CN115512791A - Particle evolution simulation method based on multi-component plasma radiation effect in tokamak - Google Patents
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Abstract
The invention discloses a particle evolution simulation method based on multi-component plasma radiation effect in tokamak, and belongs to the technical field of magnetic confinement controlled nuclear fusion. The evolution of the impurity density distribution, the electron density distribution and the ion density distribution is firstly calculated, then the continuous radiation and the radiation of the radiation are calculated, and then various plasma radiations are accurately added in the magnetic island. And then calculating the magnetic field configuration under the plasma radiation correction, and continuously calculating the total plasma radiation and the evolution of related parameters under the advanced magnetic field configuration, so that the calculation is repeated, and the simulation effect of long-time evolution is achieved. The invention not only realizes the calculation of real-time dynamic distribution of impurities, electrons and ions, but also can calculate the evolution of various plasma radiations under the true three-dimensional magnetic field configuration so as to obtain the plasma related parameter profile at any moment; and simultaneously, the space distribution condition of plasma radiation and the instability condition of the magnetic fluid under the advanced magnetic field configuration are more accurately described.
Description
Technical Field
The invention belongs to the technical field of magnetic confinement controlled nuclear fusion, and particularly relates to a particle density distribution evolution method for multi-component plasma radiation effect in tokamak.
Background
In recent years, productivity and production technology have been effectively improved due to the rapid increase of the world population, and thus human consumption of energy has been rapidly increased, resulting in the increasing exhaustion of non-renewable fossil energy. Obviously, this has led to the gradual deterioration of the environment on which human beings rely for survival in recent years, which has resulted in the rapid aggravation of the greenhouse effect, and the creation of abnormal weather and severe natural phenomena. Therefore, the search and use of clean energy is a continuous pursuit of scientists. At present, nuclear energy is relatively efficient and pollution-free energy, and the nuclear energy strategy proposed in China is as follows: the thermal neutron reactor is built in the near term, the fast neutron reactor is used in the middle term, and the fusion reactor is built in the long term. The fusion reactor refers to magnetic confinement controlled nuclear fusion. To realize the magnetic confinement controlled nuclear fusion, the steady state operation mechanism is completely mastered, and meanwhile, the instability caused by the interaction between internal plasmas, the interaction between the plasmas and the wall of the tokamak and other complex problems which can promote energy loss to cause the discharge to be extinguished are fully understood and solved. Therefore, it is important to study the tokamak energy loss in the most advanced magnetic field configurations.
Advanced magnetic field configurations can more easily confine the plasma, thereby achieving stable long pulse discharge and ultimately its commercial value. In tokamak plasma, plasma radiation, which is one of the principal energy loss mechanisms of tokamak, refers to electromagnetic waves emitted from the plasma in each frequency band. The spectrum of the radiation mainly comprises a continuous spectrum and a line spectrum, and the corresponding radiation also comprisesIt is called continuous radiation and line radiation. The main representatives of continuous radiation are bremsstrahlung radiation, which mainly includes electron cyclotron radiation and characteristic radiation. The characteristic radiation is mainly from impurity ion radiation. In general, the radiation spectrum covers all bands from infrared to X-rays. In future large magnetically confined nuclear fusion devices, high z eff Is very important and has a strong influence on the magneto-hydrodynamic instability in the plasma. Therefore, it is important to study plasma radiation and clearly grasp characteristics of the plasma radiation to realize a long pulse discharge. Therefore, the invention provides a simulation method which can be used for coupling a plurality of plasma radiation effects together under the condition of the configuration of the advanced magnetic field, simultaneously considers the influence of the distribution evolution of impurity particles, electrons and ions on the total radiation of the plasma, thereby carrying out numerical simulation research on the aspect of magnetohydrodynamic instability in Tokamak discharge.
