Spectral radiation three-dimensional chord integral calculation method for magnetic confinement device

Abstract

The invention discloses a three-dimensional chord integral calculation method for spectral radiation of a magnetic confinement device, and belongs to the field of magnetic confinement fusion. The method comprises the following steps: constructing a three-dimensional boundary plasma-neutral particle transport program EMC3-EIRENE field alignment grid; an EMC3-EIRENE program is adopted to solve a fluid equation set of plasma and impurity transportation; establishing a spectral radiation three-dimensional chord integral calculation coordinate system; and calculating spectral radiation projection distribution of plasmas and impurities in different valence states in the magnetic confinement fusion device. Through accurate coupling of the three-dimensional magnetic field configuration and plasma transportation, asymmetric distribution of impurities and main plasma in complex geometry is effectively depicted, and errors introduced by a traditional axial symmetry hypothesis are eliminated. Independent calculation and overlay analysis of main plasma bremsstrahlung radiation and impurity line radiation are supported, contribution weights of different physical processes to total radiation are determined, and a basis is provided for targeted optimization.

Description

Technical Field

[0001] The present invention relates to the field of magnetic confinement fusion, and is applicable to the calculation of spectral radiation in the field of magnetic confinement fusion. In particular, it relates to a three-dimensional chord integral calculation method for spectral radiation of a magnetic confinement device. Background Art

[0002] Magnetic confinement fusion devices are one of the core technical routes for realizing controllable nuclear fusion. During the operation of magnetic confinement fusion devices, the spatial distributions and radiation characteristics of plasma and impurities are key factors affecting the performance and safety of the devices. Plasma generates particles in different ionization states or excited states through processes such as ionization, excitation, or recombination. Its radiation spectrum not only reflects local plasma parameters but is also closely related to energy transport, radiation losses, and boundary physical processes. Therefore, accurate modeling and diagnostic analysis of the three-dimensional radiation field of plasma are important bases for optimizing confinement performance, suppressing instabilities, and evaluating the heat load on the first wall.

[0003] Traditional spectral diagnostic methods usually assume two-dimensional axisymmetry or simplified geometric models and use inverse Abel transformation or tomography techniques to reconstruct the radiation distribution. However, in modern magnetic confinement devices, the complex three-dimensional magnetic field configuration, the asymmetry of plasma transport, the asymmetry caused by gas puffing, and dynamic transient processes such as pellet injection make it difficult for two-dimensional models to accurately describe the real physical scenario. In recent years, the development of three-dimensional plasma simulation programs has provided tools for the three-dimensional transport and radiation modeling of plasma and impurities, but they still lack a direct connection with experimental spectral diagnostic data. In addition, although existing imaging techniques can separate specific spectral lines through filter films or spectroscopic elements, they are limited by spatial resolution and photon statistical noise and are difficult to analyze the radiation contribution weights of different physical processes or particle states in three-dimensional space. Therefore, there is an urgent need for a method to quickly calculate the spectral radiation of particles in different valence states based on the three-dimensional plasma and impurity distributions under a three-dimensional magnetic field configuration to determine the spatial radiation distribution of particles in different valence states and optimize the confinement performance of plasma. Summary of the Invention

[0004] The main purpose of the present invention is to provide a three-dimensional chord integral calculation method for spectral radiation of a magnetic confinement device, aiming to calculate the spectral radiation of spatial plasma and impurities by combining a three-dimensional plasma simulation program, filling the gap in the comparison means between current three-dimensional simulation programs and experimental diagnostic data, and at the same time distinguishing the radiation contributions of particles in different valence states.

[0005] To achieve the above object, the present invention provides a three-dimensional chord integral calculation method for spectral radiation of a magnetic confinement device, including the following steps:

[0006] S1. Construction of a field-aligned grid of the three-dimensional boundary plasma-neutral particle transport program EMC3-EIRENE.

[0007] S1.1. Construction of two-dimensional basic calculation grid.

[0008] Furthermore, in step S1.1, the process of constructing the two-dimensional basic calculation grid is as follows:

[0009] Based on the two-dimensional equilibrium magnetic field data (i.e., GEQDSK equilibrium file) measured experimentally for the magnetic confinement fusion device and the spatial position information of the device target plate, the two-dimensional calculation regions for plasma and neutral particles in the EMC3-EIRENE program are respectively defined on the two-dimensional (r, z) plane. Subsequently, the positions of the X-point (i.e., magnetic null point) and the core-scrape-off layer boundary are found respectively within the two-dimensional calculation region, and then the entire two-dimensional calculation region is divided into six sub-regions on the (r, z) plane, which are the core, the main scrape-off layer, the strong-field side scrape-off layer, the weak-field side scrape-off layer, the upper private flux region, and the lower private flux region in sequence. Within each sub-region, according to the spatial scale of the device, the contour lines of different poloidal fluxes ψ p are selected, i.e., the flux surfaces, and then the grid points are evenly divided along the flux surfaces, and thus the two-dimensional basic calculation grid on the (r, z) plane is obtained.

[0010] S1.2. Construction of three-dimensional field-aligned grid.

