CN112966453B - Simulation method for EAST tokamak radio frequency waveguide induced electronic temperature evolution - Google Patents
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Abstract
The invention discloses a simulation method for EAST tokamak radio frequency waveguide induced electron temperature evolution. When numerical simulation radio frequency wave is injected into an EAST tokamak device to cause an electronic temperature evolution process, the form of a heating source is determined according to hardware parameters of a radio frequency system, the evolution of the disturbance electronic temperature under a given magnetic field configuration is calculated according to an electronic transport equation under the tokamak configuration, a plasma resistor is corrected according to the evolved electronic temperature, the evolution of the magnetic field configuration is calculated by adopting the corrected resistor, the evolution of the disturbance electronic temperature is continuously calculated according to the magnetic field configuration, and repeated calculation is carried out to achieve the simulation of long-time evolution. The invention realizes the evolution of the electron temperature caused by simulating the radio frequency wave under the EAST tokamak real three-dimensional magnetic field configuration, obtains the distribution condition of the disturbance electron temperature at any moment in the three-dimensional space, makes up the defect of low precision of experimental measurement time, and has high calculation efficiency and strong numerical stability.
Description
Technical Field
The invention relates to numerical simulation of tokamak device discharge in the field of magnetic confinement controllable nuclear fusion, in particular to a simulation method for EAST tokamak radio frequency waveguide induced electron temperature evolution.
Background
The energy problem is a troublesome problem which is commonly faced by all people at present. At present, the energy used by people is mainly fossil fuel energy. Fossil fuels have a limited energy reserve and produce a large amount of harmful gases during combustion, thereby causing serious environmental pollution problems. To solve the energy problem fundamentally, the current method accepted by the scientific community is controllable nuclear fusion. In order to realize the controllable nuclear fusion, many proposals have been made, among which the experimental device which is most promising to be realized first is the tokamak device in the magnetic confinement method. Scientists in China are actively investing in the research of tokamak. At present, EAST super loop (EAST) of Anhui fertilizer in China is a full-superconducting Tokamak device, and all operation parameters are in the front of the world. To achieve steady state operation of EAST tokamak devices, the magnetic fluid instability in the tokamak configuration must be controlled. Wherein the core plasma can be heated by means of radio frequency wave injection, and the resistivity of the plasma is reduced. This suppresses resistive magnetic fluid instability.
In the EAST Tokamak discharge experiment, when radio frequency waves are injected, the distribution of the temperature of disturbance electrons in the space needs to be detected through soft X-ray diagnostic equipment, so that the instability of the magnetic fluid is better controlled. However, the electron temperature distribution measured by this method has limited space-time accuracy, and particularly, the time accuracy is not high enough, and it is difficult to satisfy the requirement of real-time measurement. Therefore, the three-dimensional spatial distribution of the temperature of the disturbance electrons at any time needs to be calculated by means of auxiliary processing of numerical simulation. Meanwhile, the magnetic field configuration in the experiment evolves along with time, and the evolution of the electronic temperature profile is closely related to the magnetic field configuration. Therefore, a simulation method capable of simulating the self-consistent nonlinear evolution of the temperature of the disturbance electrons caused by the injection of the radio frequency wave along the true three-dimensional magnetic field configuration along with time is needed. The method provided by the invention can exactly meet the requirement, can accurately describe the three-dimensional space distribution condition of the electronic temperature profile at any moment in higher time precision, has high calculation efficiency and strong numerical stability, and is an accurate and efficient numerical simulation method.
Disclosure of Invention
The invention aims to make up the defect of low time precision when the three-dimensional space distribution of the disturbed electron temperature is caused by measuring radio frequency waves in experiments, realize the nonlinear evolution of the simulated electron temperature under the EAST tokamak real three-dimensional magnetic field configuration, and obtain the distribution condition of the disturbed electron temperature in the three-dimensional space at any time with high time precision.
