A particle evolution simulation method based on multi-component plasma radiation effect in tokamak

Abstract

The application discloses a kind of particle evolution simulation methods based on multi-component plasma radiation effect in tokamak, belong to magnetic confinement controlled nuclear fusion technical field.Firstly, the evolution of impurity density distribution, electron density distribution and ion density distribution is calculated, then continuous radiation and linear radiation are calculated, and then a variety of plasma radiation is accurately added inside magnetic island.Calculating the magnetic field configuration under the plasma radiation correction, and continue to calculate the evolution of plasma total radiation and related parameters under advanced magnetic field configuration, so repeated calculation, achieve the simulation effect of long time evolution.The application realizes the calculation of impurity, electron and ion real-time dynamic distribution, and can also calculate the evolution of a variety of plasma radiation under real three-dimensional magnetic field configuration, and then obtain the plasma related parameter profile at any time;Meanwhile, the spatial distribution of plasma radiation and the situation of magnetohydrodynamic instability under advanced magnetic field configuration are more accurately described.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of magnetic confinement controlled nuclear fusion, and particularly relates to a method for evolution of particle density distribution of multi-component plasma radiation effect in a tokamak. BACKGROUND

[0002] In recent years, due to the rapid increase of the world population, the productivity and production technology have been effectively improved, so the energy consumption of human beings is also rapidly increasing, which leads to the exhaustion of non-renewable fossil energy. Obviously, this leads to the gradual deterioration of the environment on which human beings rely for survival in recent years, causing the rapid intensification of the greenhouse effect, and some abnormal weather and severe natural phenomena also emerge in an endless stream. Therefore, the search and use of clean energy have become the constant pursuit of scientists. At present, nuclear energy is a relatively efficient and pollution-free energy, and the nuclear energy strategy proposed by our country is: to build a thermal neutron reactor in the near future, to use a fast neutron reactor in the medium term, and to build a fusion reactor in the long term. The fusion reactor here refers to magnetic confinement controlled nuclear fusion. In order to realize magnetic confinement controlled nuclear fusion, the steady-state operation mechanism thereof must be completely mastered, and some instabilities caused by the interaction between internal plasmas, the interaction between plasmas and tokamak walls, and other various complex problems that can promote energy loss to cause discharge extinction must be fully understood and solved. Therefore, it is quite important to study the energy loss of the tokamak under the most advanced magnetic field configuration.

[0003] The advanced magnetic field configuration can more easily confine the plasma, thereby realizing stable long-pulse discharge and ultimately realizing its commercial value. In the tokamak plasma, as one of the main energy loss mechanisms of the tokamak, the plasma radiation refers to the electromagnetic waves emitted by the plasma at various frequency bands. The spectrum of the radiation mainly includes continuous spectrum and line spectrum, and the corresponding radiation is called continuous radiation and line radiation. The main representative of the continuous radiation is bremsstrahlung, and the line radiation mainly includes electron cyclotron radiation and characteristic line radiation. The characteristic line radiation is mainly from impurity ion radiation. Overall, the radiation spectrum covers all wave bands from infrared to X-ray. In future large-scale magnetic confinement nuclear fusion devices, high-z effThe metal impurity radiation of the plasma is very important, and it has a great influence on the magnetohydrodynamic instability in the plasma. Therefore, the research on the plasma radiation and the clear understanding of each characteristic of the plasma radiation are particularly important for realizing the long pulse discharge at present. Therefore, the application provides a simulation method which can be used for calculating the coupling of various plasma radiation effects together under the advanced magnetic field configuration, and the influence of the distribution evolution of the impurity particles, electrons and ions on the total radiation of the plasma is considered, so that the numerical simulation research on the magnetohydrodynamic instability in the tokamak discharge can be carried out, the method has high calculation efficiency and strong numerical stability, and the plasma radiation power obtained by the measurement of the spectrum line in the experiment can be compared and analyzed, so as to lay a solid foundation for realizing the magnetic confinement nuclear fusion in the future. SUMMARY

[0004] In order to fill the technical blank of the numerical simulation of the plasma radiation in the tokamak, the application provides a simulation method for the particle density distribution evolution of the plasma radiation in the tokamak under the advanced magnetic field configuration, that is, the particles used in the calculation of the plasma radiation are evolved with time. The method can be well combined with the experiment, the real-time dynamic distribution of the impurities, electrons and ions can be obtained through the calculation of the impurity density distribution evolution, the electron density distribution evolution and the ion density distribution evolution, the plasma radiation can be more accurately predicted and simulated, and the three-dimensional simulation of the nonlinear evolution of the plasma radiation is realized, so that the influence of the plasma radiation on the tokamak discharge under the advanced magnetic field configuration can be systematically researched, and the experimental results of the plasma radiation can also be provided as a reference.

