Two-dimensional full-wave simulation method considering polar magnetic field in finite element code and electronic equipment

Abstract

The invention discloses a two-dimensional full-wave simulation method considering a polar magnetic field in a finite element code and electronic equipment, and in the full-wave simulation process, the vertical movement effect of parallel wave numbers caused by the existence of the polar magnetic field is considered when plasma current is quite large or a circumferential modulus is relatively small, so that the full-wave simulation efficiency is improved. The method comprises the following steps: firstly, solving a wave equation based on an initial dielectric tensor, determining the distribution of electric fields on Tokamak magnetic surfaces, carrying out wavelet transform on the electric field on each Tokamak magnetic surface to obtain a value of a dominant polar modulus, and correcting a parallel wave number by using the value of the dominant polar modulus; according to the embodiment of the invention, the influence of a polar magnetic field (Tokamak magnetic surface) is considered in the full-wave simulation, and the value of the polar modulus is determined by using wavelet transform, so that the full-wave simulation result is obtained. The time consumption is short, and the simulation result is more accurate.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic confinement fusion, and particularly relates to a two-dimensional full-wave simulation method considering the poloidal magnetic field in a finite element code and an electronic device. Background Art

[0002] In the technical field of magnetic confinement fusion, full-wave simulation refers to a numerical simulation of electromagnetic phenomena that is complete and covers all frequency components.

[0003] In the full-wave simulation methods in the related art, when dealing with plasma systems containing complex antenna structures and irregular boundaries, higher accuracy and efficiency are demonstrated, while significantly saving computing resources and reducing computing time. However, when the plasma current is quite large or the toroidal mode number is small, due to the effect of the poloidal magnetic field causing the up and down movement of the parallel wave number, in this case, the full-wave simulation methods in the related art use spectral decomposition to calculate spatial dispersion, which not only involves complex spectral transformations but also does not consider the influence of the poloidal magnetic field, resulting in longer time consumption and inaccurate simulation results. Summary of the Invention

[0004] In order to solve the above problems existing in the prior art, the present invention provides a two-dimensional full-wave simulation method considering the poloidal magnetic field in a finite element code and an electronic device. The technical problems to be solved by the present invention are realized through the following technical solutions:

[0005] According to the first aspect of an embodiment of the present invention, a two-dimensional full-wave simulation method considering the poloidal magnetic field in a finite element code is provided, and the method includes:

[0006] Initialize the parallel wave number, calculate the current dielectric tensor, and obtain the initial dielectric tensor; the parallel wave number is the component of the ion cyclotron range frequency (ICRF) wave vector in the magnetic field direction;

[0007] Solve the wave equation based on the initial dielectric tensor, determine the distribution of the electric field on the tokamak magnetic surface, and perform wavelet transform on the electric field on each tokamak magnetic surface to obtain the spectrum of the toroidal mode number;

[0008] Determine the value of the dominant toroidal mode number on each tokamak magnetic surface according to the spectrum of the toroidal mode number, and correct the parallel wave number based on the value of the dominant toroidal mode number;

[0009] Calculate the dielectric tensor corresponding to the corrected parallel wave number to obtain the target dielectric tensor;

[0010] Solve the wave equation based on the target dielectric tensor and determine the distribution of the electric field on the tokamak magnetic surface again to obtain the final full-wave simulation result.

[0011] In one embodiment of the present invention, the initialization of the parallel wave number, the calculation of the current dielectric tensor, and the obtaining of the initial dielectric tensor include:

[0012] Set the toroidal mode number to zero and initialize the parallel wave number;

[0013] Calculate the current dielectric tensor by adding the unit tensor to the sum of the magnetic susceptibility tensors of specific types of particles to obtain the initial dielectric tensor.

[0014] In one embodiment of the present invention, the calculation of the current dielectric tensor by adding the unit tensor to the sum of the magnetic susceptibility tensors of specific types of particles to obtain the initial dielectric tensor includes:

[0015] Calculate the current dielectric tensor by the following formula to obtain the initial dielectric tensor:

[0016]

[0017] where K represents the initial dielectric tensor, I represents the unit tensor, and χ j represents the magnetic susceptibility tensor of the j-th type of particle.

[0018] In one embodiment of the present invention, the obtaining of the magnetic susceptibility tensor of the j-th type of particle includes:

[0019] In the Cartesian coordinate system of the Stix framework, when k y = 0, the Stix magnetic susceptibility tensor of the j-th type of particle is obtained through the following expression:

[0020]

[0021] where χ xx，j represents the xx component of the magnetic susceptibility tensor of the j-th type of particle; χ xy，j represents the xy component of the magnetic susceptibility tensor of the j-th type of particle; χ xz，j represents the xz component of the magnetic susceptibility tensor of the j-th type of particle; χ yy，j represents the yy component of the magnetic susceptibility tensor of the j-th type of particle; χ yz，j represents the yz component of the magnetic susceptibility tensor of the j-th type of particle; χ zx，j represents the zx component of the magnetic susceptibility tensor of the j-th type of particle; χ zz，j represents the zz component of the magnetic susceptibility tensor of the j-th type of particle; k x represents the component of the ICRF wave vector along the x direction, k y represents the component of the ICRF wave vector along the y direction, k z represents the component of the ICRF wave vector along the z direction;

[0022] Based on the Stix magnetic susceptibility tensor, obtain the magnetic susceptibility tensor of the j-th type of particle.