[0011] Furthermore, the construction method of the three-dimensional field-aligned grid in step S1.2 is as follows:

[0012] Based on the two-dimensional coordinate system (r, z), the third dimension toroidal is introduced to form a three-dimensional right-handed cylindrical coordinate system Under the three-dimensional right-handed cylindrical coordinate system, according to the poloidal current function F in the two-dimensional equilibrium magnetic field data pol and the poloidal flux ψ p , the magnetic field at each grid point on the two-dimensional (r, z) plane is calculated

[0013]

[0014] where μ0 = 4π × 10 -7 N·A -2 is the vacuum magnetic permeability. In the EMC3-EIRENE program, in order to ensure the high efficiency of the calculation, the toroidal needs to be divided into different toroidal calculation regions. Within different toroidal calculation regions, based on the magnetic field of the obtained grid points, it is extended along the magnetic field direction, and the expression of the magnetic field line in the three-dimensional right-handed cylindrical coordinate system is:

[0015]

[0016] After arrangement, the coordinate position of the magnetic field line is obtained as a function of Differential equations of variation:

[0017]

[0018] Subsequently, based on the above equations, in the toroidal The fourth-order Runge-Kutta method is used to integrate the magnetic field lines to obtain all grid points within each toroidal calculation region. During the integration of the magnetic field lines, when the magnetic field lines approach the target plate, due to the high gradient of plasma parameters, the grid needs to be refined to ensure the reliability and accuracy of the calculation results.

[0019] Between different toroidal calculation regions, the EMC3-EIRENE program uses a fast reversible magnetic field line inversion technique for rapid high-fidelity magnetic field line reconstruction to ensure the calculation coherence of different toroidal calculation regions.

[0020] S2. Solve the fluid equations of plasma and impurity transport using the EMC3-EIRENE program.

[0021] S2.1. Establishment of the fluid equations of plasma and impurity transport.

[0022] Furthermore, in step S2.1, the construction process of the fluid equations of plasma and impurity transport is as follows:

[0023] In the non-equilibrium state, the kinetic behaviors of plasma and impurities are described by the Boltzmann equation, and its general form is:

[0024]

[0025] Where is the particle distribution function at time t at position with velocity in the phase space, is the position space gradient operator, is the velocity space gradient operator, is the sum of the external forces acting on the particle, m represents the mass of the particle, and C a is the source term caused by particle collisions.

[0026] In a magnetic confinement fusion device, the electromagnetic force acting on charged particles is much greater than the gravitational force and other external forces. Therefore is expressed as:

[0027]

[0028] Where q is the particle charge, is the electric field strength, is the magnetic induction intensity, and c = 3×10 8m / s is the speed of light in vacuum. Substituting the above equation into the Boltzmann equation and integrating the velocity space of the particle distribution function from zero to the second moment respectively gives:

[0029]

[0030] where n is the particle number density, is the particle flow velocity, and T is the particle temperature.

[0031] Integrating the Boltzmann equation in velocity space and substituting it into the zero-order moment equation gives the particle continuity equation:

[0032]

[0033] Multiplying both sides of the particle continuity equation by the particle mass m and velocity and then integrating in velocity space and substituting it into the first-order moment equation gives the particle momentum conservation equation:

[0034]

[0035] where p is the pressure, is the gradient symbol, represent the unit vectors in the x, y, and z directions respectively, represents the pressure gradient, is the viscous stress tensor, defined as is the single-particle random velocity, is the identity matrix.

[0036] Multiplying both sides of the particle continuity equation by the particle energy and then integrating gives the particle energy conservation equation:

[0037]

[0038] where is the conductive heat flux, defined as

[0039] Based on the above particle continuity, momentum, and energy conservation equations, the transport process of particles in the fusion device is divided into the transport process parallel to the magnetic field line and the transport process perpendicular to the magnetic field line, and applied to electrons and ions respectively, to obtain the fluid equations for plasma and impurity transport solved by the EMC3-EIRENE program:

[0040]

[0041] Among them, the subscripts e and i represent background electrons and ions respectively, zi represents the valence states of different types of background impurity particles, and the symbols || and ⊥ represent the directions parallel and perpendicular to the magnetic field respectively. For the plasma equations: η || , κ i and κ e respectively represent the particle parallel transport coefficients, the parallel transport coefficients of ion and electron energies, which are obtained from experimental experience; D ⊥ , χ i and χ e respectively represent the particle perpendicular transport coefficients, the perpendicular transport coefficients of ion and electron energies, which are free parameters and obtained through experimental diagnostics. In addition, η ⊥ = mnD ⊥ . S p and S m are the plasma ionization source and the momentum loss caused by charge exchange respectively. S ei and S ee are the energy sources of ions and electrons respectively, and are all provided to EMC3 by the EIRENE program. T e represents the electron temperature, T i represents the ion temperature, and k = 1.380649×10 -23 J / K is the Boltzmann constant. For the impurity equation: D imp is the impurity perpendicular transport coefficient, and S zi is the impurity ion source with valence state zi caused by the ionization and recombination of impurities. s represents the coordinate along the magnetic field direction, τ s is the collision time of impurity particles with the background plasma, and f fri is the friction coefficient. The right side of the momentum conservation equation successively represents the pressure gradient force, electric field force, friction force, electron thermal gradient force, and ion thermal gradient force acting on the impurity particles. In addition, α e and β i satisfy:

[0042] α e = 0.71zi 2

[0043]

[0044] Among them, is the reduced mass of impurity particles.

[0045] S2.2. Setting of boundary conditions in the calculation region.

[0046] Furthermore, in step S2.2, the particle, momentum, and energy boundary conditions on the target plate wall are all decay boundary conditions. The decay length is selected as an appropriate value according to different magnetic confinement fusion devices. At the same time, the Bohm boundary condition is applied at the target plate and plasma boundary; for the core particle boundary, a fixed particle flux, a fixed upstream density, or gas puffing and pumping balance is selected. The momentum boundary condition is selected as the zero-momentum boundary condition, that is, the reflection boundary, while the energy boundary condition is selected as the core energy input, which is consistent with the absorption power of the experiment, and the energy is proportionally distributed to electrons and ions.

[0047] S2.3, Solving the fluid equations of plasma and impurity transport and determining the transport coefficients.