Disclosure of Invention
In order to fill the technical blank of numerical simulation of plasma radiation in tokamak, the invention provides a simulation method for particle density distribution evolution of plasma radiation in tokamak under an advanced magnetic field configuration, namely, particles used in plasma radiation are evolved along with time. The method can be well combined with experiments, real-time dynamic distribution of impurities, electrons and ions is obtained through calculation of impurity density distribution evolution, electron density distribution evolution and ion density distribution evolution, plasma radiation can be predicted and simulated more accurately, three-dimensional simulation of nonlinear evolution of plasma radiation is realized, further influence of the plasma radiation on Tokamak discharge under an advanced magnetic field configuration can be studied systematically, and meanwhile reference can be provided for experimental results of the plasma radiation.
The technical scheme adopted by the invention is as follows:
a particle evolution simulation method based on multi-component plasma radiation effects in tokamak realizes the evolution of electron, ion and impurity density distribution, further can obtain the nonlinear evolution of various plasma radiations under a real three-dimensional magnetic field configuration, and can also obtain the evolution condition of the plasma radiation at any time and the evolution section of related parameters of the plasma, thereby more accurately describing the spatial distribution condition of the tokamak plasma under the combined action of the various plasma radiations under an advanced magnetic field configuration. The method specifically comprises the following steps:
step 1: the plasma area in the discharge experiment of the tokamak device is divided into grids, and the total plasma radiation value, the magnetic flux function value and the like obtained in the plasma radiation evolution process can be stored by the divided grid nodes.
Step 2: respectively calculating initial impurity density distribution according to highest ionization state, far infrared interferometer and Thomson scattering in experiment
Initial electron density distribution
And initial electron temperature distribution
And step 3: obtaining the configuration of the initial magnetic field by adopting equipment such as a magnetic flux loop and the like in Tokamak discharge, and calculating the initial magnetic flux psi by a numerical simulation method and the like (0) And stored in the grid nodes.
And 4, step 4: the initial magnetic flux psi (0) Initial impurity density distribution
Initial electron density distribution
And initial ion density distribution
Respectively carrying out calculation in a magnetofluid equation, an impurity density distribution evolution equation, an electron density distribution evolution equation and an ion density distribution evolution equation to respectively obtain the magnetic flux psi at the next moment (1) Impurity density distribution
Electron density distribution
And ion density distribution
The method comprises the following specific steps:
the evolution equation of the impurity density distribution is:
the evolution equation of the electron density distribution is:
the evolution equation for the ion density distribution is:
wherein n is z Is the particle density distribution of the impurity, n e Denotes the electron density distribution, n i Represents an ion density distribution; phi is the potential and t is the time; d z|| And D z⊥ Impurity diffusion coefficients in the parallel direction and the perpendicular direction of the impurity, respectively; d e|| And D e⊥ Impurity diffusion coefficients in the parallel direction and the perpendicular direction of electrons, respectively; d i|| And D i⊥ Impurity diffusion coefficients in the parallel direction and the perpendicular direction of the ions, respectively;
and
gradient operators in the parallel direction and the vertical direction respectively; s radz Is a source term of impurities, S rade Being a source item of electrons, S radi Is the source term of the ions.
The specific calculation method of the evolution equation of the impurity density distribution, the electron density distribution and the ion density distribution is as follows:
step 4.1: the impurity density distribution, electron density distribution and ion density distribution are expressed by a spectrum method:
wherein, (m, n) is the module of the circumferential direction and the polar direction; r 0 Is the large radius of tokamak; theta is a polar angle; z represents the column direction; f is the particle distribution, including impurity density distribution, electron density distribution, and ion density distribution.
Step 4.2: the time advance calculation of various particle distributions was performed using a two-step prediction-correction method. The calculation format of the two-step prediction-correction method is as follows:
and (3) prediction:
and (3) correction:
wherein H represents a magnetic flux and a magnetic currentParameters in the volume equation; v is the diffusion coefficient; t is time;
represents half a time step; dt represents a time step; the subscript rhs represents the right-hand term of the magnetofluid equation,
representing the gradient in the direction of the perpendicular magnetic field.