[0023] In one embodiment of the present invention, obtaining the magnetic susceptibility tensor of the j-th type of particle based on the Stix magnetic susceptibility tensor includes:

[0024] Based on the Stix magnetic susceptibility tensor Through the formula Obtain the magnetic susceptibility tensor of the j-th type of particle;

[0025] Where R T Is the transpose matrix of R, and R is the transformation matrix:

[0026]

[0027] In one embodiment of the present invention, solving the wave equation based on the initial dielectric tensor, determining the distribution of the electric field on the tokamak magnetic surface, and performing wavelet transform on the electric field on each tokamak magnetic surface to obtain the spectrum of the poloidal mode number includes:

[0028] Based on the initial dielectric tensor, solve the wave equation through the following formula:

[0029]

[0030] Where Is the double curl of the electric field E, ω represents the wave frequency, c represents the speed of light, K represents the initial dielectric tensor, μ is the vacuum permeability, J ant Represents the antenna current, Represents the plasma current;

[0031] According to the solution result of the wave equation, determine the distribution of the electric field on the tokamak magnetic surface, and perform wavelet transform on the electric field on each tokamak magnetic surface to obtain the spectrum of the poloidal mode number.

[0032] In one embodiment of the present invention, obtaining the plasma current includes:

[0033] Obtain the plasma current through the following formula:

[0034]

[0035] Where j represents the particle species number, ω represents the wave frequency, ε 0 Represents the vacuum permittivity, χ j Represents the magnetic susceptibility tensor of the j-th type of particle, E represents the electric field tensor, q j Represents the charge of the j-th type of particle, γ j Is the adiabatic coefficient, k B Is the Boltzmann constant, T j0 Is the unperturbed fluid temperature, mj represents the particle mass of the j-th kind of particle, Λ j is the fluid thermal pressure correction term, n j1 is the plasma number density of linear perturbation.

[0036] In one embodiment of the present invention, determining the value of the dominant poloidal mode number on each tokamak magnetic surface according to the spectrum of the poloidal mode number includes:

[0037] According to the spectrum of the poloidal mode number, identifying the mode components at different frequencies and scales, where the mode components correspond to the poloidal mode number;

[0038] According to the corresponding relationship between the mode components and the poloidal mode number, determining the value of the dominant poloidal mode number on each tokamak magnetic surface.

[0039] In one embodiment of the present invention, correcting the parallel wave number based on the value of the dominant poloidal mode number includes:

[0040] Based on the value of the dominant poloidal mode number, correcting the parallel wave number through the following formula:

[0041]

[0042] where k ∥ represents the parallel wave number of the ICRF, represents the toroidal mode number, m represents the poloidal mode number, R represents the major radius of the all-superconducting tokamak fusion experimental device EAST, N θ is the minor radius representing the EAST, and θ represents the arctangent of the ratio of the poloidal magnetic field to the toroidal magnetic field.

[0043] According to the second aspect of the embodiments of the present invention, there is provided an electronic device, and the device includes:

[0044] One or more processors;

[0045] A computer-readable medium configured to store one or more programs;

[0046] When the one or more programs are executed by the one or more processors, the one or more processors implement the two-dimensional full-wave simulation method considering the poloidal magnetic field in the finite element code as described in any item of the first aspect.

[0047] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0048] The two-dimensional full-wave simulation method and electronic device considering the poloidal magnetic field in the finite element code provided by the embodiments of the present invention first initialize the parallel wavenumber, calculate the current dielectric tensor, and obtain the initial dielectric tensor; the parallel wavenumber is the component of the ion cyclotron range wave (ICRF) wavevector in the magnetic field direction; then solve the wave equation based on the initial dielectric tensor, determine the distribution of the electric field on the tokamak magnetic surface, and perform wavelet transform on the electric field on each tokamak magnetic surface to obtain the spectrum of the poloidal mode number; then determine the value of the dominant poloidal mode number on each tokamak magnetic surface according to the spectrum of the poloidal mode number, and correct the above parallel wavenumber based on the value of the dominant poloidal mode number; then calculate the dielectric tensor corresponding to the corrected parallel wavenumber to obtain the target dielectric tensor; solve the above wave equation based on the target dielectric tensor, and determine the distribution of the electric field on the tokamak magnetic surface again to obtain the final full-wave simulation result. In the process of full-wave simulation in the embodiments of the present invention, considering that when the plasma current is quite large or the toroidal mode number is small, due to the existence of the poloidal magnetic field, there will be an up-and-down shift effect on the parallel wavenumber. Therefore, first solve the wave equation based on the initial dielectric tensor, determine the distribution of the electric field on the tokamak magnetic surface, and perform wavelet transform on the electric field on each tokamak magnetic surface to obtain the spectrum of the poloidal mode number; then determine the value of the dominant poloidal mode number according to the spectrum of the poloidal mode number, and use the value of the dominant poloidal mode number to correct the above parallel wavenumber; finally, obtain the target dielectric tensor based on the corrected parallel wavenumber, and finally solve the wave equation based on the target dielectric tensor to obtain the final full-wave simulation result. The embodiments of the present invention not only consider the influence of the poloidal magnetic field (tokamak magnetic surface) in the full-wave simulation, but also use wavelet transform to determine the value of the dominant poloidal mode number, resulting in shorter time consumption and more accurate simulation results.

