the circumferential direction (equivalent to saving the number of grids required in the circumferential direction), thereby greatly simplifying the computational scale of the problem and improving computational efficiency in principle.

[0014] (3) This invention solves the problem of constructing the difference format of singular point X by using the generalized finite difference method, so that the mesh can directly contain X point and interface, which can better reflect the influence of the generation of X point in the simulation.

[0015] (4) The present invention combines the mesh selection method with the unit magnetic surface coordinate system, which can more accurately calculate geometric quantities and partial derivative coefficients, and can more accurately study the influence of geometric effects on plasma. At the same time, the mesh density is no longer limited by geometric quantities, and a lower density mesh can be achieved to save computational resources. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the process of the present invention;

[0017] Figure 2 A schematic diagram of geometric quantities;

[0018] Figure 3 This is a schematic diagram of the partial derivative coefficients;

[0019] Figure 4 The diagram shows the pressure disturbance distribution of an ideal balloon mold.

[0020] Figure 5 A schematic diagram of radial pressure disturbance distribution for an ideal balloon model with different circumferential moduli.

[0021] Figure 6 This is a schematic diagram illustrating the evolution of the disturbance pressure amplitude over time. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, this invention adopts the following technical solution.

[0023] This invention provides a method for simulating boundary plasma in a unit magnetic surface coordinate system, such as... Figure 1 As shown, it includes the following parts:

[0024] (1) Use operators in the unit magnetic surface coordinate system to express the physical model.

[0025] For a plasma model to be simulated, i.e. a system of partial differential equations, all differential operators in the equations are first expressed in a unit magnetic coordinate system. Using the properties of the unit magnetic coordinate system, all tensor differential operators can be combined with the basic directional derivative differential operators using geometric quantities.

[0026] The unit magnetic surface coordinate system does not exhibit singularities near point X, making it possible to use a grid containing point X in the magnetic surface coordinate system. The unit magnetic surface coordinate system can also well reflect the strong anisotropy of plasma in the tokamak, that is, the direction along the magnetic field line, the direction perpendicular to the magnetic surface, and the direction within the magnetic surface perpendicular to the magnetic field are strictly distinguished. The unit magnetic surface coordinate system can well separate the geometric effects of the magnetic field configuration from the physical field, and the magnitude of the components of physical quantities is not affected by geometry in the unit magnetic surface coordinate system.

[0027] (2) The circumferential coordinates processed by Fourier series are combined with the difference along the magnetic field lines to improve computational efficiency and simulation accuracy. This step is to express the numerical format of the operators in the unit magnetic surface coordinate system so that these operators can be operated on in the program, that is, to discretize them.

[0028] The circumferential Fourier series representation and the field-line difference method are of great significance for the computational efficiency and accuracy of magnetic confinement fusion plasma simulation. When simulating linear problems, using Fourier series to represent circumferential coordinates allows for the separate simulation of each circumferential modulus, reducing the computational system from a three-dimensional mesh to a two-dimensional mesh on the circumferential cross-section, greatly improving computational efficiency. When simulating nonlinear problems, it also allows for better simulation of the required number of circumferential modes, reducing wasted computational resources. The field-line difference method reduces the requirements for the poloidal mesh and also reduces numerical dissipation, making it an important tool for simulating microscopic instabilities such as plasma turbulence. This first-ever combination of the circumferential Fourier series representation and the field-line difference method fully leverages the advantages of both.

[0029] (3) Use the generalized finite difference method and the coordinate system transformation to process point X and its neighboring points.

[0030] This step is to specifically handle the numerical format of the operator at point X, because the method in step (2) cannot be used near point X. A generalized finite difference method is used to handle the difference format at point X, and a variable coordinate system method is used to handle points near point X. This allows point X to be directly included in the mesh, thus enabling accurate simulation of the influence of point X on the plasma. Simultaneously, this approach better matches the physical characteristics near point X.