[0048] Furthermore, in step S2.3, under the regional boundary conditions of step S2.2, the EMC3-EIRENE program is used to solve the fluid equations of plasma and impurity transport. According to the measured profiles in the experiment, the perpendicular transport coefficients D ⊥ , χ i and χ e of ions and electrons, as well as the perpendicular transport coefficient D imp of impurities are fitted. After multiple iterations of convergence until the transport coefficients with the smallest error from the experimental profiles are obtained, the spatial density and temperature distributions of the plasma and impurities at these transport coefficients are then obtained.

[0049] S3. Establishing the coordinate system for three-dimensional chord integral calculation of spectral radiation.

[0050] S3.1, Determining the camera observation direction.

[0051] Furthermore, in step S3.1, the steps for establishing the coordinate system for three-dimensional chord integral calculation of spectral radiation are as follows:

[0052] Denote the center position of the vacuum wall of the magnetic confinement fusion device as At the same time, define this point as the center position of the integral projection screen, and denote the position of the experimental diagnostic camera as Convert the point and position coordinates in the three-dimensional right-handed cylindrical coordinate system to the position coordinates in the rectangular coordinate system, then there are

[0053]

[0054] p1 - p0 is the camera observation direction.

[0055] S3.2, Constructing the integral projection screen and the calculation coordinate system.

[0056] Furthermore, an integrated projection screen is defined, which is the screen for the deposition of the spectral radiation energy of the plasma and impurities. An integrated projection screen is established passing through point p0 on the plane perpendicular to the camera observation direction in step S3.1. The horizontal a and vertical b directions of the integrated projection screen are respectively represented as the toroidal and poloidal directions, and p0 is taken as the coordinate origin of the integrated projection screen. The basis vectors in the toroidal and poloidal directions on the integrated projection screen are respectively denoted as v a and v b . Since the basis vectors in the two directions are perpendicular to each other and simultaneously perpendicular to the camera observation direction, the direction vectors v′ a and v′ b in the directions of v a and v b in the rectangular coordinate system have the following relationships:

[0057]

[0058] where represents the direction vector in the vertical direction of the magnetic confinement fusion device. Substituting points p0 and p1 into the above formula, the toroidal and poloidal basis vectors in the normalized form in the rectangular coordinate system are obtained:

[0059]

[0060] If p0 and p1 are on the same plane, then in the three-dimensional right-handed cylindrical coordinate system, it can be further simplified to the following form:

[0061]

[0062] where ΔR = R1 - R0. Up to this point, any point p2 on the integrated projection screen can be represented by the basis vectors v a and v b and the spectral radiation three-dimensional chord integral calculation coordinate system (a, b), that is:

[0063] p2(a, b) = p0 + av a + bv b

[0064] Meanwhile, any point p on the observation chord in the camera observation direction can be expressed by the distance l between p and p1:

[0065]

[0066] S4. Calculation of the projection distribution of the spectral radiation of different valence states of plasma and impurities in the magnetic confinement fusion device.

[0067] S4.1. Establishment of the spectral radiation formula on the integrated projection screen.

[0068] Further, in step S4.1, the establishment process of the spectral radiation formula on the integral projection screen is as follows:

[0069] Assume that a continuous visible light source is deposited on the above-mentioned integral projection screen. The radiation deposited on the integral projection screen along the true observation chord can form a radiation projection plan view, that is, a three-dimensional chord integral plasma and impurity spectral radiation distribution map. The integral projection screen is divided into finite widths Δa and Δb along the poloidal and toroidal directions. Assume that the effective aperture of the observation camera lens is D d , then the three-dimensional radiation quantity F(a, b) can be obtained by integrating the local radiation quantity f(p(a, b; l)) along the true observation chord, that is:

[0070]

[0071] Among them, the volume element dV can be expressed as dV = ΔSdl, and ΔS is the area element corresponding to the position of point p on the true observation chord, which can be expressed by Δa and Δb as:

[0072]

[0073] Combining the previous derivation and substituting the relevant quantities into the three-dimensional radiation quantity expression, the number of photons deposited on each finite width in the radiation projection plan view is obtained as:

[0074]

[0075] Express a and b as a = (i + 1 / 2)Δa and b = (j + 1 / 2)Δb respectively, where i and j are the toroidal and poloidal cell numbers respectively. Then, the number of photons deposited at any cell (i, j) in the radiation projection plan view can be expressed as: F i,j = F((i + 1 / 2)Δa, (j + 1 / 2)Δb).

[0076] S4.2. Calculation of spectral radiation in a magnetic confinement fusion device.

[0077] Further, in step S4.2, combining the spatial density temperature distribution of plasma and impurities calculated by the EMC3-EIRENE program in step S2 and the photon emission coefficient in the OPEN-ADAS database, the local radiation quantity distribution f(p(a, b; l)) in space is calculated. Substitute the local radiation quantity distribution into the above photon number deposition formula, and ensure that Δt, Δp, and Δl are less than the grid size of the EMC3-EIRENE program, then the spectral radiation projection plan views of plasma and impurities with different valence states can be obtained.

[0078] Advantages of the present invention:

[0079] (1) By accurately coupling the three-dimensional magnetic field configuration with plasma transport, the asymmetric distributions of impurities and the main plasma in complex geometries are effectively characterized, and the errors introduced by the traditional axisymmetric assumption are eliminated. It supports the independent calculation and superposition analysis of the bremsstrahlung of the main plasma and impurity line radiation, clarifies the contribution weights of different physical processes to the total radiation, and provides a basis for targeted optimization.

[0080] (2) By customizing the viewing angle of the CCD camera and the coordinate system of the projection screen, any experimental diagnostic geometry is compatible, and direct comparison between simulation data and experimental observations is achieved.