The technical scheme of the invention is as follows:
a simulation method for EAST tokamak radio frequency waveguide induced electron temperature evolution realizes self-consistent nonlinear evolution of an electron temperature profile under EAST real magnetic field configuration, can describe the space distribution condition of disturbance electron temperature by adopting a mode with higher time precision, has high calculation efficiency and strong numerical stability, and specifically comprises the following steps:
step 1: according to the geometric configuration of the EAST tokamak device, grid division is carried out on a core high-temperature plasma region in a discharge experiment, and physical quantities generated in the numerical simulation process are stored through nodes obtained through grid division;
step 2: according to the RF system used by the EAST Tokamak device, a Gaussian function is used to describe the RF wave heating source S ec The concrete form is as follows:
wherein R is a horizontal coordinate, Z is a vertical coordinate,
as a circumferential coordinate, S 0 The amplitude of the heating source can be calculated according to the transmitting power of a radio frequency system, R 0 、Z 0 And
respectively the horizontal direction, the vertical direction and the circumferential direction of the RF wave action region, Delta R d 、ΔZ d And
respectively horizontal direction, vertical direction and circumferential action width.
Initializing relevant parameters of a heating source according to experimental parameters such as the physical size of an antenna of the radio frequency system, the transmitting power of the radio frequency system and the like, wherein the relevant parameters comprise a spatial distribution function, an intensity amplitude value, a heating area and the like of the heating source. And initializing basic parameters such as a transport coefficient in an electron heat transport equation under the Tokamak configuration and a Sibirez resistance coefficient in a Sibirez resistance equation according to the experimental discharge parameters. Simultaneously obtaining the disturbance electron temperature delta T at the initial moment e (0) ；
And 3, step 3: the initial magnetic field configuration (namely the distribution information of the magnetic flux function in the three-dimensional space) is measured by adopting diagnostic equipment such as a magnetic detection ring, a magnetic flux ring and the like on an EAST Tokamak device, and a cubic spline interpolation method is usedThe measured magnetic flux function is converted to the grid divided in step 1, so as to obtain the magnetic flux function psi at the initial moment (0) And stored in the grid nodes.
And 4, step 4: calculating the evolution of the temperature of the disturbance electron along the magnetic field configuration at the current moment along with the time according to the electron heat transport equation under the Tokamak configuration, and calculating to obtain the temperature delta T of the disturbance electron at the next moment e (1) 。
The heat transport equation solved here is:
wherein, T e Is electron temperature and T e ＝T e0 +δT e ，T e0 And δ T e Equilibrium electron temperature and disturbance electron temperature, respectively, t is time, v is magnetofluid velocity, k // And kappa ⊥ The transport coefficients of electrons along the parallel and vertical magnetic lines of force respectively,// and ^ subscript denote the parallel and vertical directions respectively, S ec Representing a heating source.
And 5: according to the electron temperature of the current moment obtained by calculating the electron heat transport equation in the step 4, calculating the plasma resistance eta of the current moment according to the sibez resistance equation (1) 。
The stezizer resistance equation solved here is:
where eta is the plasma resistivity, kappa S Is the sbez resistivity.
And 6: substituting the plasma resistance obtained in the step 5 into the magnetic fluid equation, numerically calculating the magnetic flux at the next moment and obtaining the magnetic flux psi after nonlinear evolution (1) 。
The evolution equation of the magnetic flux solved here is:
where ψ is the magnetic flux, φ is the electric potential, η is the plasma resistivity, j is the total plasma current, j is the plasma current bs Is the bootstrap current.
And 7: will disturb the electron temperature deltaT e Outputting the three-dimensional space distribution information to a file for storage;
and 8: calculating the magnetic field configuration at the current moment according to the magnetic flux obtained in the step 6, and repeating the steps 4-8 to obtain the three-dimensional space distribution delta T of the disturbance electron temperature at any moment e (n) 。
Has the advantages that: the method realizes the nonlinear evolution of the electron temperature profile after the injection of the numerical simulation radio frequency wave under the EAST tokamak real three-dimensional magnetic field configuration, can obtain the distribution condition of the disturbance electron temperature at any moment in a three-dimensional space, makes up the defect of low experimental measurement time precision, has high calculation efficiency and strong numerical stability, and is a stable and efficient numerical simulation method.