[0005] The technical scheme adopted by the application is as follows:

[0006] A particle evolution simulation method based on the multi-component plasma radiation effect in the tokamak realizes the evolution of the electron, ion and impurity density distribution, and then the nonlinear evolution of various plasma radiations under the real three-dimensional magnetic field configuration can be obtained, and the evolution profile of the plasma related parameters and the evolution profile of the plasma radiation at any time can also be obtained, so that the spatial distribution of the tokamak plasma under the combined action of various plasma radiations under the advanced magnetic field configuration can be more accurately described. The method specifically includes the following steps:

[0007] Step 1: The plasma region in the tokamak device discharge experiment is divided into grids, and the total plasma radiation value and the magnetic flux function value obtained in the plasma radiation evolution process can be stored by the grid nodes.

[0008] Step 2: The initial impurity density distribution is calculated according to the highest ionization state, the far infrared interferometer and the Thomson scattering in the experiment. Initial electron density distribution and initial electron temperature distribution

[0009] Step 3: Obtain the initial magnetic field configuration by using a magnetic flux ring and other devices in the tokamak discharge, and calculate the initial magnetic flux ψ by numerical simulation method, etc. (0) and store it in the grid nodes.

[0010] Step 4: Bring the initial magnetic flux ψ (0) , initial impurity density distribution initial electron density distribution and initial ion density distribution into the magnetohydrodynamic equation, impurity density distribution evolution equation, electron density distribution evolution equation and ion density distribution evolution equation respectively for calculation, to obtain the magnetic flux ψ (1) , impurity density distribution electron density distribution and ion density distribution at the next time, respectively. The specific steps are as follows:

[0011] The evolution equation of the impurity density distribution is:

[0012]

[0013] The evolution equation of the electron density distribution is:

[0014]

[0015] The evolution equation of the ion density distribution is:

[0016]

[0017] Where n z is the particle density distribution of the impurity, n e represents the electron density distribution, n i represents the ion density distribution; φ is the electric potential, t is the time; D z|| and D z⊥ are the impurity diffusion coefficients in the parallel and perpendicular directions, respectively; D e|| and D e⊥ are the electron diffusion coefficients in the parallel and perpendicular directions, respectively; D i|| and D i⊥ are the ion diffusion coefficients in the parallel and perpendicular directions, respectively; and are the gradient operators in the parallel and perpendicular directions, respectively; S radz is the source term of the impurity, S rade is the source term of the electron, Sradi The source term is ion.

[0018] The specific calculation method of the impurity density distribution, electron density distribution and ion density distribution evolution equation is as follows:

[0019] Step 4.1: Express the impurity density distribution, electron density distribution and ion density distribution by using the spectral method:

[0020]

[0021] Where (m, n) is the toroidal and poloidal mode number; R0 is the major radius of the tokamak; θ is the poloidal angle; z represents the cylindrical direction; f is the particle distribution, including the impurity density distribution, electron density distribution and ion density distribution.

[0022] Step 4.2: Use the two-step prediction-correction method to perform time marching calculation of various particle distributions. The calculation format of the two-step prediction-correction method is as follows:

[0023] Prediction:

[0024]

[0025] Correction:

[0026]

[0027] Where H represents the magnetic flux and the parameter in the magnetohydrodynamic equation; v is the diffusion coefficient; t is the time; represents half a time step; dt represents a time step; the subscript rhs represents the right-hand side of the magnetohydrodynamic equation, represents the gradient in the direction of the vertical magnetic field.

[0028] The impurity density distribution, electron density distribution and ion density distribution evolution equation can be solved by steps 4.1 and 4.2. The reason for using the spectral method and the prediction-correction method is that they can more accurately, quickly and stably calculate the impurity density distribution, electron density distribution and ion density distribution at each time, and then couple the evolution equation of the impurity density distribution, the evolution equation of the electron density distribution, the evolution equation of the ion density distribution and the magnetohydrodynamic equation, so as to self-consistently calculate the distribution of impurities, electrons and ions at any time.

[0029] Step 5: According to step 4, the impurity density distribution is calculated, and when the impurity density distribution in the core of the tokamak reaches the set threshold, the plasma radiation calculation module is opened, so as to calculate the evolution of the magnetic field configuration with time and obtain the total plasma radiation at this time The specific steps are as follows:

[0030] Step 5.1: Calculate the value of the radiative cooling rate L(T e ) according to the value of the electron temperature distribution T e and the generated impurity species.

