Search

CN-121809190-B - Boundary plasma simulation method under unit magnetic surface coordinate system

CN121809190BCN 121809190 BCN121809190 BCN 121809190BCN-121809190-B

Abstract

The invention 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, using a unit magnetic surface coordinate system to express a physical model, realizing separation of physical quantity and geometric effect by using a unit base vector to avoid singularities near an X point, secondly, combining a circumferential Fourier series representation with a difference along a magnetic field line to reduce the problem dimension and numerical dissipation, thirdly, adopting a generalized finite difference method and a transformation coordinate system to process the X point and adjacent points thereof so that the grid can directly contain the X point, and finally, pre-calculating geometric quantity and difference coefficient under a high-density grid by a grid screening method to improve the calculation precision of the geometric effect. The invention can accurately simulate the influence of the X point on the stability of the boundary plasma, obviously reduce the consumption of computing resources and improve the simulation efficiency and accuracy.

Inventors

  • Dong Tianzuo
  • SUN YOUWEN
  • YE MINYOU
  • MAO SHIFENG

Assignees

  • 中国科学技术大学

Dates

Publication Date
20260512
Application Date
20260311

Claims (9)

  1. 1. The boundary plasma simulation method under the unit magnetic surface coordinate system is characterized by comprising the following steps of: Defining a unit magnetic plane coordinate system according to the Tokamak magnetic field configuration, utilizing the unit magnetic plane coordinate system to express tensor differential operators in combination by using basic direction derivative differential operators, and calculating geometric quantity to describe geometric effect of the magnetic field configuration so as to realize separation of physical quantity and geometric effect near X point; dividing grids on the circumferential section of the Tokamak, carrying out Fourier decomposition on the circumferential coordinates to obtain Fourier coefficients of each circumferential modulus, constructing a transformation matrix which is connected with a basic operator and a partial derivative by means of deriving a differential operator expression along the magnetic field line coordinates, expressing the basic differential operator under a coordinate system along the magnetic field line, and adopting finite differential dispersion on the radial direction and the parallel direction, and adopting Fourier series dispersion on the circumferential direction; Step 3, transforming the coordinate system to process the X point and the adjacent points thereof, wherein, for the situation that the phase translation angle is infinite and is inapplicable in the vicinity of the X point in the step 2, for the X point, the third base vector of the unit magnetic surface coordinate system is directly utilized to obtain the difference along the direction of the magnetic field line, for the adjacent points of the X point, the difference operator is directly expressed in the unit magnetic surface coordinate system without carrying out the phase translation along the magnetic field line, the difference format is determined, thereby establishing the numerical format suitable for the singular point in the X point and the peripheral area, and Pre-calculating geometric quantity and differential coefficient, namely pre-calculating the geometric quantity and partial derivative coefficient required by the steps 1 to 3 under the grid higher than the density required by simulation, and screening out the grid with the proper density for simulation calculation; in the step 2, the magnetic field line coordinates are measured by introducing variables Realization of the variables From the following components Definition wherein As a safety factor, the safety factor of the device, For the correction of the angle of the straight field line, Is the polar flux, the transformation matrix is used for mapping basic operators to Partial derivatives in a coordinate system The matrix is formed by a matrix of, Is the normalized radial coordinate of the lens, Is the angle of the polar direction, Is the circumferential angle.
  2. 2. The boundary plasma simulation method according to claim 1, wherein in the step 1, the first base vector is defined as a radial unit base vector of the cylindrical coordinate system at the X point, and the second base vector is defined as a negative value of an axial unit base vector of the cylindrical coordinate system to supplement mathematical definition of the normal direction of the magnetic plane at the X point.
  3. 3. The boundary plasma simulation method according to claim 1, wherein in the step 1, the geometry includes nine independent geometries, the nine independent geometries are determined by dot products of a basis vector of a unit magnetic plane coordinate system and a gradient vector thereof, and dimensions thereof are consistent with curvature windings for constructing all first-order and second-order differential operators in combination.
  4. 4. The boundary plasma simulation method according to claim 1, wherein in the step 2, the difference in the parallel direction is achieved by multiplying the fourier coefficients of adjacent polar grid points by a phase shift factor, and the phase shift factor is determined according to the circumferential angle change along the field line and the circumferential modulus.
  5. 5. The boundary plasma simulation method according to claim 1, wherein in the step 3, for the neighboring points of the X point, a magnetic surface coordinate system is used Rather than along the magnetic field line coordinate system Expressing a difference operator, centering on the projection of X points on the circumferential section The grid points are regarded as scattered points on the plane, so that a generalized finite difference method is applied to establish a difference format.
  6. 6. The boundary plasma simulation method according to claim 1, wherein in the step 3, the difference in the direction of the magnetic field lines at the X point is directly achieved by the inherent phase variation of the toroidal fourier basis function, namely by And determining, wherein n is the circumferential modulus, Is the radius of the large ring at the point X, Is the magnetic field direction vector and, Is a vector differential operator, In imaginary units.
  7. 7. The boundary plasma simulation method according to claim 1, wherein in step 4, the pre-calculation is performed on a high-density magnetic surface grid containing X points generated by a plasma inverse equilibrium solver to ensure that rapidly changing geometric quantities around X points are accurately captured, the screening being performed by extracting subsets from the high-density magnetic surface grid.
  8. 8. The boundary plasma simulation method according to claim 1, wherein the differential format is constructed by the method of the step 2 in a region far from the X point, and the differential format is constructed by the method of the step 3 in the X point and the neighboring points thereof, thereby achieving consistent numerical dispersion in the entire simulation region including the X point.
  9. 9. The boundary plasma simulation method according to claim 1, wherein the partial derivative coefficients include a transformation matrix and its respective partial derivatives, and only values corresponding to simulation grid points are extracted for the simulation calculation of steps 1 to 3 after the geometric quantity and partial derivative coefficients are calculated in advance on the high-density magnetic surface grid of step 4.