[0049] The following will further elaborate on the present invention in conjunction with the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a flowchart of the steps of a two-dimensional full-wave simulation method considering the poloidal magnetic field in the finite element code provided by the embodiments of the present invention;

[0051] Figure 2a It is a one-dimensional distribution diagram of the electron density ne, electron temperature Te, and ion temperature Ti under D(H) minority ion heating;

[0052] Figure 2b It is the field distribution considering the poloidal magnetic field, including the distribution diagrams of the left-handed electric field E+, ion absorption, electron absorption, and the dominant poloidal mode number;

[0053] Figure 2c It is a comparison of the left-handed electric field E+ distribution calculated by the full-wave simulation program and the TORIC program provided by the embodiments of the present invention;

[0054] Figure 2d The field distribution diagram calculated by the INTFLUK program for finite elements;

[0055] Figure 2e The field distribution diagram calculated by the TORIC program;

[0056] Figure 3 The schematic structural diagram of an electronic device provided by an embodiment of the present invention. Specific embodiments

[0057] The present invention will be further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0058] Embodiment 1

[0059] Referring to Figure 1 , a flowchart showing the steps of a two-dimensional full-wave simulation method considering the poloidal magnetic field in a finite element code according to Embodiment 1 of the present invention is shown.

[0060] The two-dimensional full-wave simulation method considering the poloidal magnetic field in the finite element code of this embodiment includes the following steps:

[0061] Step 101: Initialize the parallel wave number, calculate the current dielectric tensor, and obtain the initial dielectric tensor.

[0062] The above parallel wave number is the component of the ion cyclotron range frequency wave (ICRF) wave vector in the magnetic field direction. This method can be carried out in a tokamak device. After the tokamak device is powered on, an electric field and a magnetic field will be generated, and the magnetic field includes a toroidal magnetic field and a poloidal magnetic field. In this embodiment, the relationship between the parallel wave number k ∥ of the ion cyclotron range frequency wave (ICRF) and the poloidal mode number m can be expressed as:

[0063]

[0064] where k ∥ represents the parallel wave number of the ICRF, represents the toroidal mode number, m represents the poloidal mode number, R represents the major radius of the Experimental Advanced Superconducting Tokamak (EAST), N θ is the minor radius representing EAST, and θ represents the arctangent of the ratio of the poloidal magnetic field to the toroidal magnetic field.

[0065] Specifically, when initializing the parallel wave number, calculating the current dielectric tensor, and obtaining the initial dielectric tensor, the poloidal mode number can be set to zero to initialize the parallel wave number; then, the current dielectric tensor is calculated by adding the sum of the susceptibility tensors of specific types of particles to the unit tensor, and the initial dielectric tensor is obtained.

[0066] When the poloidal mode number m = 0, the initialized parallel wave number is obtained:

[0067]

[0068] Among them, θ represents the arctangent of the ratio of the poloidal magnetic field to the toroidal magnetic field. Then, through the following formula, the dielectric tensor at present (when m = 0) is calculated to obtain the initial dielectric tensor:

[0069]

[0070] Among them, K represents the initial dielectric tensor, χ j represents the magnetic susceptibility tensor of the j-th kind of particle, and I represents the unit tensor:

[0071]

[0072] Furthermore, the acquisition of the magnetic susceptibility tensor χ j of the above-mentioned j-th kind of particle includes:

[0073] First, in the Cartesian coordinate system of the Stix framework, when k y = 0, the Stix magnetic susceptibility tensor of the j-th kind of particle is obtained through the following expression:

[0074]

[0075] Among them, χ xx，j represents the xx component of the magnetic susceptibility tensor of the j-th kind of particle; χ xy，j represents the xy component of the magnetic susceptibility tensor of the j-th kind of particle; χ xz，j represents the xz component of the magnetic susceptibility tensor of the j-th kind of particle; χ yy，j represents the yy component of the magnetic susceptibility tensor of the j-th kind of particle; χ yz，j represents the yz component of the magnetic susceptibility tensor of the j-th kind of particle; χ zx，j represents the zx component of the magnetic susceptibility tensor of the j-th kind of particle; χ zz，j represents the zz component of the magnetic susceptibility tensor of the j-th kind of particle; k x represents the component of the ICRF wave vector along the x direction, k y represents the component of the ICRF wave vector along the y direction, k z represents the component of the ICRF wave vector along the z direction; then, based on the Stix magnetic susceptibility tensor, the magnetic susceptibility tensor of the j-th kind of particle is obtained.

[0076] Obviously, k x , k y , k z are all components of the ICRF wave vector in different directions. The aforementioned k ∥ represents the component of the wave vector in the magnetic field direction. Usually, the magnetic field direction is from top to bottom. Therefore, k ∥It is usually k z . Therefore, it can be known that the magnetic susceptibility tensor is affected by the parallel wave number.

[0077] Furthermore, where ω pj represents the plasma frequency of the j-th particle, e is the Euler number, ω represents the ICRF wave frequency, k z represents the component of the ICRF wave vector along the z direction, v j represents the thermal velocity, n represents the order of the Bessel function, I n represents the modified Bessel function of the n-th order, Z(ζ n ,j) represents the dispersion function.