[0031] Step 5.2: Calculate the total plasma radiation, including continuous radiation and line radiation.

[0032] According to the continuous radiation formula:

[0033]

[0034] and the electron cyclotron radiation formula:

[0035] P c = 5.4 x 10 -25 n e B 2 T e erg s -1 cm -3

[0036] and the calculation formula of characteristic line radiation:

[0037] P z = n e n z ∑L(T e ) erg s -1 cm -3

[0038] Calculate the size of the three radiations, then add up the three radiations to get the total plasma radiation where P b represents the size of continuous radiation, P c represents the size of electron cyclotron radiation, and P z represents the size of line radiation; z eff is the effective charge distribution.

[0039] Step 6: Couple the calculated total plasma radiation into the magnetohydrodynamic equation to calculate the evolution of the magnetic flux in a unit time step, and obtain the magnetic flux

[0040] Step 7: Output the three-dimensional spatial distribution information of the total plasma radiation calculated in step 5.

[0041] Step 8: Further calculate the current magnetic field configuration according to the magnetic flux considering the total plasma radiation obtained after calculation in step 6, and continue to repeat steps 5-8 to obtain the total plasma radiation and magnetic flux taking into account total plasma radiation

[0042] The method can calculate the evolution of electron density distribution, ion density distribution and impurity density distribution, can characterize the evolution process of each parameter in the tokamak plasma in real time, can calculate various plasma radiation, can carry out numerical simulation and analysis on the magnetic fluid instability in the discharge of the tokamak device under the advanced magnetic field configuration, can provide reference for the experimental results of plasma radiation, has high calculation efficiency and strong numerical stability, and is a stable and efficient numerical simulation method. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 It is a schematic diagram of the three-dimensional real magnetic field configuration of the tokamak experimental device suitable for the application, which contains magnetic islands and total plasma radiation.

[0044] Figure 2 It is the calculation result of the spatial distribution of the total plasma radiation evolution with time calculated by the method under the advanced magnetic field configuration after the evolution of impurities, electrons and ions; wherein (a) is the radiation spatial distribution at 55τ A , (b) is the radiation spatial distribution at 60τ A , (c) is the radiation spatial distribution at 65τ A , and (d) is the radiation spatial distribution at 75τ A . Wherein τ A is the Alfen time.

[0045] Figure 3 It is the main flow chart of the method for simulating and calculating various plasma radiation effects under the advanced magnetic field configuration. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical scheme and advantages of the application more clear and obvious, the specific embodiments of the application will be described in detail below with reference to the drawings.

[0047] The tokamak device is a toroidal device similar to a tire, and its schematic diagram is shown in Figure 1 , which is a layer of nested magnetic surface, and the magnetic lines of force are wound along the toroidal and poloidal directions, and magnetic islands will be generated under unstable conditions. Figure 2The space scale of the plasma radiation is continuously evolved, and increases with the increase of the magnetic island width, and the impurity density distribution, the electron density distribution and the ion density distribution are evolved over time, so that the evolution process of the impurity density distribution, the electron density distribution and the ion density distribution over time in the tokamak can be calculated, and the complete plasma radiation in the magnetic island can be added, so that the self-consistent nonlinear evolution of the magnetic island width is realized.

[0048] The specific implementation steps are as follows:

[0049] Step 1: The plasma region in the tokamak discharge experiment is meshed, and the total plasma radiation value and the magnetic flux function value obtained in the plasma radiation evolution process can be stored by the mesh nodes.

[0050] Step 2: The initial impurity density distribution is calculated according to the highest ionization state in the experiment, the far-infrared interferometer and the Thomson scattering. The initial electron density distribution And the initial electron temperature distribution

[0051] Step 3: The initial magnetic field configuration is obtained by using the magnetic flux ring in the tokamak discharge, and the initial magnetic flux ψ is calculated by the numerical simulation method. (0) And stored in the grid nodes.