Description

Boundary plasma simulation method under unit magnetic surface coordinate system Technical Field The invention belongs to the technical field of magnetic confinement Tokamak boundary plasma simulation, and particularly relates to a boundary plasma simulation method under a unit magnetic surface coordinate system. Background The prior tokamak mainly works under the shape of a divertor, the shape of the magnetic field of the core part of the divertor is a nested closed magnetic surface, the outer side of the interface is an open magnetic surface, and a special point with a polar magnetic field of zero is arranged on the interface, which is called an X point. In simulating a partial filter configuration Tokamak boundary plasma, the simulation area needs to cross the interface, so that the X point and the processing method of the interface are particularly needed to be considered. The internationally existing boundary plasma simulation framework mainly has bout++, which adopts a simulation method for expressing operators along a field line coordinate system. However, because of the singularities at the plasma interface and X points along the field line coordinate system, bout++ must avoid this singularity by avoiding the plasma interface and X points, and it is not possible to simulate a divertor potential boundary plasma using a grid containing X and interface. However, this method cannot accurately consider the important influence of the interface and the X point on the physical properties of the plasma, and in particular cannot accurately consider the stabilizing effect of the X point on the boundary plasma. Moreover, BOUT++ simplifies the operator and ignores the effect of the partial derivative of the second order operator along the direction of the magnetic field line, but this approximation may not be applicable near the X point because the magnetic field near the X point is very close to the circumferential direction, and the length of the connection between adjacent points (the length of the magnetic field line connecting the two points) may vary greatly even if the rate of change along the field line is low, and cannot be ignored as in other locations. These problems result in non-physical results that may occur near the X point when bout++ is used to simulate a boundary plasma. On the other hand, BOUT++ uses a three-dimensional grid to simulate Tokamak plasma, which does not take good advantage of the circumferential symmetry of the plasma in Tokamak, which makes it difficult to specifically consider interactions between certain specific circumferential moduli, such as when studying a number of circumferential modes focused onIf a resonant magnetic disturbance of n=1 is introduced, all of the components must be continuously considered in the BOUTAnd at this time thereinPart of this is wasted computing resources. Further, the low efficiency rate is more pronounced when linear simulations are performed. There are also some boundary plasma fluid simulation programs such as JOREK, CLT, etc. that are suitable for tokamak, but they are mainly simulations of a defined set of plasma fluid equations, the contents of which cannot be freely changed, and which cannot be called a simulation framework. And although they can solve the X-point simulation problem, they use a non-magnetic surface coordinate system, which may introduce large numerical dissipation and require a high density grid to be partitioned in the very-upward direction to handle simulations when the circumferential modulus is large. The lack of using a magnetic plane coordinate system and differential calculation along the magnetic field direction is a major disadvantage because it does not exploit the strong anisotropy in good tokamaks along the magnetic field direction. Disclosure of Invention In order to solve the technical problems, the invention provides a boundary plasma simulation method under a unit magnetic surface coordinate system, which comprises the following specific technical scheme: a boundary plasma simulation method under a unit magnetic surface coordinate system comprises the following steps: Defining a unit magnetic surface coordinate system according to a Tokamak magnetic field configuration, wherein the unit magnetic surface coordinate system is provided with three base vectors, a first base vector faces outwards perpendicularly to a magnetic surface, a third base vector is a magnetic field direction, a second base vector is a cross product of the third base vector and the first base vector, a tensor differential operator is expressed by combining basic direction derivative differential operators by using the unit magnetic surface coordinate system, and geometric quantities are calculated to describe the geometric effect of the magnetic field configuration, so that singularities are avoided near an X point, and separation of the physical quantities and the geometric effect is realized; Dividing grids on the circumferential sec