[0078] where i is the imaginary unit, ε j represents the dielectric tensor, ω pj represents the plasma frequency of the j-th particle, e is the Euler number, ω represents the ICRF wave frequency, represents the FLR parameter, ρ Lj represents the Larmor radius, k x represents the component of the ICRF wave vector along the x direction, k z represents the component of the ICRF wave vector along the z direction, v j represents the thermal velocity, n represents the order of the Bessel function, I n represents the modified Bessel function of the n-th order, Z(ζ n ,j) represents the dispersion function.

[0079] where ω pj represents the plasma frequency of the j-th particle, e is the Euler number, ω represents the ICRF wave frequency, represents the FLR parameter, ρ Lj represents the Larmor radius, k x represents the component of the ICRF wave vector along the x direction, k z represents the component of the ICRF wave vector along the z direction, v j represents the thermal velocity, n represents the order of the Bessel function, I n represents the modified Bessel function of the n-th order, Z(ζ n ,j) represents the dispersion function.

[0080] where ω pj represents the plasma frequency of the j-th particle, ω represents the wave frequency, e is the Euler number, represents the FLR parameter, ρ Lj represents the Larmor radius, k x represents the component of the ICRF wave vector along the x direction, k zDenotes the z - component of the ICRF wave vector, k x Denotes the x - component of the ICRF wave vector, ω cj Denotes the cyclotron frequency of the j - th species of particles, n denotes the order of the Bessel function, I n Denotes the modified Bessel function of the n - th order, Z‘(ζ n ,j) denotes the dispersion function.

[0081] Where, i is the imaginary unit, ε j Denotes the dielectric tensor, k x Denotes the x - component of the ICRF wave vector, ω pj Denotes the plasma frequency of the j - th particle, ω denotes the ICRF wave frequency, e is the Euler's number, Denotes the FLR parameter, ρ Lj Denotes the Larmor radius, k x Denotes the x - component of the ICRF wave vector, k z Denotes the z - component of the ICRF wave vector, ω cj Denotes the cyclotron frequency of the j - th species of particles, n denotes the order of the Bessel function, I n Denotes the modified Bessel function of the n - th order, Z’(ζ n ,j) denotes the dispersion function.

[0082] Where ω pj Denotes the plasma frequency of the j - th particle, ω denotes the ICRF wave frequency, e is the Euler's number, Denotes the FLR parameter, ρ Lj Denotes the Larmor radius, k x Denotes the x - component of the ICRF wave vector, k z Denotes the z - component of the ICRF wave vector, v j Denotes the thermal velocity, I n Denotes the modified Bessel function of the n - th order, Z‘(ζ n ,j) denotes the dispersion function.

[0083] Specifically, when obtaining the susceptibility tensor of the j - th species of particles based on the Stix susceptibility tensor, based on the Stix susceptibility tensor The susceptibility tensor of the j - th species of particles is obtained through the formula to obtain the susceptibility tensor of the j - th species of particles.

[0084] Where, R T is the transpose matrix of R, and R is the transformation matrix:

[0085]

[0086] Thus, the initial dielectric tensor can be obtained.

[0087] Step 102: Solve the wave equation based on the initial dielectric tensor, determine the distribution of the electric field on the Tokamak magnetic surface, and perform wavelet transform on the electric field on each Tokamak magnetic surface to obtain the spectrum of the poloidal mode number.

[0088] Specifically, based on the initial dielectric tensor, solve the wave equation through the following formula:

[0089]

[0090] where is the double curl of the electric field E, ω represents the ICRF wave frequency, c represents the speed of light, K represents the initial dielectric tensor, μ 0 is the vacuum permeability, J ant represents the antenna current, represents the plasma current.

[0091] The acquisition of the above plasma current includes obtaining the plasma current through the following formula:

[0092]

[0093] where j represents the particle species number, ω represents the wave frequency, ε 0 represents the vacuum permittivity, χ j represents the magnetic susceptibility tensor of the j-th particle, E represents the electric field tensor, q j represents the charge of the j-th particle, γ j is the adiabatic coefficient, k B is the Boltzmann constant, T j0 is the unperturbed fluid temperature, m j represents the particle mass of the j-th particle, Λ j is the fluid thermal pressure correction term, n j1 is the linearly perturbed plasma number density. For the linearly perturbed plasma number density n in the plasma current j1 the acquisition is as follows:

[0094]

[0095] where ε 0 represents the vacuum permittivity, q j represents the charge of the j-th particle, χ j H is its Hermitian part, E represents the electric field tensor, γ j is the adiabatic coefficient, k B is the Boltzmann constant, T j0 is the unperturbed fluid temperature, ω represents the wave frequency, m jDenote the particle mass of the j-th kind of particle, Λ j is the fluid thermal pressure correction term, n j1 is the plasma number density of linear perturbation.

[0096] For the antenna current J ant it can be calculated and obtained according to the existing methods.

[0097] Then, according to the solution results of the wave equation, determine the distribution of the electric field on the tokamak magnetic surface, and perform wavelet transform on the electric field distribution on each tokamak magnetic surface to obtain the spectrum of the poloidal mode number.