[0081] (3) It is applicable to various magnetic confinement devices such as tokamaks, stellarators, and spherical tori, and is compatible with different magnetic field configurations. Moreover, by updating the atomic database and radiation coefficients, it can be extended to multi-band spectral analysis such as extreme ultraviolet and X-ray, meeting the full-wavelength diagnostic requirements. Description of the Drawings

[0082] Figure 1 The image obtained by the CCD camera, the spatial position of the CCD camera, and the two-dimensional basic calculation grid of the EMC3-EIRENE program;

[0083] Figure 2 According to the positions of the CCD camera and the projection screen, the spectral radiation distribution on the projection screen is calculated. Among them, (a) is the captured image of the CCD camera, (b) is the spectral radiation distribution of Li II impurities on the projection screen calculated using the present invention, and (c) is the D α spectral radiation distribution calculated by the present invention. Detailed Embodiment

[0084] It should be understood that the specific embodiments described below are only used to explain the present invention and are not used to limit the application scope of the present invention. The implementation, implementation method, functional characteristics, and advantages of the present invention will be further described with reference to the embodiments and the drawings.

[0085] S1. Construction of the field-aligned grid of the three-dimensional boundary plasma-neutral particle transport program EMC3-EIRENE.

[0086] S1.1. Construction of the two-dimensional basic calculation grid.

[0087] Further, in step S1.1, the process of constructing the two-dimensional basic calculation grid is specifically as follows:

[0088] Based on the two-dimensional equilibrium magnetic field data (i.e., GEQDSK equilibrium file) measured experimentally for the magnetic confinement fusion device and the spatial position information of the device target plate, the two-dimensional calculation regions of the plasma and neutral particles in the EMC3-EIRENE program are defined respectively in the two-dimensional (r,z) plane. Subsequently, the positions of the X-point (i.e., magnetic null point) and the core-scrape-off layer boundary are found respectively within the two-dimensional calculation region, and then the entire two-dimensional calculation region is divided into six sub-regions in the (r,z) plane, namely the core, the main scrape-off layer, the strong-field side scrape-off layer, the weak-field side scrape-off layer, the upper private flux region, and the lower private flux region. Within each sub-region, according to the spatial scale of the device, the contour lines of different poloidal fluxes ψ p are selected, that is, the flux surfaces, and then the grid points are evenly divided along the flux surfaces, and then the two-dimensional basic calculation grid in the (r,z) plane is obtained.

[0089] S1.2, Construction of three-dimensional field-aligned grid.

[0090] Furthermore, the construction method of the three-dimensional field-aligned grid in step S1.2 is as follows:

[0091] Based on the two-dimensional coordinate system (r,z), a third dimension, toroidal is introduced to form a three-dimensional right-handed cylindrical coordinate system Under the three-dimensional right-handed cylindrical coordinate system, according to the poloidal current function F in the two-dimensional equilibrium magnetic field data pol and the poloidal flux ψ p , the magnetic field at each grid point in the two-dimensional (r,z) plane is calculated

[0092]

[0093]

[0094] Among them, μ0 = 4π×10 -7 N·A -2 is the vacuum magnetic permeability. In the EMC3-EIRENE program, in order to ensure the efficiency of the calculation, the toroidal needs to be divided into different toroidal calculation regions. Within different toroidal calculation regions, based on the magnetic field of the obtained grid points, it is extended along the magnetic field direction, and the expression of the magnetic field line in the three-dimensional right-handed cylindrical coordinate system is:

[0095]

[0096] After sorting, the differential equation group of the magnetic field line coordinate position changing with is obtained:

[0097]

[0098] Subsequently, based on the above equations, in the toroidal the magnetic field lines are integrated using the fourth-order Runge-Kutta method to obtain all grid points within each toroidal calculation region. During the integration of the magnetic field lines, when the magnetic field lines approach the target plate, due to the high gradients of plasma parameters, the grid needs to be refined to ensure the reliability and accuracy of the calculation results.

[0099] Between different toroidal calculation regions, the EMC3-EIRENE code uses a fast reversible magnetic field line inversion technique for fast high-fidelity magnetic field line reconstruction to ensure the calculation coherence between different toroidal calculation regions.

[0100] S2. Solve the fluid equations for plasma and impurity transport using the EMC3-EIRENE code.

[0101] S2.1. Establishment of the fluid equations for plasma and impurity transport.

[0102] Furthermore, in step S2.1, the construction process of the fluid equations for plasma and impurity transport is as follows:

[0103] In the non-equilibrium state, the kinetic behaviors of plasma and impurities are described by the Boltzmann equation, and its general form is:

[0104]

[0105] where is the particle distribution function at position at time t in the phase space, with velocity , is the gradient operator in the position space, is the gradient operator in the velocity space, is the sum of the external forces acting on the particle, m represents the mass of the particle, and C a is the source term caused by particle collisions.

[0106] In a magnetic confinement fusion device, the electromagnetic force acting on charged particles is much greater than the gravitational force and other external forces. Therefore is expressed as:

[0107]

[0108] where q is the particle charge, is the electric field strength, is the magnetic induction intensity, and c = 3×10 8 m / s is the speed of light in vacuum. After substituting the above equation into the Boltzmann equation, the velocity space of the particle distribution function is integrated from zero to the second moment to obtain:

[0109]

[0110] where n is the particle number density, is the particle flow velocity, and T is the particle temperature.