[0031] (4) Using a grid selection method, the geometric quantities and difference coefficients are pre-calculated under an extremely high-density grid, and then a grid of appropriate density is extracted for simulation calculation. This step is to calculate the geometric quantities and difference coefficients required in steps (1), (2), and (3) more accurately. This method allows the geometric effects to be considered more accurately without the need to increase the grid density, especially for the geometric effects of the rapidly changing magnetic field configuration near point X.

[0032] Step (1) specifically involves using the unit magnetic surface coordinate system.

[0033] The unit magnetic coordinate system is defined based on the magnetic field configuration in a tokamak, and it has three basis vectors. ,in Perpendicular to the magnetic plane and outwards, Indicates the direction of the magnetic field. .

[0034] In the unit magnetic coordinate system, the fundamental operator is the first-order directional derivative. and second-order directional derivative , This is a vector differential operator; other first- and second-order differential operators can be composed of basic operators and geometric quantities. The geometric quantities are... Due to symmetry, there are nine independent physical quantities whose dimensions are consistent with curvature and tensor deflection, hence they are called geometric quantities. Based on these nine geometric quantities and tensor arithmetic rules, all first- and second-order differential operators can be expressed.

[0035] By first expressing the basic operators and calculating the geometric quantities in the simulation program, all the difference operators needed in the physical model can be combined.

[0036] Specifically, at point X, it is stipulated that... , This is because there is no concept of a magnetic surface at point X, therefore the magnetic surface normal no longer has a mathematical definition and no special physical characteristics. Adding this definition allows us to express the difference operator at point X (where...). The unit basis vector in the macrocyclic coordinate system is a cylindrical coordinate system defined based on the axial symmetry of the tokamak. Using the axis of symmetry of the tokamak device as the Z-axis of the cylindrical coordinate system, and taking upward as the positive direction, a right-handed coordinate system can be determined. ).

[0037] Step (2) specifically involves using a method that combines circumferential Fourier series representation with field line difference.

[0038] The simulation program requires magnetic surface coordinates to represent partial derivatives and mesh. Let the magnetic surface coordinates be denoted as... At a certain circumferential section of the tokamak, i.e. The space is divided into grids, and Fourier decomposition is performed in the ring direction. It is the normalized radial coordinate, and it is the poloidal magnetic flux. The function, specified It gradually increases in size from the inside out; It is a polar angle, whose direction is defined to ensure Construct a right-handed coordinate system; It is the circumferential angle, with the direction of increase being counterclockwise when viewed from above the tokamak. and These represent the contravariant metric and the covariant metric of the coordinate system, respectively. Each can be taken as ), Indicates Jacobi. Also defines... ;in It is a poloidal magnetic field. It is a circumferential magnetic field. denoted as , where is the magnetic field strength.

[0039] For any physical quantity The circumferential Fourier decomposition method is adopted, and the program stores the Fourier coefficients of each object as a modulus of n. :

[0040] ;

[0041] To achieve the difference along the magnetic field lines, it is necessary to use the coordinates along the magnetic field lines to derive the expression of the difference operator. However, note that this coordinate system is introduced here only as part of the derivation process.

[0042] Introducing variables It is calculated using the following formula:

[0043] ,

[0044] ;

[0045] in, For safety factors. For straight field angle correction, It is a polar magnetic flux. Let f be the flux function. pole magnetic flux relative to radial coordinates The derivative of .

[0046] Now use one matrix The basic operators are associated with partial derivatives, denoted as (where the same index represents summation, i.e., Einstein's summation rule). Each refers to one of the three coordinate quantities, such as or ):

[0047] ;

[0048] The expressions for second-order basic operators can be obtained using the expressions for first-order basic operators:

[0049] ;

[0050] Now, let's switch to a specific coordinate system. In the coordinate system, the three first-order fundamental differential operators can be represented as follows, specifically, the matrix is ​​denoted as... :

[0051] ;

[0052] , Represents the components of the contravariant metric tensor. Represents the covariant metric tensor components;

[0053] To perform numerical calculations, these partial derivatives need to be numerically discretized using finite difference methods. The following section describes the process using a mesh. Write down the three fundamental partial derivatives. , , Finite difference scheme:

[0054] Radial difference scheme:

[0055] ;

[0056] in, The finite difference coefficients represent the first-order radial partial derivatives. The finite difference coefficients represent the second-order radial partial derivatives.