[0098] In this embodiment, the wavelet transform is a transform analysis method. Based on the idea of the short-time Fourier transform, through dilation and translation operations, it performs multi-scale refinement analysis on the signal, providing a "time-frequency" window that varies with frequency.

[0099] Using the wavelet transform, the electric field distribution on each tokamak magnetic surface can be decomposed into sub-signals of different scales and frequency bands, simply called wavelet basis functions. The advantage of the wavelet transform is that it can achieve time-frequency localization analysis of the signal, that is, at each spatial point, the frequency characteristics of this point changing with time can be obtained. By analyzing the spectral structure and modal characteristics of each sub-signal, the modal components at different frequencies and scales can be effectively identified, and these modal components correspond to different poloidal mode numbers m in ICRF.

[0100] Step 103: Determine the value of the dominant poloidal mode number on each tokamak magnetic surface according to the spectrum of the poloidal mode number, and based on the value of the dominant poloidal mode number, correct the above parallel wave number.

[0101] Specifically, according to the spectrum of the poloidal mode number, identify the modal components at different frequencies and scales; then, according to the correspondence between the modal components and the poloidal mode number, determine the value of the dominant poloidal mode number on each magnetic surface.

[0102] After identifying all the modal components, by comparing the energy or influence degree of each mode, it can be determined which mode is the dominant poloidal mode number. The dominant poloidal mode number is usually the mode with the largest energy or the most significant influence within a specific frequency range, so that the dominant poloidal mode number can be determined from multiple poloidal mode numbers, and then the value of the dominant poloidal mode number can be determined.

[0103] Then, take the value of the dominant poloidal mode number as the new m value and substitute it into the following formula to correct the parallel wave number:

[0104]

[0105] where, k ∥ represents the parallel wave number of ICRF, denotes the toroidal mode number, m denotes the dominant poloidal mode number here, R denotes the major radius of the Experimental Advanced Superconducting Tokamak (EAST), N θ is the minor radius of the said EAST, θ denotes the arctangent of the ratio of the poloidal magnetic field to the toroidal magnetic field; thus the corrected parallel wave number k is obtained ∥ .

[0106] Step 104: Calculate the dielectric tensor corresponding to the corrected parallel wave number to obtain the target dielectric tensor.

[0107] In this embodiment, the calculation formula of the target dielectric tensor is the same as that of the aforementioned initial dielectric tensor, which will not be elaborated here. Obviously, since the parallel wave number has changed, the susceptibility tensor will change, and further the result of the dielectric tensor will change, that is, a new dielectric tensor - the target dielectric tensor is obtained.

[0108] Step 105: Solve the above wave equation based on the target dielectric tensor, and determine the distribution of the electric field on the tokamak magnetic surface again to obtain the final full-wave simulation result.

[0109] In this embodiment, the process of solving the wave equation based on the target dielectric tensor is similar to that of Step 102, with the only difference being that the value of the target dielectric tensor has changed, so it will not be elaborated here.

[0110] The two-dimensional full-wave simulation method considering the poloidal magnetic field in the finite element code provided by the embodiments of the present invention first initializes the parallel wave number, calculates the current dielectric tensor, and obtains the initial dielectric tensor; the parallel wave number is the component of the wave vector of the ion cyclotron range frequency (ICRF) wave in the magnetic field direction; then, based on the initial dielectric tensor, the wave equation is solved to determine the distribution of the electric field on the tokamak magnetic surface, and the wavelet transform is performed on the electric field on each tokamak magnetic surface to obtain the spectrum of the poloidal mode number; then, according to the spectrum of the poloidal mode number, the value of the dominant poloidal mode number on each tokamak magnetic surface is determined, and based on the value of the dominant poloidal mode number, the above parallel wave number is corrected; then, the dielectric tensor corresponding to the corrected parallel wave number is calculated to obtain the target dielectric tensor; based on the target dielectric tensor, the above wave equation is solved, and the distribution of the electric field on the tokamak magnetic surface is determined again to obtain the final full-wave simulation result. In the process of full-wave simulation in the embodiments of the present invention, considering that when the plasma current is quite large or the toroidal mode number is small, the presence of the poloidal magnetic field will cause the up-and-down movement effect of the parallel wave number. Therefore, first, based on the initial dielectric tensor, the wave equation is solved to determine the distribution of the electric field on the tokamak magnetic surface, and the wavelet transform is performed on the electric field on each tokamak magnetic surface to obtain the spectrum of the poloidal mode number; then, according to the spectrum of the poloidal mode number, the value of the dominant poloidal mode number is determined, and the above parallel wave number is corrected by using the value of the dominant poloidal mode number; finally, based on the corrected parallel wave number, the target dielectric tensor is obtained, and finally, based on the target dielectric tensor, the wave equation is solved to obtain the final full-wave simulation result. The embodiments of the present invention not only consider the influence of the poloidal magnetic field (tokamak magnetic surface) in the full-wave simulation, but also use the wavelet transform to determine the value of the dominant poloidal mode number, so that the time consumption is short and the simulation result is more accurate.