[0111] Integrating the Boltzmann equation in velocity space and substituting it into the zero-order moment equation, the particle continuity equation is obtained:

[0112]

[0113] Multiply both sides of the particle continuity equation by the particle mass m and velocity and then integrate in velocity space and substitute it into the first-order moment equation to obtain the particle momentum conservation equation:

[0114]

[0115] where p is the pressure, is the gradient symbol, represent the unit vectors in the x, y, and z directions respectively, represents the pressure gradient, is the viscous stress tensor, defined as is the single-particle random velocity, is the identity matrix.

[0116] Multiply both sides of the particle continuity equation by the particle energy and then integrate to obtain the particle energy conservation equation:

[0117]

[0118] where is the conductive heat flux, defined as

[0119] Based on the above particle continuity, momentum, and energy conservation equations, the transport process of particles in the fusion device is divided into the transport process parallel to the magnetic field line and the transport process perpendicular to the magnetic field line, and is applied to electrons and ions respectively, to obtain the fluid equations for plasma and impurity transport solved by the EMC3-EIRENE program:

[0120]

[0121] where the subscripts e and i represent background electrons and ions respectively, zi represents the valence states of different types of background impurity particles, and the symbols || and ⊥ represent the directions parallel and perpendicular to the magnetic field respectively. For the plasma equation: η || , κ i and κ erespectively represent the parallel particle transport coefficient, the parallel ion and electron energy transport coefficients, which are obtained from experimental experience; D ⊥ , χ i and χ e respectively represent the perpendicular particle transport coefficient, the perpendicular ion and electron energy transport coefficients, which are free parameters obtained through experimental diagnostics. In addition, η ⊥ = mnD ⊥ . S p and S m are respectively the plasma ionization source and the momentum loss due to charge exchange. S ei and S ee are the energy sources of ions and electrons, respectively, which are provided to EMC3 by the EIRENE program. T e represents the electron temperature, T i represents the ion temperature, k = 1.380649×10 -23 J / K is the Boltzmann constant. For the impurity equation: D imp is the perpendicular impurity transport coefficient, S zi is the impurity ion source with valence zi caused by the ionization and recombination of impurities. s represents the coordinate along the magnetic field direction, τ s is the collision time of impurity particles with the background plasma, f fri is the friction coefficient. The right side of the momentum conservation equation represents successively the pressure gradient force, the electric field force, the friction force, the electron thermal gradient force, and the ion thermal gradient force acting on the impurity particles. In addition, α e and β i satisfy:

[0122] α e = 0.71zi 2

[0123]

[0124] where, is the reduced mass of the impurity particles.

[0125] S2.2, Setting the boundary conditions of the calculation region.

[0126] Furthermore, in step S2.2, the particle, momentum, and energy boundary conditions on the target plate wall are all decay boundary conditions, and the decay length is selected as an appropriate value according to different magnetic confinement fusion devices. At the same time, the Bohm boundary condition is applied to the target plate and the plasma boundary; for the core particle boundary, a fixed particle flux, a fixed upstream density, or gas puffing and pumping balance are selected, the momentum boundary condition is selected as the zero momentum boundary condition, i.e., the reflection boundary, and the energy boundary condition is selected as the core energy input, which is consistent with the absorption power in the experiment, and the energy is proportionally distributed to electrons and ions.

[0127] S2.3, Solving the fluid equations of plasma and impurity transport and determining the transport coefficients.

[0128] Further, in step S2.3, under the regional boundary conditions of step S2.2, use the EMC3 - EIRENE program to solve the fluid equations of plasma and impurity transport. According to the experimentally measured profiles, fit the vertical transport coefficients D ⊥ , χ i and χ e of ions and electrons, as well as the vertical transport coefficient D imp of impurities. After multiple iterations of convergence until the transport coefficients with the smallest error from the experimental profiles are obtained, and then obtain the spatial density temperature distributions of plasma and impurities at these transport coefficients.

[0129] S3. Establishment of the coordinate system for three - dimensional chord integral calculation of spectral radiation.

[0130] S3.1. Determination of the camera observation direction.

[0131] Further, in step S3.1, the steps for establishing the coordinate system for three - dimensional chord integral calculation of spectral radiation are as follows:

[0132] Denote the central position of the vacuum wall of the magnetic confinement fusion device as At the same time, define this point as the central position of the integral projection screen, and denote the position of the experimental diagnostic camera as Convert the point and position coordinates in the three - dimensional right - hand cylindrical coordinate system to position coordinates in the rectangular coordinate system, then there are

[0133]

[0134] p1 - p0 is the camera observation direction.

[0135] S3.2. Construction of the integral projection screen and the calculation coordinate system.

[0136] Further, define the integral projection screen, that is, the screen where the spectral radiation energy of plasma and impurities is deposited. On the plane perpendicular to the camera observation direction in step S3.1, establish the integral projection screen passing through point p0. The horizontal a and vertical b directions of the integral projection screen are respectively represented as toroidal and poloidal, and p0 is the coordinate origin of the integral projection screen. Denote the basis vectors in the toroidal and poloidal directions of the integral projection screen as v a and v b , the basis vectors in the two directions are perpendicular to each other and simultaneously perpendicular to the camera observation direction, then the direction vectors v′ a and v′ b in the v a and v b directions in the rectangular coordinate system have the following relationship:

[0137]

[0138] Among them, represents the direction vector in the vertical direction of the magnetic confinement fusion device. Substituting the two points p0 and p1 into the above formula, the toroidal and poloidal basis vectors in the normalized form in the rectangular coordinate system are obtained:

[0139]

[0140] If p0 and p1 are on the same plane, then in the three-dimensional right-handed cylindrical coordinate system, it can be further simplified to the following form:

[0141]

[0142] Among them, ΔR = R1 - R0. Here, any point p2 on the integral projection screen can be represented by the basis vectors v a and v b and the spectral radiation three-dimensional chord integral calculation coordinate system (a, b), that is:

[0143] p2(a, b) = p0 + av a + bv b

[0144] At the same time, any point p on the observation chord in the camera observation direction can be represented by the distance l between p and p1:

[0145]

[0146] S4. Calculation of the spectral radiation projection distribution of different valence states of plasma and impurities in the magnetic confinement fusion device.