[0052] Step 4: The initial magnetic flux v (0) , the initial impurity density distribution The initial electron density distribution And the initial ion density distribution (According to the actual research situation) are brought into the magnetic fluid equation, the impurity density distribution evolution equation, the electron density distribution evolution equation and the ion density distribution evolution equation respectively for calculation, to obtain the magnetic flux ψ (1) , the impurity density distribution The electron density distribution And the ion density distribution The specific calculation method of the impurity density distribution evolution equation, the electron density distribution evolution equation and the ion density distribution evolution equation is as follows:

[0053] The evolution equation of the impurity density distribution is:

[0054]

[0055] The evolution equation of the electron density distribution is:

[0056]

[0057] The evolution equation of the ion density distribution is:

[0058]

[0059] Where, n z Let n be the particle density distribution of the impurities. e Represents the electron density distribution, n i Represents the ion density distribution; φ is the electric potential, t is time; D z|| and D z⊥ These are the impurity diffusion coefficients in the parallel and perpendicular directions of the impurity, respectively; D e|| and D e⊥ These are the impurity diffusion coefficients in the parallel and perpendicular directions of the electrons, respectively; D i|| and D i⊥ These are the impurity diffusion coefficients in the parallel and perpendicular directions of the ions, respectively. and These are the gradient operators in the parallel and perpendicular directions, respectively; S radz For impurities, S is the source term; for electrons, S is the source term. radi This is the source term for ions.

[0060] The specific calculation methods for the evolution equations of impurity density distribution, electron density distribution, and ion density distribution are as follows:

[0061] Step 4.1: Express the impurity density distribution, electron density distribution, and ion density distribution using spectroscopic methods:

[0062]

[0063] Where (m,n) are the circumferential and poloidal moduli; R0 is the large radius of the tokamak; θ is the poloidal angle; z represents the cylindrical direction; and f is the particle distribution, including impurity density distribution, electron density distribution, and ion density distribution.

[0064] Step 4.2: Perform time-progression calculations for various particle distributions using a two-step prediction-correction method. The calculation format for the two-step prediction-correction method is as follows:

[0065] predict:

[0066]

[0067] Correction:

[0068]

[0069] Where H represents the magnetic flux and the parameters in the magnetohydrodynamic equation; v is the diffusion coefficient; and t is time. dt represents half a time step; dt represents one time step; the subscript rhs indicates the right-hand term of the magnetohydrodynamic equation. Gradient of the perpendicular magnetic field direction.

[0070] The impurity density distribution, electron density distribution and ion density distribution evolution equations can be solved by steps 4.1 and 4.2. The spectral method and the prediction-correction method are used because they can more accurately, quickly and stably calculate the impurity density distribution, electron density distribution and ion density distribution at each time, and then the impurity density distribution evolution equation, the electron density distribution evolution equation and the ion density distribution evolution equation are coupled with the magnetohydrodynamic equation to calculate the distribution of impurities, electrons and ions at any time.

[0071] Step 5: According to the calculation of step 4, the impurity density distribution is calculated, and when the impurity density distribution of the tokamak core reaches the set threshold value (the threshold value needs to be determined according to the specific research situation, for example, n z = 1 × 10 -5 n e ), the plasma radiation calculation module is opened, so as to calculate the evolution of the magnetic field configuration with time and obtain the total plasma radiation The specific steps are as follows:

[0072] Step 5.1: According to the numerical value of the electron temperature distribution T e and the generated impurity species, the numerical value of the corresponding radiation cooling rate L(T e ) is calculated.

[0073] Step 5.2: Calculate the total plasma radiation, including continuous radiation and line radiation.

[0074] According to the continuous radiation formula:

[0075]

[0076] And the electron cyclotron radiation formula:

[0077] P c = 5.4 × 10 -25 n e B 2 T e erg s -1 cm -3

[0078] And the calculation formula of the characteristic line radiation:

[0079] P z = n e n z ∑L(T e ) erg s -1 cm -3

[0080] The sizes of the three radiations are calculated, and then the three radiations are accumulated to obtain the total radiation of the plasma P b represents the size of the continuous radiation, P c represents the size of the electron cyclotron radiation, P z represents the size of the line radiation, z eff is the effective charge distribution.

[0081] Step 6: The calculated total radiation of the plasma is coupled into the magnetohydrodynamic equation, the evolution of the magnetic flux under a unit time step is calculated, and the magnetic flux after the total radiation of the plasma is added is obtained

[0082] Step 7: The three-dimensional spatial distribution information of the total radiation of the plasma calculated in step 5 is output.