Drawings
FIG. 1 is a schematic cross-sectional view of an EAST tokamak apparatus to which the present invention is applicable.
FIG. 2 is a cross-sectional view of the initial magnetic field configuration used in the numerical simulation of the present invention.
FIG. 3(a) is a cross-sectional view of the simulation result of the temperature evolution of the perturbed electrons at a time 2ms after the injection of the RF wave in the EAST tokamak apparatus to which the present invention is applied.
FIG. 3(b) is a cross-sectional view of the simulation result of the temperature evolution of the perturbed electrons at 4ms after the injection of the RF wave in the EAST tokamak apparatus.
FIG. 4 is a main flow chart for numerically simulating the temperature evolution of the perturbed electrons according to the present invention.
Detailed Description
The following further describes a specific embodiment of the present invention with reference to the drawings and technical solutions.
The EAST tokamak device has a cross-sectional configuration as shown in fig. 1, where the core location is the region containing the plasma during the experimental discharge. EAST tokamak is equipped with a soft X-ray system to measure the spatial distribution of perturbed electron temperature. The core plasma region is first gridded according to the EAST geometry shown in fig. 1. In EAST tokamak discharge experiments, suppression of magnetic islands is one of the main effects of rf wave heating, so the initial magnetic field configuration usually includes a magnetic island structure, as shown in fig. 2, where magnetic lines of force are coupled to form a magnetic island chain structure including three magnetic islands in one period of polar direction. The rf wave injection site is generally centered on the magnetic island. The electron temperature of disturbance caused by radio frequency wave injection can be subjected to self-consistent nonlinear evolution along a specific magnetic field configuration, and finally, steady-state distribution is achieved in space. This embodiment describes the heating source using a gaussian function. EAST experiments usually use electron cyclotron emission systems to generate rf waves, and gaussian functions can better describe the heating source. Then, the heating source is initialized and the initial magnetic field information and the initial electron temperature spatial distribution information are stored in the grid nodes. And calculating the nonlinear evolution of the temperature of the disturbance electrons along a specific magnetic line according to an electron heat transport equation in the Tokamak configuration. And calculating the resistivity of the plasma at the moment according to the electron temperature at the current moment through a Spanish resistance equation. Substituting the calculated plasma resistivity into a magnetic flux evolution equation to calculate the correction of the magnetic field at the last moment by the injection of the radio frequency wave, and obtaining the corrected magnetic field. And finally, taking the corrected magnetic field as the magnetic field configuration at the current moment, calculating the nonlinear evolution of the temperature of the disturbed electrons, and repeating the previous steps for multiple times to obtain the three-dimensional stable distribution of the electron temperature at any moment with high time precision, as shown in fig. 3, wherein a cross section diagram of the spatial distribution of the disturbed electron temperature at two moments is shown.
The specific implementation steps are as follows:
step 1: according to the geometric configuration of the EAST tokamak device, grid division is carried out on a core high-temperature plasma region in a discharge experiment, and physical quantities generated in the numerical simulation process are stored through nodes obtained through grid division;
step 2: mining according to EAST tokamak apparatusRF system for use therein, where the RF wave heating source S is described by a Gaussian function ec The concrete form is as follows:
wherein R is a horizontal coordinate, Z is a vertical coordinate,
as a circumferential coordinate, S 0 The amplitude of the heating source can be calculated according to the transmitting power of a radio frequency system, R 0 、Z 0 And
the horizontal direction, the vertical direction and the circumferential direction of the radio frequency wave action region, delta R d 、ΔZ d And
respectively horizontal direction, vertical direction and circumferential action width.