The evolution equations of impurity density distribution, electron density distribution and ion density distribution can be solved through the steps 4.1 and 4.2. The reason for adopting the spectrum method and the prediction-correction method is that the spectrum method and the prediction-correction method can more accurately, quickly and stably calculate the impurity density distribution, the electron density distribution and the ion density distribution at each moment, further couple the evolution equation of the impurity density distribution, the evolution equation of the electron density distribution and the evolution equation of the ion density distribution with the magnetofluid equation, and can calculate the distribution of impurities, electrons and ions at any moment in a self-consistent manner.
And 5: calculating the impurity density distribution according to the step 4, and when the impurity density distribution of the Tokamak core reaches a set threshold value, further opening a calculation module of plasma radiation, thereby calculating the evolution of the magnetic field configuration along with the time and obtaining the total radiation of the plasma at the moment
The method comprises the following specific steps:
step 5.1: according to electron temperature distribution T e The corresponding radiation cooling rate L (T) is calculated according to the value of (A) and the generated impurity species e ) The numerical value of (c).
And step 5.2: calculating the total radiation of the plasma, including continuous radiation and line radiation.
According to the formula of continuous radiation:
and electron cyclotron radiation formula:
P c ＝5.4×10 -25 n e B 2 T e erg s -1 cm -3
and the calculation formula of the characteristic line radiation:
P z ＝n e n z ∑L(T e )erg s -1 cm -3
calculating the magnitude of the three kinds of radiation, and then accumulating the three kinds of radiation to obtain the total radiation of the plasma
Wherein, P b Representing the magnitude of the continuous radiation, P c Representing the magnitude of electron cyclotron radiation, P z Represents the magnitude of the line radiation; z is a radical of eff Is the effective charge distribution.
And 6: coupling the calculated plasma total radiation into a magnetofluid equation, calculating the evolution of magnetic flux at a unit time step length, and obtaining the magnetic flux added with the evolution of the plasma total radiation
And 7: the total radiation of the plasma obtained by the calculation in the step 5 is used
And outputting the three-dimensional space distribution information.
And 8: according to the magnetic flux which is obtained after the calculation in the step 6 and takes the total radiation of the plasma into consideration
Further calculating the current magnetic field configuration, and further continuously repeating the steps 5-8 to obtain the total plasma radiation at any moment
And magnetic flux after total radiation of plasma
The invention has the beneficial effects that: the method can calculate the electron density distribution evolution, the ion density distribution evolution and the impurity density distribution evolution, can represent the evolution process of each parameter in the tokamak plasma in real time, and can calculate the radiation of various plasmas, thereby being capable of carrying out numerical simulation and analysis on the instability of the magnetofluid in the discharge of the tokamak device under the advanced magnetic field configuration, providing reference for the experimental result of the radiation of the plasmas, having high calculation efficiency and strong numerical stability, and being a stable and efficient numerical simulation method.
Drawings
Fig. 1 is a schematic diagram of a three-dimensional real magnetic field configuration of a tokamak experimental apparatus suitable for the present invention, including total radiation of magnetic islands and plasma.
FIG. 2 is a calculation result of the spatial distribution of the total plasma radiation over time, which is calculated by the method after the evolution of impurities, electrons and ions under the configuration of the advanced magnetic field; wherein (a) is 55 tau A Spatial distribution of radiation in time, (b) is 60. Tau A Spatial distribution of radiation in time, (c) is 65 τ A Spatial distribution of the radiation in time, (d) is 75. Tau A Spatial distribution of radiation. Wherein tau is A Is the alfen time.