[0111] The present invention incorporates the poloidal magnetic field into the two-dimensional finite element full-wave simulation, accurately considers the up-and-down movement of the parallel wave number during the full-wave simulation, and proposes a method of using wavelet transform to determine the poloidal mode number at each spatial point to handle the spatial dispersion effect (that is, the parallel wave number is corrected by the dominant poloidal mode number, so that the spatial dispersion effect is corrected, where the dependence of the dielectric tensor or the magnetic susceptibility tensor on k ∥ is called spatial dispersion), so that the spatial dispersion of a single poloidal mode can be well approximated as the effect jointly produced by multiple poloidal modes at a given spatial point, further enhancing the ability to capture the complex details of wave propagation and improving the accuracy of the simulation, and significantly reducing the computational resources and time.

[0112] Embodiment 2

[0113] The following will perform code tests on the two-dimensional full-wave simulation method considering the poloidal magnetic field in the finite element code implemented by the present invention in EAST.

[0114] In the test, a numerical poloidal flux surface function is adopted, denoted as ψ = ψ(R, Z). The major radius of EAST is 1.85 m, and the minor radius is 0.45 m. The center of the antenna strap is located at 2.35 m, and the length of the antenna strap is 0.754 m. To achieve minority H ion heating at the axis, the central magnetic field strength is set to 2.54 T, the antenna frequency is set to 37 MHz, and the toroidal mode number is set to 25.

[0115] Test 1: Select the D(H) minority ion heating scenario and observe the distributions of its electron density ne, electron temperature Te, and ion temperature Ti, as well as the plasma parameter distribution. As Figure 2a , for the D(H) minority ion heating, it is the one-dimensional distribution diagram of the electron density ne, electron temperature Te, and ion temperature Ti.

[0116] Test 2: Considering the poloidal magnetic field, set the concentration of minority ions to 20%, and observe the distributions of the left-handed electric field E+, ion absorption, electron absorption, and the dominant poloidal mode number. Refer to Figure 2b , which is the field distribution considering the poloidal magnetic field, including the schematic diagrams of the distributions of the left-handed electric field E+, ion absorption, electron absorption, and the dominant poloidal mode number. From Figure 2b (a) and (c), it can be seen the up-down asymmetric electric field generated by the ion Bernstein wave (IBW) after mode conversion and the self-consistent electron absorption phenomenon. Figure 2b (d) shows the distribution of the main poloidal mode m obtained by performing wavelet transform on E+ at each constant magnetic surface.

[0117] Test 3: To verify the effectiveness of the up-down movement effect in the code of the present invention, we compared two programs, TORIC and INTFLUK of the finite element method. The distributions of the left-handed electric field E+ with and without the poloidal magnetic field calculated by the two programs are both shown in Figure 2c , Figure 2c is the comparison of the distributions of the left-handed electric field E+ calculated by the full-wave simulation program provided by the embodiment of the present invention and the TORIC program. In Figure 2c (b) and (d), the up-down asymmetry of the ion Bernstein wave (IBW) caused by the poloidal magnetic field is observed in both programs.

[0118] The following Table 1 shows the power distribution of the full-wave simulation program provided by the present invention and the TORIC program considering the presence and absence of the poloidal magnetic field respectively. For the same case, the integration error between the two programs is less than 10%, and both reflect that considering the poloidal magnetic field will lead to a slight decrease in electron absorption compared with the case without the poloidal magnetic field.

[0119] Table 1 Power distribution of the full-wave simulation program provided by the present invention and the TORIC program considering the presence and absence of the poloidal magnetic field respectively

[0120]

[0121]

[0122] Test 4: A special heating scenario was selected: the concentrations of D ions, H ions, and He-3 ions were set to 21%, 33%, and 23% respectively, the wave frequency was selected as 25 MHz, and this heating scenario was proven to be able to effectively excite slow ion cyclotron waves (ICW) and heat electrons. The field distributions calculated by the INTFLUK program and the TORIC program of the finite element method Figure 2d and Figure 2e are shown as follows; Figure 2d is the field distribution calculated for the present invention under the special heating scenario where the concentrations of D ions, H ions, and He-3 ions are set to 21%, 33%, and 23% respectively, and the wave frequency is selected as 25 MHz, including the distributions of the left-handed electric field E+, the right-handed electric field E-, the parallel electric field E / / , and the electron absorption Pe; Figure 2e is the field distribution calculated by the TORIC program under the special heating scenario where the concentrations of D ions, H ions, and He-3 ions are set to 21%, 33%, and 23% respectively, and the wave frequency is selected as 25 MHz, including the distributions of the left-handed electric field E+, the right-handed electric field E-, the parallel electric field E / / , and the electron absorption Pe. The slow ion cyclotron wave ICW (short wavelength) after mode conversion propagating towards the low-field side was observed by both programs, which also verified the effectiveness of the INTFLUK program of the finite element method in capturing the up-and-down movement effect.

[0123] Table 2 shows the power distribution considering the toroidal magnetic field for the program provided by the present invention and the TORIC program under special scenario heating, and the integration error is still less than 10%.

[0124] Table 2 Power distribution considering the toroidal magnetic field for the program provided by the present invention and the TORIC program under special scenario heating

[0125]

[0126] Example 3

[0127] The embodiment of the present invention also provides an electronic device, as Figure 3 shown, including a processor 301, a communication interface 302, a memory 303, and a communication bus 304, wherein the processor 301, the communication interface 302, and the memory 303 communicate with each other through the communication bus 304,

[0128] the memory 303 is used to store a computer program;

[0129] when the processor 301 is used to execute the program 305 stored on the memory 303, the following steps are implemented:

[0130] Initialize the parallel wave number, calculate the current dielectric tensor, and obtain the initial dielectric tensor; the parallel wave number is the component of the ion cyclotron range of frequency (ICRF) wave vector in the magnetic field direction.