[0057] Parallel direction difference scheme:

[0058] ;

[0059] in, The finite difference coefficients represent the partial derivatives in the first parallel direction. The finite difference coefficients represent the partial derivatives in the second parallel direction.

[0060] Circular difference scheme:

[0061] ;

[0062] Mixed partial derivative difference scheme:

[0063] ;

[0064] in, The finite difference coefficients represent the mixed partial derivatives.

[0065] The aforementioned finite difference coefficients vary depending on the mesh size and the accuracy of the chosen difference scheme. The phase shift angle... The difference is defined locally near each point, which ensures that the difference at other locations on the plasma interface is unaffected by the singularity of point X. The above result can also be derived without using the field line coordinate system; it can be directly understood as translating the grid points originally on a circumferential section to the same magnetic field line and then performing the difference.

[0066] For grid points near point X, this method cannot be used for translation if point X is needed in the difference scheme. This is because... At point X, the number is infinite, making numerical processing impossible. For these grid points adjacent to point X, the magnetic coordinate system is directly used. The difference operator is expressed in the middle, without performing a phase shift. This approach aligns with the physical reality near point X, because the magnetic field lines near X are almost entirely circumferential. Therefore, the distance from points near X to X via the magnetic field lines is very large. Even if the physical quantity changes slowly along the direction of the magnetic field lines, as the length of the magnetic field lines approaches infinity, significant changes will occur, making difference operations along the magnetic field lines less advantageous. In this case, performing the difference directly within the circumferential section is more accurate. Expressed using physical formulas, the formula holds true near point X:

[0067] ;

[0068] in, This represents the distance between two points in the direction perpendicular to the magnetic field lines. This represents the distance between two points in the direction parallel to the magnetic field lines. This represents the rate of change in the direction perpendicular to the magnetic field. This represents the rate of change parallel to the direction of the magnetic field. The magnetic coordinate system is described below. The representation of the basic difference operator:

[0069] ;

[0070] Let the above matrix be denoted as Using the same The basic form of the second-order basic operator can be obtained by having a completely consistent expression under coordinates, which will not be listed here.

[0071] Step (3) uses the generalized finite difference method to process point X, including:

[0072] At point X, the magnetic field lines are circumferential, and therefore directly connected to... This allows us to obtain the difference along the direction of the magnetic field lines, directly... Where n is the circumferential modulus, Let X be the radius of the large loop at point X. For vector differential operators, The unit is the imaginary unit. For differences within a circumferential section, in Finding the difference scheme in coordinates. Regardless of how the mesh attached to the magnetic surface is divided, some points near point X can always be found. These can be treated as a group of scattered points rather than a mesh. The generalized finite difference method is used to find the difference scheme for scattered points on a two-dimensional plane, thus finding the required difference scheme. In other words, while using a structured mesh and finite difference method in the main computational domain, the singular point X of the structured mesh is handled by generalized finite difference.

[0073] Step (4) The grid selection method accurately calculates geometric quantities and difference coefficients, including:

[0074] The partial derivative coefficients are required in the fundamental difference operator in the unit magnetic coordinate system. and And their partial derivatives, and other operators require geometric quantities when constructed using the basic operators; therefore, the computational quality of these geometric quantities and partial derivative coefficients is crucial to the accuracy of the simulation. Calculating these geometric quantities and partial derivative coefficients requires a magnetically fitted mesh and plasma equilibrium data defined at the mesh points. To further consider point X, a mesh containing point X and equilibrium data defined on it is needed. This can be obtained using a plasma inverse equilibrium solver (such as FDEQ).