FIG. 3 is a flow chart of the present invention for simulating and calculating various plasma radiation effects under advanced magnetic field configurations.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
The tokamak device is a toroidal device shaped like a tire, schematically shown in fig. 1, in which magnetic surfaces are nested one upon another, and magnetic lines of force are wound in circumferential and polar directions, which may generate magnetic islands in case of instability. Fig. 2 shows that the spatial scale of plasma radiation is continuously evolved and is increased along with the increase of the width of the magnetic island, and simultaneously, the impurity density distribution, the electron density distribution and the ion density distribution are evolved along with time, so that the method not only can calculate the evolution process of the impurity density distribution, the electron density distribution and the ion density distribution in tokamak along with time, but also can completely add various plasma radiations into the magnetic island, so that the plasma radiations are self-consistent and nonlinearly evolved along with the evolution of the width of the magnetic island.
The specific implementation steps are as follows:
step 1: the plasma area in the discharge experiment of the tokamak device is divided into grids, and the total plasma radiation value, the magnetic flux function value and the like obtained in the plasma radiation evolution process can be stored by the divided grid nodes.
Step 2: respectively calculating initial impurity density distribution according to highest ionization state, far infrared interferometer and Thomson scattering in experiment
Initial electron density distribution
And initial electron temperature distribution
And step 3: the configuration of an initial magnetic field is obtained by adopting a magnetic flux loop in Tokamak discharge, and the initial magnetic flux psi is obtained by calculating through a numerical simulation method (0) And stored in the grid nodes.
And 4, step 4: will initiate a magnetic flux v (0) Initial impurity density distribution
Initial electron density distribution
And initial ion density distribution
Respectively carrying out calculation in a magnetofluid equation, an impurity density distribution evolution equation, an electron density distribution evolution equation and an ion density distribution evolution equation to obtain the magnetic flux psi at the next moment (1) Impurity density distribution
Electron density distribution
And ion density distribution
The specific calculation method of the evolution equation of the impurity density distribution, the electron density distribution and the ion density distribution is as follows:
the evolution equation for the impurity density distribution is:
the evolution equation of the electron density distribution is:
the evolution equation for the ion density distribution is:
wherein n is z Is the particle density distribution of the impurity, n e Denotes the electron density distribution, n i Represents an ion density distribution; phi is the potential and t is the time; d z|| And D z⊥ Impurity diffusion coefficients in the parallel direction and the perpendicular direction of the impurity, respectively; d e|| And D e⊥ Impurity diffusion coefficients in the parallel direction and the perpendicular direction of electrons, respectively; d i|| And D i⊥ Impurity diffusion coefficients in the parallel direction and the perpendicular direction of the ions, respectively;
and
gradient operators in the parallel direction and the perpendicular direction respectively; s radz Is a source term of impurities, is a source term of electrons, S radi Is the source term of the ions.
The specific calculation method of the evolution equation of the impurity density distribution, the electron density distribution and the ion density distribution is as follows:
step 4.1: the impurity density distribution, electron density distribution and ion density distribution are expressed by a spectrum method:
wherein, (m, n) is the module of the circumferential direction and the polar direction; r is 0 Is the large radius of tokamak; theta is a polar angle; z represents the column direction; f is the particle distribution, including impurity density distribution, electron density distribution, and ion density distribution.
And 4.2: the time advance calculation of various particle distributions was performed using a two-step prediction-correction method. The calculation format of the two-step prediction-correction method is as follows:
and (3) prediction:
and (3) correction:
wherein H represents the magnetic flux and parameters in the magnetic fluid equation; v is the diffusion coefficient; t is time;
represents half a time step; dt represents a time step; the subscript rhs represents the right-hand term of the magnetofluid equation,
representing the gradient in the direction of the perpendicular magnetic field.
The evolution equations of impurity density distribution, electron density distribution and ion density distribution can be solved through the steps 4.1 and 4.2. The reason for adopting the spectrum method and the prediction-correction method is that the spectrum method and the prediction-correction method can more accurately, quickly and stably calculate the impurity density distribution, the electron density distribution and the ion density distribution at each moment, further couple the evolution equation of the impurity density distribution, the evolution equation of the electron density distribution and the evolution equation of the ion density distribution with the magnetofluid equation, and can calculate the distribution of impurities, electrons and ions at any moment in a self-consistent manner.