Initializing relevant parameters of a heating source according to experimental parameters such as the physical size of an antenna of the radio frequency system, the transmitting power of the radio frequency system and the like, wherein the relevant parameters comprise a spatial distribution function, an intensity amplitude value, a heating area and the like of the heating source. And initializing basic parameters such as a transport coefficient in an electron heat transport equation under the Tokamak configuration and a Sibirez resistance coefficient in a Sibirez resistance equation according to the experimental discharge parameters. The specific parameters used in this example are as follows:
S 0 ＝1.5MW、R 0 ＝1.9m、Z 0 ＝0.3m、
ΔR d ＝0.1m、ΔZ d 0.1m and
in this embodiment, the RF system is turned on at the initial time becauseThe temperature delta T of the disturbance electrons caused by the radio frequency system at the initial moment e (0) Is zero;
and step 3: measuring initial magnetic field configuration (namely distribution information of the magnetic flux function in a three-dimensional space) by adopting diagnostic equipment such as a magnetic probe ring and a magnetic flux ring on an EAST tokamak device, and converting the measured magnetic flux function to the grid divided in the step 1 by a cubic spline interpolation method, thereby obtaining the magnetic flux function psi at the initial moment (0) And stored in grid nodes, the magnetic flux function psi (0) The contour plot is shown in figure 2.
And 4, step 4: calculating the evolution of the temperature of the disturbance electron along the magnetic field configuration at the current moment along with the time according to the electron heat transport equation under the Tokamak configuration, and calculating to obtain the temperature delta T of the disturbance electron at the next moment e (1) 。
The heat transport equation solved here is:
wherein, T e Is electron temperature and T e ＝T e0 +δT e ，T e0 And δ T e Equilibrium electron temperature and disturbance electron temperature, respectively, t is time, v is magnetofluid velocity, k // And kappa ⊥ The transport coefficients of electrons along the parallel and vertical magnetic lines of force respectively,// and ^ subscript denote the parallel and vertical directions respectively, S ec Representing a heating source.
The specific parameters used in this example are as follows:
v～400m/s，κ // ＝1.6×10 6 m 2 s and kappa ⊥ ＝1.6×10 -3 m 2 /s，S ec Can be calculated by the data in step 2.
And 5: according to the electron temperature of the current moment obtained by calculating the electron heat transport equation in the step 4, calculating the plasma resistance eta of the current moment according to the sibez resistance equation (1) 。
The stezizer resistance equation solved here is:
where eta is the plasma resistivity, kappa S When the value is 1.0, the sbuzer resistivity is obtained.
Step 6: substituting the plasma resistance obtained in the step 5 into the magnetic fluid equation, numerically calculating the magnetic flux at the next moment and obtaining the magnetic flux psi after nonlinear evolution (1) 。
The evolution equation of the magnetic flux solved here is:
where ψ is the magnetic flux, φ is the potential, the potential is measured by Langmuir probe, η is the plasma resistivity, j is the total plasma current, j is the plasma resistivity bs For bootstrap currents, the current profile can be obtained by inversion of the equilibrium profile.
And 7: will disturb the electron temperature deltaT e Outputting the three-dimensional space distribution information to a file for storage;
and 8: calculating the magnetic field configuration at the current moment according to the magnetic flux obtained in the step 6, and repeating the steps 4-8 to obtain the three-dimensional space distribution delta T of the disturbance electron temperature at any moment e (n) 。
In this example, dt is 1 × 10 -9 s time steps for simulation (i.e. 1X 10 simulation time passes for each round of 4-8 steps) -9 s), passing through 2X 10 6 The round simulation can obtain the disturbance electron temperature space distribution at the time t-2 ms, as shown in fig. 3(a), and then 2 × 10 6 The round simulation can obtain the situation of the disturbance electron temperature space distribution at the moment t-4 ms, as shown in fig. 3 (b).