[0147] S4.1. Establishment of the spectral radiation formula on the integral projection screen.

[0148] Furthermore, in step S4.1, the process of establishing the spectral radiation formula on the integral projection screen is as follows:

[0149] Assume that a continuous visible light source is deposited on the above integral projection screen. The radiation deposited on the integral projection screen along the real observation chord can form a radiation projection plan view, that is, the three-dimensional chord integral plasma and impurity spectral radiation distribution map. Divide the integral projection screen into finite widths Δa and Δb along the poloidal and toroidal directions. Assume that the effective aperture of the observation camera lens is D d , then the three-dimensional radiation quantity F(a, b) can be obtained by integrating the local radiation quantity f(p(a, b; l)) along the real observation chord, that is:

[0150]

[0151] Among them, the volume element dV can be expressed as dV = ΔSdl, where ΔS is the area element corresponding to the position of point p on the true observation chord, and can be expressed by Δa and Δb as:

[0152]

[0153] Combining the previous derivations and substituting the relevant quantities into the three-dimensional radiation quantity expression, the number of photons deposited on each finite width in the radiation projection plan view is obtained as:

[0154]

[0155] Express a and b as a = (i + 1 / 2)Δa and b = (j + 1 / 2)Δb respectively, where i and j are the unit numbers in the toroidal and poloidal directions. Then, the number of photons deposited at any unit (i, j) in the radiation projection plan view can be expressed as: F i,j = F((i + 1 / 2)Δa, (j + 1 / 2)Δb).

[0156] S4.2, Calculation of spectral radiation in a magnetic confinement fusion device.

[0157] Furthermore, in step S4.2, combining the spatial density temperature distributions of the plasma and impurities calculated by the EMC3 - EIRENE program in step S2 and the photon emission coefficients in the OPEN - ADAS database, the local radiation quantity distribution f(p(a, b; l)) in space is calculated. Substituting the local radiation quantity distribution into the above photon number deposition formula, and ensuring that Δt, Δp, and Δl are less than the grid size of the EMC3 - EIRENE program, the spectral radiation projection plan views of the plasma and impurities with different valence states can be obtained.

[0158] Example: Calculation of spectral radiation of the boundary plasma and impurities in the EAST device

[0159] The EAST device is a fully superconducting tokamak device independently developed in China. The major radius of the device is 1.85 m, the minor radius is 0.45 m, and the volume of the toroidal vacuum chamber is about 30 cubic meters. The toroidal magnetic field can reach 3.5 - 4.0 Tesla, and the plasma current can reach the megampere level. At the same time, the CCD camera installed on EAST can take spectral radiation images of the plasma and impurities inside the device, providing a good platform for the qualitative comparison between the experimental observation images and the images obtained by the three - dimensional chord integral calculation of this method.

[0160] In the EAST device, the CCD camera is located at R = 2.89 m, Z = 0.0155 m, toroidal position, and the imaging plane of the camera (i.e., the spectral radiation projection screen) is located toroidally In this embodiment, the lithium impurity is at R = 1.57 m, Z = 1.05 m, toroidal The position is injected into the EAST device through the upper private area. After the plasma reaches a steady state, the image obtained by the CCD camera is as shown in Figure 1 the left figure.

[0161] For the above EAST device structure, the toroidal two-dimensional basic calculation grid of the EMC3-EIRENE program is as shown in Figure 1 the right figure. The boundary conditions adopted in the simulation calculation are as follows: the heating power is 270 kW, the energy is evenly distributed to ions and electrons, the upstream density is fixed at 5.5×10 18 m -3 , the boundary decay lengths of plasma and impurity particles are 2.4 cm, the momentum boundary decay length is 2.4 cm, and the energy boundary decay lengths of ions and electrons are 5 cm. Under the above boundary conditions, the experimentally fitted particle and energy perpendicular transport coefficients are D ⊥ =1.0 m 2 s -1 and χ ⊥ =3.0 m 2 s -1 , and the impurity perpendicular transport coefficient is set to D imp =1.0 m 2 s -1 .

[0162] Based on the above parameters, the EMC3-EIRENE program is used to solve the fluid equations of plasma and impurity transport. At the same time, according to the positions of the CCD camera and the projection screen, the spectral radiation distribution on the projection screen is calculated, and the results are shown in Figure 2 . Among them, (a) is the captured image of the CCD camera, (b) is the spectral radiation distribution of divalent lithium impurities on the projection screen calculated using the present invention, and (c) is the D α spectral radiation distribution on the projection screen calculated by the present invention. It can be seen that the projection screen image calculated by the present invention is highly consistent with the image captured by the CCD camera, verifying the correctness and rationality of the calculation of the present invention.

Claims

1. A three-dimensional chord integral calculation method for spectral radiation of a magnetic confinement device, characterized in that The steps are as follows: S1. Construction of the field-aligned grid of the three-dimensional boundary plasma-neutral particle transport code EMC3-EIRENE; S2. Solving the fluid equations of plasma and impurity transport using the EMC3-EIRENE code; S3. Establishment of the coordinate system for the three-dimensional chord integral calculation of spectral radiation; S4. Calculation of the projection distribution of spectral radiation of different valence states of plasma and impurities in a magnetic confinement fusion device.

2. The three-dimensional chord integral calculation method of the spectral radiation of a magnetic confinement device according to claim 1, wherein, Step S1 specifically includes: S1.