[0083] Step 8: According to the magnetic flux after the total radiation of the plasma is considered obtained after calculation in step 6 the magnetic field configuration at the moment is further calculated, and then steps 5-8 are repeatedly continued to obtain the total radiation of the plasma at any moment and the magnetic flux after the total radiation of the plasma is considered

[0084] The above is a detailed description of one example of the numerical simulation and calculation of the plurality of plasma radiations in the Tokamak under the advanced magnetic field configuration according to the present application, and the specific implementation of the present application cannot be limited to these descriptions. For ordinary skilled persons in the technical field to which the present application belongs, simple deductions and substitutions can be made without departing from the concept of the present application, and all should be regarded as the protection scope of the present application.​

Claims

1. A method of simulation of particle evolution based on effects of multi-component plasma radiation in a tokamak, characterized in that, The method comprises the following steps: Step 1: the plasma region in the tokamak device discharge experiment is meshed, and the total radiation value and the magnetic flux function value obtained in the plasma radiation evolution process are stored by the meshed grid nodes; Step 2: Calculate the initial impurity density distribution from the highest ionization state in the experiment, the far infrared interferometer, and the Thomson scattering Initial electron density distribution and initial electron temperature distribution Step 3: The initial magnetic field configuration is obtained by using the flux surfaces in tokamak discharge, and the initial magnetic flux ψ is calculated (0) and stored in the grid nodes; Step 4: the initial magnetic flux ψ (0) , the initial impurity density distribution , the initial electron density distribution , and the given initial ion density distribution are respectively brought into the equations of the magnetic fluid, 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 to calculate the magnetic flux ψ (1) , the impurity density distribution , the electron density distribution , and the ion density distribution at the next moment, respectively. The specific steps are as follows: The evolution equation of the impurity density distribution is: The evolution equation of the electron density distribution is: The evolution equation of the ion density distribution is: where n z is the particle density distribution of the impurity, n e represents the electron density distribution, n i represents the ion density distribution; φ is the electric potential, t is time; D z|| and D z⊥ are the impurity diffusion coefficients of the impurity in the parallel and perpendicular directions, respectively; D e|| and D e⊥ are the impurity diffusion coefficients of the electron in the parallel and perpendicular directions, respectively; D i|| and D i⊥ are the impurity diffusion coefficients of the ion in the parallel and perpendicular directions, respectively; and are the gradient operators in the parallel and perpendicular directions, respectively; S radz is the source term of the impurity, S rade is the source term of the electron, S radi is the source term of the ion; Step 5: Calculate the impurity density profile according to step 4, when the impurity density profile of the tokamak core reaches a set threshold, then open the plasma radiation calculation module to calculate the evolution of the magnetic field configuration over time and get the first total plasma radiation Step 6: The calculated total plasma radiation is coupled into the MHD equations to calculate the evolution of the magnetic flux for one time step and to obtain the first magnetic flux with the total plasma radiation added Step 7: output the three-dimensional spatial distribution information of the total plasma radiation calculated in Step 5 of the total plasma radiation calculated in Step 5 Step 8: The first magnetic flux after considering the total plasma radiation according to the calculation in Step 6 Further calculate the magnetic field configuration at the moment, and then continue to repeat steps 5-8 to obtain the total plasma radiation at any time And the magnetic flux at any time after considering the total plasma radiation 2. The method of claim 1, wherein, In the step 4, the specific calculation method of the evolution equations of the impurity density distribution, the electron density distribution and the ion density distribution is as follows: (1) the impurity density distribution, the electron density distribution and the ion density distribution are expressed by using a spectral method: Wherein, m and n are the toroidal and poloidal mode numbers; R0 is the major radius of the tokamak; θ is the poloidal angle; z represents the columnar direction; f is the particle distribution, including the impurity density distribution, the electron density distribution and the ion density distribution; (2) the two-step prediction-correction method is used for time advancing calculation of various particle distributions; wherein, the calculation format of the two-step prediction-correction method is as follows: Prediction: Correction: where H represents the magnetic flux and a parameter in the MHD equation; v is a diffusion coefficient; t is time; represents half a time step; dt represents a time step; the subscript rhs represents the right-hand side of the MHD equation, represents the gradient of the perpendicular magnetic field direction.

3. The method according to claim 1 or 2, characterized in that, The specific steps of the step 5 are as follows: Step 5.1 : Calculate the value of the radiative cooling rate L(T e ) from the value of the electronic temperature distribution T e and the generated impurity species. Step 5.2: calculate the total plasma radiation, including continuous radiation and line radiation; According to the continuous radiation formula: And the electron cyclotron radiation formula: P c = 5.4 x 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 where P b represents the size of the continuous radiation, P c represents the size of the electron cyclotron radiation, P z represents the size of the line radiation; z eff is the effective charge distribution; The magnitude of the three radiations is calculated and the three radiations are summed to obtain the first total plasma radiation

Images