[0075] These geometric quantities are calculated by increasing the mesh density, for example, when planning to use When simulating using a mesh, then when solving for equilibrium, use... The grid structure allows for sufficiently high accuracy in solving for geometric quantities and partial derivative coefficients, preventing the inaccurate consideration of variations in these quantities along the polar direction due to a smaller grid size. After calculating the geometric quantities and partial derivative coefficients, a selection is then made from them. Plasma simulations are performed using a high-density mesh. This allows for a more rigorous consideration of the impact of geometric effects on plasma without increasing computational load, making low-density mesh simulations more reliable. It is particularly important to note that the high-density mesh and equilibrium must be directly generated by the equilibrium solver. Using a low-density mesh interpolated to obtain a high-density mesh for calculating geometric quantities will not result in more accurate geometric quantities, because essentially only equilibrium information from the low-density mesh is ultimately used.

[0076] This method of pre-solving geometric quantities and partial derivative coefficients using a high-density grid is particularly effective for point X, because the geometric quantities near point X change rapidly, and accurate geometric information about the vicinity of point X cannot be obtained without a high-density grid.

[0077] The following are specific examples:

[0078] This framework is used to simulate the linear instability of the ideal balloon mode in a tokamak. The equations for the ideal balloon mode are as follows:

[0079] ;

[0080] For parallel currents, The permeability of free space, The gradient operator is perpendicular to the direction of the background magnetic field. It is a parallel magnetic vector potential. It is the electrostatic potential; The magnetic field strength, This is a vortex disturbance; The unit vector representing the direction of the background magnetic field. The magnetic field curvature vector, For pressure disturbance, The gradient operator is parallel to the direction of the background magnetic field. The pressure is in equilibrium. Background plasma density;

[0081] (1) First, the FDEQ equilibrium solver was used to generate an H-mode tokamak equilibrium and divide it. The mesh, under these equilibrium parameters, will trigger the ideal balloon model instability.

[0082] (2) Then calculate the geometric quantities and partial derivative coefficients, such as Figure 2 (a), (b) and Figure 3 As shown in (a)-(d). Figure 2 (a) and (b) are geometric quantities respectively. and The diagram shows that... , , which are the components of the curvature vector of the magnetic field lines in two directions, respectively. Figure 3 (a)-(d) are respectively , , , A schematic diagram.

[0083] (3) Then filter out The grid is used to obtain the coefficients of the difference scheme, which expresses the difference operator required in the ideal balloon model equation.

[0084] (4) Set initial perturbations for the evolution of the equations. The initial perturbations can be set arbitrarily as long as the boundary conditions are met.

[0085] (5) Use the Runge-Kutta display format for time progression or use a semi-implicit method for time progression.

[0086] (6) The final result is as follows Figures 3-6 As shown.

[0087] It can be seen that the results obtained by the simulation framework of this invention are consistent with the calculation results of some generally accepted programs, which reflects the reliability of our calculation method.

[0088] Meanwhile, in this embodiment, the result of the present invention can be completed in just over ten seconds on a personal computer, while calculating the same content using BOUT++ would require several minutes using 128 CPUs on a server. This demonstrates the high efficiency of the method of the present invention.