1. Construction of the two-dimensional basic calculation grid; Based on the two-dimensional equilibrium magnetic field data measured experimentally for the magnetic confinement fusion device and the spatial position information of the device target plate, the two-dimensional calculation regions of the plasma and neutral particles in the EMC3-EIRENE program are defined respectively in the two-dimensional (r,z) plane; subsequently, the positions of the X-point and the core-scrape-off layer boundary are found respectively within the two-dimensional calculation region, and then the entire two-dimensional calculation region is divided into six sub-regions in the (r,z) plane, which are the core, the main scrape-off layer, the strong-field side scrape-off layer, the weak-field side scrape-off layer, the upper private flux region, and the lower private flux region in sequence; within each sub-region, according to the spatial scale of the device, the contour lines of different poloidal fluxes ψ p are selected, that is, the flux surfaces, and then the grid points are evenly divided along the flux surfaces, and then the two-dimensional basic calculation grid in the (r,z) plane is obtained; S1.

2. Construction of the three-dimensional field-aligned grid; Based on the two-dimensional coordinate system (r, z), a third dimension, the toroidal direction, is introduced. This forms a three-dimensional right-handed cylindrical coordinate system. In the three-dimensional right-handed cylindrical coordinate system, according to the poloidal current function F in the two-dimensional equilibrium magnetic field data pol and the poloidal magnetic flux ψ p , the magnetic field at each grid point on the two-dimensional (r, z) plane is calculated. Among them, μ0 = 4π×10 -7 N·A -2 is the magnetic permeability of vacuum; in the EMC3-EIRENE program, in order to ensure the efficiency of the calculation, the toroidal needs to be divided into different toroidal calculation regions; within different toroidal calculation regions, based on the magnetic field of the obtained grid points, it is extended along the magnetic field direction to obtain the expression of the magnetic field line in the three-dimensional right-handed cylindrical coordinate system as: After sorting out, the differential equations for the change of the coordinate positions of the magnetic field lines with variation are obtained: Subsequently, based on the above equation, in the toroidal direction the fourth-order Runge-Kutta method is used to integrate the magnetic field lines to obtain all grid points within each toroidal calculation region; during the integration of the magnetic field lines, when the magnetic field lines approach the target plate, due to the high gradient of plasma parameters, the grid needs to be refined to ensure the reliability and accuracy of the calculation results; Between different toroidal calculation regions, the EMC3-EIRENE code uses the fast reversible magnetic field line inversion technique to perform fast high-fidelity magnetic field line reconstruction to ensure the calculation coherence of different toroidal calculation regions.

3. A method for calculating the three-dimensional chord integral of the spectral radiation of a magnetic confinement device according to claim 1, characterized in that Step S2 specifically includes: S2.

1. Establishment of the fluid equations of plasma and impurity transport; In the non-equilibrium state, the kinetic behaviors of plasma and impurities are described by the Boltzmann equation, and its general form is: Among them, is the particle distribution function at time t at position with velocity in the phase space, is the gradient operator in the position space, is the gradient operator in the velocity space, is the sum of the external forces acting on the particle, m represents the mass of the particle, and C a is the source term caused by particle collisions; In a magnetic confinement fusion device, the electromagnetic force acting on charged particles is much greater than gravity and other external forces. Therefore It is expressed as: where q is the particle charge, is the electric field strength, is the magnetic induction intensity, c = 3×10 8 m / s is the speed of light in vacuum; After substituting the above formula into the Boltzmann equation, perform an integration of the zeroth to second moments on the velocity space of the particle distribution function to obtain respectively: where n is the particle number density, is the particle flow velocity, and T is the particle temperature; Performing velocity space integration on the Boltzmann equation and substituting it into the zero-order moment equation to obtain the particle continuity equation: Multiply both sides of the particle continuity equation by the particle mass m and velocity Then integrate over the velocity space and substitute into the first moment equation to obtain the particle momentum conservation equation: where p is the pressure, is the gradient symbol, represent the unit vectors in the x, y, and z directions respectively, and ▽p represents the pressure gradient, is the viscous stress tensor, defined as is the single-particle random velocity, is the identity matrix; Multiply both sides of the particle continuity equation by the particle energy After integration, the particle energy conservation equation is obtained: wherein is the conductive heat flux, defined as Based on the above particle continuity, momentum, and energy conservation equations, the transport process of particles in the fusion device is divided into the transport process parallel to the magnetic field line and the transport process perpendicular to the magnetic field line, and they are respectively applied to electrons and ions to obtain the fluid equations of plasma and impurity transport solved by the EMC3-EIRENE code: Among them, the subscripts e and i represent background electrons and ions respectively, zi represents the valence states of different types of background impurity particles, and the symbols || and ⊥ represent the directions parallel and perpendicular to the magnetic field respectively; for the plasma equations: η || , κ i and κ e respectively represent the particle parallel transport coefficients, the parallel transport coefficients of ion and electron energies, which are obtained from experimental experience; D ⊥ , χ i and χ e respectively represent the particle perpendicular transport coefficients, the perpendicular transport coefficients of ion and electron energies, which are free parameters obtained through experimental diagnosis. In addition, η ⊥ = mnD ⊥ ; S p and S m are respectively the plasma ionization source and the momentum loss caused by charge exchange. S ei and S ee are the energy sources of ions and electrons respectively, which are all provided to EMC3 by the EIRENE program; T e represents the electron temperature, T i represents the ion temperature, and k = 1.380649×10 -23 J / K is the Boltzmann constant; for the impurity equation: D imp is the impurity perpendicular transport coefficient, and S zi is the impurity ion source with valence state zi caused by the ionization and recombination of impurities; s represents the coordinate along the magnetic field direction, τ s is the collision time of impurity particles with the background plasma, and f fri is the friction coefficient; the right side of the momentum conservation equation successively represents the pressure gradient force, electric field force, friction force, electron thermal gradient force, and ion thermal gradient force acting on the impurity particles; in addition, α e and β i satisfy: α e = 0.71zi 2 Among them, is the reduced mass of impurity particles; S2.