The above description is further detailed in connection with the preferred embodiments of the present invention, and it is not intended to limit the practice of the invention to these descriptions. It will be apparent to those skilled in the art that various modifications, additions, substitutions, and the like can be made without departing from the spirit of the invention.
Claims (1)
1. A simulation method for EAST tokamak radio frequency waveguide-induced electron temperature evolution realizes self-consistent nonlinear evolution of an electron temperature profile after radio frequency wave injection under a real EAST tokamak three-dimensional magnetic field configuration, obtains an electron temperature profile at any moment and provides an electron temperature spatial distribution condition; the method is characterized by comprising the following steps:
step 1: according to the geometric configuration of the EAST tokamak device, grid division is carried out on a core high-temperature plasma region in a discharge experiment, and physical quantities generated in the numerical simulation process are stored through nodes obtained through grid division;
step 2: according to the radio frequency system adopted by the EAST tokamak device, a Gaussian function is adopted to describe the radio frequency wave heating source S ec The concrete form is as follows:
wherein, R is a horizontal coordinate; z is a vertical coordinate;
is a circumferential coordinate; s 0 Calculating the amplitude of the heating source according to the transmitting power of the radio frequency system; r 0 、Z 0 And
respectively the horizontal direction, the vertical direction and the circumferential direction of the RF wave action region, Delta R d 、ΔZ d And
the action widths in the horizontal direction, the vertical direction and the annular direction are respectively;
initializing relevant parameters of a heating source according to the physical size of an antenna of the radio frequency system and the transmitting power of the radio frequency system, wherein the relevant parameters comprise a spatial distribution function, an intensity amplitude and a heating area of the heating source; initializing a transport coefficient in an electronic heat transport equation under a Tokamak potential form and a Sibirez resistance coefficient in a Sibirez resistance equation according to experimental discharge parameters; simultaneously obtaining the disturbance electron temperature delta T at the initial moment e (0) ；
And step 3: measuring the initial magnetic field configuration, namely the distribution information of the magnetic flux function in the three-dimensional space by adopting a magnetic detection ring and a magnetic flux ring on an EAST tokamak device, and converting the measured magnetic flux function to the grids divided in the step 1 by a cubic spline interpolation method, thereby obtaining the magnetic flux function psi at the initial moment (0) And stored in the grid nodes;
and 4, step 4: calculating the evolution of the temperature of the disturbance electron along the magnetic field configuration at the current moment along with the time according to the electron heat transport equation under the Tokamak configuration, and calculating to obtain the temperature delta T of the disturbance electron at the next moment e (1) ；
The heat transport equation solved is:
wherein, T e Is electron temperature and T e ＝T e0 +δT e ，T e0 And δ T e Equilibrium electron temperature and disturbance electron temperature, respectively, t is time, v is magnetofluid velocity, k // And kappa ⊥ The transport coefficients of electrons along the parallel and vertical magnetic lines of force respectively,// and ^ subscript denote the parallel and vertical directions respectively, S ec Represents a heating source;
and 5: according to the electron temperature of the current moment obtained by calculating the electron heat transport equation in the step 4, calculating the plasma resistance eta of the current moment according to the sibez resistance equation (1) ；
The stezizer resistance equation solved is:
where eta is the plasma resistivity, kappa S Has a Sibirez resistivity;
step 6: substituting the plasma resistivity obtained in the step 5 into a magnetic flux evolution equation, calculating the magnetic flux at the next moment and obtaining the magnetic flux psi after nonlinear evolution (1) ；
The magnetic flux evolution equation solved is:
where ψ is the magnetic flux, φ is the electric potential, η is the plasma resistivity, j is the total plasma current, j is the plasma current bs Is a bootstrap current;
and 7: will disturb the electron temperature deltaT e Outputting the three-dimensional space distribution information to a computer for storage;
and 8: calculating the magnetic field configuration at the current moment according to the magnetic flux obtained in the step 6, and then repeating the steps 4-8 to obtain the disturbance electron temperature three-dimensional space distribution delta T at any moment e (n) 。
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