[0131] Solve the wave equation based on the initial dielectric tensor, determine the distribution of the electric field on the tokamak magnetic surface, and perform wavelet transform on the electric field on each tokamak magnetic surface to obtain the spectrum of the poloidal mode number.

[0132] Determine the value of the dominant poloidal mode number on each tokamak magnetic surface according to the spectrum of the poloidal mode number, and correct the parallel wave number based on the value of the dominant poloidal mode number.

[0133] Calculate the dielectric tensor corresponding to the corrected parallel wave number to obtain the target dielectric tensor.

[0134] Solve the wave equation based on the target dielectric tensor and determine the distribution of the electric field on the tokamak magnetic surface again to obtain the final full-wave simulation result.

[0135] The communication bus mentioned in the above electronic device can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus can be divided into an address bus, a data bus, a control bus, etc. For the sake of representation, only a thick line is shown in the figure, but it does not mean that there is only one bus or one type of bus.

[0136] The communication interface is used for communication between the above electronic device and other devices.

[0137] The memory can include a Random Access Memory (RAM), and can also include a Non-Volatile Memory (NVM), such as at least one disk memory. Optionally, the memory can also be at least one storage device located far from the aforementioned processor.

[0138] The above-mentioned processor may be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it may also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, and discrete hardware components.

[0139] The method provided by the embodiments of the present invention can be applied to an electronic device. Specifically, the electronic device may be: a desktop computer, a portable computer, a smart mobile terminal, a server, etc. There is no limitation here. Any electronic device that can implement the present invention belongs to the protection scope of the present invention.

[0140] For the embodiments of the electronic device / storage medium, since they are basically similar to the method embodiments, the description is relatively simple. For the relevant parts, please refer to the partial description of the method embodiments.

[0141] It should be noted that the electronic device and storage medium of the embodiments of the present invention are respectively the electronic device and storage medium that apply the two-dimensional full-wave simulation method considering the poloidal magnetic field in the above-mentioned finite element code. Then, all embodiments of the two-dimensional full-wave simulation method considering the poloidal magnetic field in the above-mentioned finite element code are applicable to the electronic device and storage medium, and can achieve the same or similar beneficial effects.

[0142] By applying the terminal device provided by the embodiments of the present invention, proper nouns and / or fixed phrases can be displayed for the user to select, thereby reducing the user input time and improving the user experience.

[0143] The terminal device exists in various forms, including but not limited to:

[0144] (1) Mobile communication device: The characteristic of this type of device is that it has mobile communication functions and mainly aims to provide voice and data communication. This type of terminal includes: smart phones (such as iPhone), multimedia phones, functional phones, and low-end phones, etc.

[0145] (2) Ultra-mobile personal computer device: This type of device belongs to the category of personal computers, has computing and processing functions, and generally also has the characteristic of mobile Internet access. This type of terminal includes: PDA, MID, and UMPC devices, etc., such as iPad.

[0146] (3) Portable entertainment devices: Such devices can display and play multimedia content. Such devices include: audio and video players (such as iPods), handheld game consoles, e-books, as well as smart toys and portable in-vehicle navigation devices.

[0147] (4) Other electronic devices with data interaction functions.

[0148] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, "a plurality" means two or more unless otherwise specifically defined.

[0149] In the description of this specification, the description with reference to terms such as "an embodiment", "some embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic descriptions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification.

[0150] Although the present application has been described in connection with various embodiments herein, however, in the process of implementing the claimed present application, those skilled in the art can understand and achieve other variations of the disclosed embodiments by viewing the accompanying drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "one" does not exclude a plurality. A single processor or other unit can implement several functions recited in the claims. Certain measures are recited in mutually different dependent claims, but this does not mean that these measures cannot be combined to produce good results.

[0151] Those skilled in the art should understand that the embodiments of the present application can be provided as methods, apparatuses (devices), or computer program products. Therefore, the present application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects, which are collectively referred to as "modules" or "systems" herein. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The computer program is stored / distributed in a suitable medium, provided together with other hardware or as part of the hardware, or can also be in other distribution forms, such as through the Internet or other wired or wireless telecommunication systems.

[0152] The present application is described with reference to the flowcharts and / or block diagrams of the methods, apparatuses (devices), and computer program products of the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, and the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0153] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that implement the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0154] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0155] The above content is a further detailed description of the present invention in combination with specific preferred embodiments. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A two-dimensional full-wave simulation method considering poloidal magnetic field in a finite element code, characterized in that: The method comprises: Initialize the parallel wave number, calculate the current dielectric tensor, and obtain the initial dielectric tensor; the parallel wave number is the component of the ion cyclotron frequency band wave ICRF wave vector in the magnetic field direction; Solving the wave equation based on the initial dielectric tensor to determine the distribution of the electric field on the tokamak magnetic surface, and performing wavelet transformation on the electric field on each tokamak magnetic surface to obtain the spectrum of the poloidal modulus; Determine the value of the dominant poloidal modulus on each tokamak magnetic surface according to the frequency spectrum of the poloidal modulus, and correct the parallel wave number based on the value of the dominant poloidal modulus; Calculate the dielectric tensor corresponding to the corrected parallel wave number to obtain the target dielectric tensor; The wave equation is solved based on the target dielectric tensor, and the distribution of the electric field on the tokamak magnetic surface is determined again to obtain the final full-wave simulation result.