Claims

1. A method for simulating boundary plasma in a unit magnetic surface coordinate system, characterized in that, include: Step 1: Express the physical model using operators in the unit magnetic surface coordinate system: Define the unit magnetic surface coordinate system based on the tokamak magnetic field configuration, use the unit magnetic surface coordinate system to express the tensor differential operators by combining the basic directional derivative differential operators, and calculate the geometric quantities to describe the geometric effects of the magnetic field configuration, thereby achieving the separation of physical quantities and geometric effects near point X. Step 2: The processed circumferential coordinates are combined with the difference along the magnetic field lines for numerical discretization: The circumferential section of the tokamak is divided into grids, the circumferential coordinates are decomposed into Fourier coefficients of each circumferential modulus, the expression of the difference operator is derived with the help of the coordinates along the magnetic field lines, the transformation matrix connecting the basic operator and the partial derivatives is constructed, the basic differential operator is expressed in the coordinate system along the magnetic field lines, and the radial and parallel directions are discretized by finite difference, and the circumferential direction is discretized by Fourier series. Step 3, transform the coordinate system to process point X and its neighboring points: In view of the case that Step 2 is not applicable near point X due to the infinite phase translation angle, for point X, the difference along the direction of the magnetic field line is obtained directly using the third basis vector of the unit magnetic surface coordinate system. For the neighboring points of point X, the difference operator is directly expressed in the unit magnetic surface coordinate system without performing phase translation along the magnetic field line to determine the difference format, thereby establishing a numerical format suitable for singular points in point X and the surrounding area. as well as, Step 4, pre-calculate geometric quantities and difference coefficients: pre-calculate the geometric quantities and partial derivative coefficients required in steps 1 to 3 under a grid density higher than that required for the simulation, and select a suitable grid density for the simulation calculation. In step 2, the coordinates along the magnetic field line are determined by introducing variables. Implement, the variable Depend on Define, where As a safety factor, For straight field angle correction, It is the poloidal flux, and the transformation matrix maps the basic operators to... Partial derivatives in coordinate system matrix, These are normalized radial coordinates. It is a polar angle. It is a circumferential angle.

2. The boundary plasma simulation method according to claim 1, characterized in that, In step 1, at point X, the first basis vector is defined as the radial unit basis vector of the cylindrical coordinate system, and the second basis vector is the negative value of the axial unit basis vector of the cylindrical coordinate system, to supplement the mathematical definition of the magnetic surface normal at point X.

3. The boundary plasma simulation method according to claim 1, characterized in that, In step 1, the geometric quantities include nine independent geometric quantities, which are determined by the dot product of the basis vector and the gradient vector of the unit magnetic surface coordinate system. Their dimensions are consistent with the curvature and deflection, and they are used to combine and construct all first-order and second-order differential operators.

4. The boundary plasma simulation method according to claim 1, characterized in that, In step 2, the difference in the parallel direction is achieved by multiplying the Fourier coefficients of adjacent poloidal grid points by a phase shift factor and then performing a finite difference. The phase shift factor is determined based on the circumferential angle change along the field line and the circumferential modulus.

5. The boundary plasma simulation method according to claim 1, characterized in that, In step 3, for points near point X, a magnetic coordinate system is used. Instead of the magnetic field line coordinate system The difference operator is expressed with the projection of point X onto the circumferential section as the center. On the plane, grid points are treated as scattered points, and a difference scheme is established by applying the generalized finite difference method.

6. The boundary plasma simulation method according to claim 1, characterized in that, In step 3, the difference along the magnetic field lines at point X is directly achieved using the inherent phase transformation of the circumferential Fourier basis functions, i.e., by... Determined, where n is the circumferential modulus. Let X be the radius of the large loop at point X. The direction vector of the magnetic field. For vector differential operators, It is the imaginary unit.

7. The boundary plasma simulation method according to claim 1, characterized in that, In step 4, the pre-calculation is performed on a high-density magnetic surface mesh containing point X, generated by the plasma inverse equilibrium solver, to ensure that rapidly changing geometric quantities near point X are accurately captured, and the filtering is achieved by extracting a subset from the high-density magnetic surface mesh.

8. The boundary plasma simulation method according to claim 1, characterized in that, The difference scheme is constructed using the method described in step 2 in the region far from point X, and the difference scheme is constructed using the method described in step 3 in the region at point X and its neighboring points, thereby achieving consistent numerical discretization over the entire simulation region containing point X.

9. The boundary plasma simulation method according to claim 1, characterized in that, The partial derivative coefficients include the transformation matrix and its partial derivatives of each order. After the geometric quantities and partial derivative coefficients are pre-calculated on the high-density magnetic surface grid in step 4, only the values ​​corresponding to the simulated grid points are extracted for the simulation calculations in steps 1 to 3.

Images