And 5: the impurity density distribution is calculated according to step 4, when the impurity density distribution of the tokamak core reaches a set threshold value (which needs to be determined according to the specific study, case, for example, n) z ＝1×10 -5 n e ) And then opening a calculation module of plasma radiation, thereby calculating the evolution of the magnetic field configuration along with the time and obtaining the total plasma radiation at the moment
The method comprises the following specific steps:
step 5.1: according to electron temperature distribution T e The corresponding radiation cooling rate L (T) is calculated according to the value of (A) and the generated impurity species e ) The numerical value of (c).
Step 5.2: calculating the total radiation of the plasma, including continuous radiation and line radiation.
According to the formula of continuous radiation:
and electron cyclotron radiation formula:
P c ＝5.4×10 -25 n e B 2 T e erg s -1 cm -3
and the calculation formula of the characteristic line radiation:
P z ＝n e n z ∑L(T e )erg s -1 cm -3
calculating the magnitude of the three kinds of radiation, and then accumulating the three kinds of radiation to obtain the total radiation of the plasma
Wherein, P b Representing the magnitude of the continuous radiation, P c Representing the magnitude of electron cyclotron radiation, P z Representing the magnitude of the radiation of the line, z eff Is the effective charge distribution.
Step 6: coupling the calculated plasma total radiation into a magnetofluid equation, calculating the evolution of magnetic flux under a unit time step length, and obtaining the magnetic flux added with the plasma total radiation evolution
And 7: the total radiation of the plasma obtained by the calculation in the step 5 is used
And outputting the three-dimensional space distribution information.
And step 8: according to the magnetic flux which is obtained after the calculation in the step 6 and takes the total radiation of the plasma into consideration
Further calculating the current magnetic field configuration, and further continuously repeating the steps 5-8 to obtain the total plasma radiation at any moment
And magnetic flux after total radiation of plasma
The above is a detailed description of an example of the present invention for numerical simulation calculation of multiple plasma radiations in an advanced magnetic field configuration tokamak, and the specific implementation of the present invention is not considered to be limited 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 (3)
1. A particle evolution simulation method based on multi-component plasma radiation effect in tokamak is characterized by comprising the following steps:
step 1: carrying out grid division on a plasma region in a discharge experiment of the tokamak device, and storing data of a total plasma radiation value and a magnetic flux function value obtained in the plasma radiation evolution process by the divided grid nodes;
and 2, step: respectively calculating initial impurity density distribution according to highest ionization state, far infrared interferometer and Thomson scattering in experiment
Initial electron density distribution
And initial electron temperature distribution
And step 3: obtaining the configuration of an initial magnetic field by adopting a magnetic flux loop in Tokamak discharge, and calculating to obtain an initial magnetic flux psi (0) And stored in the grid nodes;
and 4, step 4: the initial magnetic flux psi (0) Initial impurity density distribution
Initial electron density distribution
And a given initial ion density distribution
Respectively carrying into a magnetic fluid equation, an impurity density distribution evolution equation, an electron density distribution evolution equation and an ion density distribution evolution equation for calculation to respectively obtain the magnetic flux psi at the next moment (1) Impurity density distribution
Electron density distribution
And ion density distribution
The method comprises the following specific steps:
the evolution equation of the impurity density distribution is:
the evolution equation for the electron density distribution is:
the evolution equation for the ion density distribution is:
wherein n is z Is the particle density distribution of the impurity, n e Representing electron densityCloth, n i Represents an ion density distribution; phi is the potential and t is the time; d z|| And D z⊥ Impurity diffusion coefficients in the parallel direction and the perpendicular direction of the impurity, respectively; d e|| And D e⊥ Impurity diffusion coefficients in the parallel direction and the perpendicular direction of electrons, respectively; d i|| And D i⊥ Impurity diffusion coefficients in the parallel direction and the perpendicular direction of the ions, respectively;