2. Setting of the boundary conditions of the calculation region; The particle, momentum, and energy boundary conditions on the target plate wall are all attenuation boundary conditions, and the attenuation length is selected as an appropriate value according to different magnetic confinement fusion devices. At the same time, the Bohm boundary condition is applied to the target plate and the plasma boundary; for the core particle boundary, a fixed particle flux, a fixed upstream density, or gas puffing and pumping balance are selected. The momentum boundary condition selects the zero momentum boundary condition, that is, the reflection boundary, and the energy boundary condition selects the core energy input, which is consistent with the absorption power of the experiment, and the energy is proportionally distributed to electrons and ions; S2.

3. Solving the fluid equations of plasma and impurity transport and determining the transport coefficients; Under the regional boundary conditions of step S2.2, use the EMC3-EIRENE program to solve the fluid equations of plasma and impurity transport. According to the experimentally measured profiles, fit the perpendicular transport coefficients D ⊥ , χ i and χ e of ions and electrons, as well as the perpendicular transport coefficient D imp of impurities. After multiple iterations of convergence, until the transport coefficients with the smallest error from the experimental profiles are obtained, and then the spatial density temperature distributions of the plasma and impurities at these transport coefficients are obtained.

4. A method for calculating the three-dimensional chord integral of spectral radiation of a magnetic confinement device according to claim 1, characterized in that Step S3 specifically includes: S3.

1. Determination of the camera observation direction; The steps for establishing the coordinate system for the three-dimensional chord integral calculation of spectral radiation are as follows: Denote the central position of the vacuum wall of the magnetic confinement fusion device as At the same time, define this point as the central position of the integral projection screen, and denote the position of the experimental diagnostic camera as Convert the point and position coordinates in the three-dimensional right-handed cylindrical coordinate system into position coordinates in the rectangular coordinate system, then we have p1 - p0 is the camera observation direction; S3.

2. Construction of the integral projection screen and the calculation coordinate system; Define an integral projection screen, i.e., a screen for the deposition of the spectral radiation energy of plasma and impurities; on the plane perpendicular to the camera observation direction in step S3.1, establish an integral projection screen passing through point p0; the horizontal a and vertical b directions of the integral projection screen are respectively represented as toroidal and poloidal, and p0 is taken as the coordinate origin of the integral projection screen; denote the basis vectors in the toroidal and poloidal directions of the integral projection screen as v a and v b , the basis vectors in the two directions are perpendicular to each other and simultaneously perpendicular to the camera observation direction, then the direction vectors v′ a and v b in the directions of v a and v′ b have the following relationship: Among them, represents the direction vector in the vertical direction of the magnetic confinement fusion device; substituting the two points p0 and p1 into the above formula, the toroidal and poloidal basis vectors in the normalized form in the rectangular coordinate system are obtained: If p0 and p1 are on the same plane, it can be further simplified into the following form in a three-dimensional right-handed cylindrical coordinate system: where, ΔR = R1 - R0; thus, any point p2 on the integral projection screen can be represented by the basis vectors v a and v b and the three-dimensional spectral radiation chord integral calculation coordinate system (a, b), that is: p2(a,b) = p0 + av a + bv b At the same time, any point p on the observation chord in the camera observation direction can be expressed by the distance l between p and p1:

5. A method for calculating the three-dimensional chord integral of spectral radiation of a magnetic confinement device according to claim 1, characterized in that, Step S4 specifically includes: S4.

1. Establishment of the spectral radiation formula on the integral projection screen; The establishment process of the spectral radiation formula on the integral projection screen is as follows: Assume that a visible light source with continuity is deposited on the above integral projection screen. The radiation deposited on the integral projection screen along the true observation chord can form a radiation projection plan view, that is, a three-dimensional chord integral plasma and impurity spectral radiation distribution map. The integral projection screen is divided into finite widths Δa and Δb in the poloidal and toroidal directions. Assume that the effective aperture of the observation camera lens is D d , then the three-dimensional radiation quantity F(a, b) can be obtained by integrating the local radiation quantity f(p(a, b; l)) along the true observation chord, that is: Among them, the volume element dV can be expressed as dV = ΔSdl, and ΔS is the area element corresponding to the position of point p on the real observation chord, which can be expressed by Δa and Δb as: Combining the previous derivations and substituting the relevant quantities into the three-dimensional radiation quantity expression, the number of photons deposited on each finite width in the radiation projection plan view is obtained as: Express a and b as a = (i + 1 / 2)Δa and b = (j + 1 / 2)Δb respectively, where i and j are the element numbers in the circumferential and polar directions respectively. Then, the number of photons deposited at any element (i, j) in the radiation projection plan view can be expressed as: F i,j = F((i + 1 / 2)Δa, (j + 1 / 2)Δb); S4.

2. Calculation of spectral radiation in a magnetic confinement fusion device; Combined with the spatial density temperature distributions of the plasma and impurities calculated by the EMC3-EIRENE program in step S2 and the photon emission coefficients in the OPEN-ADAS database, calculate the local radiation quantity distribution f(p(a, b; l)) in space; substitute the local radiation quantity distribution into the above photon number deposition formula, and at the same time ensure that Δt, Δp, and Δl are less than the grid size of the EMC3-EIRENE program, then the spectral radiation projection plan view of the plasma and impurities with different valence states can be obtained.

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