2. The method according to claim 1, characterized in that: The initializing parallel wave number, calculating the current dielectric tensor, and obtaining the initial dielectric tensor include: Set the poloidal modulus to zero and initialize the parallel wave number; The initial dielectric tensor is obtained by calculating the current dielectric tensor by adding the unit tensor to the sum of the magnetic susceptibility tensors of the specific type of particles.

3. The method according to claim 2, characterized in that The current dielectric tensor is calculated by adding the unit tensor to the sum of the magnetic susceptibility tensors of the specific type of particles to obtain the initial dielectric tensor, including: The current dielectric tensor is calculated using the following formula to obtain the initial dielectric tensor: Where K represents the initial dielectric tensor, I represents the unit tensor, and χ j represents the magnetic susceptibility tensor of the j-th particle.

4. The method according to claim 3, characterized in that The acquisition of the magnetic susceptibility tensor of the i-th particle includes: In the Cartesian coordinate system of the Stix frame, when k y = 0, then the Stix magnetic susceptibility tensor of the j-th particle is obtained by the following expression: Among them, χ xx，j represents the xx component of the magnetic susceptibility tensor of the jth particle; xy，j represents the xy component of the magnetic susceptibility tensor of the jth particle; xz，j represents the xz component of the magnetic susceptibility tensor of the jth particle; yy，j represents the yy component of the magnetic susceptibility tensor of the jth particle; yx，j represents the yz component of the magnetic susceptibility tensor of the jth particle; zx，j represents the zx component of the magnetic susceptibility tensor of the jth particle; x zz，j represents the zz component of the magnetic susceptibility tensor of the jth particle; k x represents the component of the ICRF wave vector along the x direction, k y represents the component of the ICRF wave vector along the y direction, k z represents the component of the ICRF wave vector along the z direction; Based on the Stix magnetic susceptibility tensor, the magnetic susceptibility tensor of the j-th particle is obtained.

5. The method according to claim 4, characterized in that The step of obtaining the magnetic susceptibility tensor of the j-th particle based on the Stix magnetic susceptibility tensor comprises: Based on the Stix magnetic susceptibility tensor By formula Obtaining the magnetic susceptibility tensor of the j-th particle; Among them, R T is the transposed matrix of R, where R is the transformation matrix:

6. The method according to claim 1, characterized in that The wave equation is solved based on the initial dielectric tensor to determine the distribution of the electric field on the tokamak magnetic surface, and the electric field on each tokamak magnetic surface is subjected to wavelet transformation to obtain the spectrum of the poloidal modulus, including: Based on the initial dielectric tensor, the wave equation is solved by the following formula: in, is the double curl of the electric field E, ω represents the wave frequency, c represents the speed of light, K represents the initial dielectric tensor, μ is the vacuum permeability, J ant represents the antenna current, represents the plasma current; According to the solution result of the wave equation, the distribution of the electric field on the tokamak magnetic surface is determined, and the electric field on each tokamak magnetic surface is subjected to wavelet transformation to obtain the frequency spectrum of the poloidal modulus.

7. The method according to claim 6, characterized in that The acquisition of the plasma current comprises: The plasma current is obtained by the following formula: Where j is the particle type number, ω is the wave frequency, ε0 ​​is the vacuum dielectric constant, and χ j represents the magnetic susceptibility tensor of the jth particle, E represents the electric field tensor, q j represents the charge of the jth particle, γ j is the adiabatic coefficient, k B is the Boltzmann constant, T j0 is the undisturbed fluid temperature, m j represents the mass of the jth particle, Λ j is the fluid thermal pressure correction term, n j1 is the linearly perturbed plasma number density.

8. The method according to claim 1, characterized in that Determining the value of the dominant poloidal modulus on each tokamak magnetic surface according to the frequency spectrum of the poloidal modulus comprises: identifying modal components at different frequencies and scales according to the frequency spectrum of the poloidal modulus, the modal components corresponding to the poloidal modulus; According to the corresponding relationship between the modal components and the poloidal moduli, the value of the dominant poloidal modulus on each tokamak magnetic surface is determined.

9. The method according to claim 1, characterized in that: The step of correcting the parallel wave number based on the value of the dominant poloidal modulus comprises: Based on the value of the dominant poloidal mode, the parallel wave number is corrected by the following formula: Among them, k ∥ represents the parallel wave number of the ICRF, represents the toroidal modulus, m represents the poloidal modulus, R represents the maximum radius of the fully superconducting tokamak nuclear fusion experimental device EAST, N θ is the small radius of the EAST, and θ is the inverse tangent of the ratio of the poloidal magnetic field to the toroidal magnetic field.

10. An electronic device, characterized in that: The device comprises: one or more processors; A computer readable medium configured to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the two-dimensional full-wave simulation method considering the poloidal magnetic field in the finite element code as described in any one of claims 1-9.

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