and
gradient operators in the parallel direction and the vertical direction respectively; s radz Is a source term of impurities, S rade Being a source item of electrons, S radi A source term for an ion;
and 5: calculating the impurity density distribution according to the step 4, and when the impurity density distribution of the Tokamak core reaches a set threshold value, further opening a calculation module of plasma radiation, thereby calculating the evolution of the magnetic field configuration along with the time and obtaining the total radiation of the plasma at the moment
Step 6: coupling the calculated plasma total radiation into a magnetofluid equation, calculating the evolution of magnetic flux at a unit time step length, and obtaining the magnetic flux added with the evolution of the plasma total radiation
And 7: the total radiation of the plasma obtained by the calculation in the step 5 is used
Outputting the three-dimensional space distribution information;
and 8: according to the magnetic flux which is obtained after the calculation in the step 6 and takes the total radiation of the plasma into consideration
Further calculating the current magnetic field configuration, and further continuously repeating the steps 5-8 to obtain the total plasma radiation at any moment
And magnetic flux after total radiation of plasma
2. The method as claimed in claim 1, wherein in step 4, the specific calculation method of the evolution equation of the impurity density distribution, the electron density distribution and the ion density distribution is as follows:
(1) The impurity density distribution, electron density distribution and ion density distribution are expressed by a spectrum method:
wherein, (m, n) is the module of the circumferential direction and the polar direction; r 0 Is the large radius of tokamak; theta is a polar angle; z represents the column direction; f is particle distribution, including impurity density distribution, electron density distribution and ion density distribution;
(2) Adopting a two-step prediction-correction method to carry out time advance calculation of various particle distributions; the calculation format of the two-step prediction-correction method is as follows:
and (3) prediction:
and (3) correction:
wherein H represents the magnetic flux and parameters in the magnetic fluid equation; v is the diffusion coefficient; t is time;
represents half a time step; dt represents a time step; the subscript rhs represents the right-hand term of the magnetofluid equation,
representing the gradient in the direction of the perpendicular magnetic field.
3. The method according to claim 1 or 2, wherein the specific steps of the step 5 are as follows:
step 5.1: according to electron temperature distribution T e The corresponding radiation cooling rate L (T) is calculated according to the value of (A) and the generated impurity species e ) The value of (d);
step 5.2: calculating the total radiation of the plasma, including continuous radiation and line radiation;
according to the formula of continuous radiation:
and electron cyclotron radiation formula:
P c ＝5.4×10 -25 n e B 2 T e erg s -1 cm -3
and the calculation formula of the characteristic line radiation:
wherein, P b Representing the magnitude of the continuous radiation, P c Representing the magnitude of electron cyclotron radiation, P z Represents the magnitude of the line radiation; z is a radical of eff Is available electricityDistributing the load;
calculating the magnitude of three kinds of radiation, and then accumulating the three kinds of radiation to obtain the total radiation of the plasma
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116679863A (en) * | 2023-07-28 | 2023-09-01 | 中国科学院合肥物质科学研究院 | Data processing system suitable for EAST radiation divertor inflation system |
| CN116679863B (en) * | 2023-07-28 | 2023-10-24 | 中国科学院合肥物质科学研究院 | Data processing system suitable for EAST radiation divertor inflation system |
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Inventor after: Wang Jincheng Inventor after: Xu Gui Inventor after: Jiang Shuai Inventor after: Wang Zhengxiong Inventor after: Liu Tong Inventor after: Tang Weikang Inventor after: Wei Lai Inventor before: Wang Zhengxiong Inventor before: Jiang Shuai Inventor before: Liu Tong Inventor before: Tang Weikang Inventor before: Wei Lai |