CN114996631A - Light-weight reconstruction method for Tokamak plasma equilibrium configuration - Google Patents

Light-weight reconstruction method for Tokamak plasma equilibrium configuration Download PDF

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CN114996631A
CN114996631A CN202210550935.1A CN202210550935A CN114996631A CN 114996631 A CN114996631 A CN 114996631A CN 202210550935 A CN202210550935 A CN 202210550935A CN 114996631 A CN114996631 A CN 114996631A
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plasma
iteration
tokamak
balance
magnetic flux
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鲍娜娜
闫星廷
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Anhui University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
    • G21B—FUSION REACTORS
    • G21B1/00—Thermonuclear fusion reactors
    • G21B1/05—Thermonuclear fusion reactors with magnetic or electric plasma confinement
    • G21B1/057—Tokamaks
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E30/00—Energy generation of nuclear origin
    • Y02E30/10—Nuclear fusion reactors

Abstract

The invention discloses a lightweight reconstruction method for Tokamak plasma equilibrium configuration, which comprises the following specific steps of obtaining various types of electromagnetic measurement data and presetting model constant parameters; selecting and loading balance data of the tokamak device as an initial balance configuration; setting an iteration error, determining an error value, and then solving a Tokamak plasma equilibrium configuration; and outputting the result after iteration convergence, and displaying the balance configuration. According to the invention, through concise interface design, efficient numerical calculation format realization, visual result display and flexible and rich function module calling, the plasma balance reconstruction operation process is greatly simplified, the platform dependence is reduced, the physical analysis efficiency is improved, the calculation error and higher operation threshold caused by the complexity of the plasma balance physical principle are avoided to a great extent, and the method is a powerful tool for assisting scientific researchers in carrying out experiments and physical analysis.

Description

Lightweight reconstruction method for Tokamak plasma equilibrium configuration
Technical Field
The invention relates to the technical field of plasma physics, in particular to a lightweight reconstruction method for Tokamak plasma equilibrium configuration.
Background
Plasma balance is an important starting point for Tokamak physical research, and accurate and reliable plasma balance distribution information is of great importance for research on problems such as magnetic fluid instability analysis, plasma parameter performance evaluation, plasma control and the like.
However, the plasma equilibrium contains a large amount of physical parameter distribution and tokamak configuration characteristics, and the current limited experimental diagnosis technology cannot directly measure and obtain complete equilibrium distribution information. Therefore, the commonly adopted method is to reconstruct and calculate to obtain the plasma equilibrium configuration by using the plasma equilibrium reconstruction technology based on the limited electromagnetic measurement signals.
The existing plasma balance reconstruction method has the disadvantages that the existing plasma balance reconstruction method usually has the problems of high requirements on software and hardware environment, poor user friendliness, high requirements on professional experience of operators and the like, and has the risk of human misoperation, and the problems restrict the effective development of plasma physical analysis and the large-scale popularization of the plasma balance reconstruction method and are not favorable for the smooth implementation of scientific research work.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and in order to realize the aim, a lightweight reconstruction method of the Tokamak plasma equilibrium configuration is adopted to solve the problems in the background technology.
A lightweight reconstruction method for Tokamak plasma equilibrium configuration comprises the following specific steps:
s1, acquiring various types of electromagnetic measurement data, and presetting model constant parameters;
s2, selecting and loading balance data of the tokamak device as an initial balance configuration;
s3, setting an iteration error, determining an error value, and then solving the equilibrium configuration of the Tokamak plasma;
and S4, outputting the result after iterative convergence, and displaying the balance configuration.
As a further aspect of the invention: the various types of electromagnetic measurement data include plasma current, magnetic field, and magnetic flux.
As a further aspect of the invention: the model constant parameters comprise a Green function table, a plasma grid region and division precision, and an expansion order of the polynomial current model.
As a further aspect of the invention: the S3 sets an iteration error, and the specific steps of solving the equilibrium configuration of the Tokamak plasma after determining the error value comprise:
firstly, setting an iteration error, wherein the iteration error is smaller than a threshold value K;
constructing a plasma current equation, wherein the plasma current equation is as follows:
Figure BDA0003655019440000021
in the formula (I), the compound is shown in the specification,
Figure BDA0003655019440000022
and
Figure BDA0003655019440000023
the expansion of (a) is:
Figure BDA0003655019440000024
Figure BDA0003655019440000025
wherein R is a horizontal coordinate, Z is a vertical coordinate, P is a plasma pressure, and F is RB t ，B t Is the circumferential magnetic induction intensity, psi is the magnetic flux, mu 0 Is a vacuum permeability,. psi N To normalize the magnetic flux, a n And gamma n Is the expansion coefficient, n p And n F The highest order of the expansion;
constructing a response matrix gamma according to the Green function table;
solving the plasma current based on the electromagnetic diagnostic data and the response matrix, wherein the relation is as follows:
F·D＝(F·Γ)×U；
wherein F is a matrix formed by weighted values, D represents a matrix of electromagnetic diagnostic data, and U represents a matrix of plasma current;
based on the obtained plasma current distribution, a Picard iteration format is utilized to solve a Grad-Shafranov equation for describing the Tokamak plasma balance, and the magnetic flux distribution obtained in the step (n + 1) is as follows:
Figure BDA0003655019440000026
where ψ is a magnetic flux, R is a large radius, Z is a vertical coordinate, μ 0 Is a vacuum permeability, J φ For the plasma current, n and n +1 both represent the number of iteration steps;
the magnetic flux values for the X point and the magnetic axis position are optimized.
As a further aspect of the invention: the specific steps of outputting the result after iterative convergence of the S4 and displaying the balance bit pattern include:
comparing the difference value of the iteration result and the last iteration result;
if the difference value is larger than the iteration error, continuing the iteration step, otherwise outputting the current magnetic flux distribution as a result;
and simultaneously, storing the result in a discharge experiment database, and carrying out graphic visual display and output.
Compared with the prior art, the invention has the following technical effects:
by adopting the technical scheme, the electromagnetic measurement diagnosis signal is obtained by utilizing the physical principle of plasma balance reconstruction, and the position and shape of the plasma balance parameter are reconstructed and calculated. By the aid of the method, operation procedures of scientific researchers are simplified, problem analysis efficiency is improved, and reconstruction result errors caused by complex operation procedures and poor professional experience of the scientific researchers are avoided.
Drawings
The following detailed description of embodiments of the invention refers to the accompanying drawings in which:
FIG. 1 is a schematic diagram of steps of a plasma equilibrium configuration lightweight reconstruction method according to some embodiments disclosed herein;
FIG. 2 is a schematic flow diagram of a plasma equilibrium configuration lightweight reconstruction method according to some embodiments disclosed herein;
fig. 3 is a visual display of the results of the plasma equilibrium configuration lightweight reconstruction method according to some embodiments of the present disclosure.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1 and fig. 2, in an embodiment of the present invention, a method for lightweight reconstruction of tokamak plasma equilibrium configuration includes the following specific steps:
s1, acquiring various types of electromagnetic measurement data, and presetting model constant parameters;
the various types of electromagnetic measurement data include plasma current, magnetic field, and magnetic flux. In a specific embodiment, the plasma current is measured by a rocco coil, the magnetic field is measured by a magnetic probe, and the magnetic flux is measured by a single turn loop;
the model constant parameters comprise a Green function table for measuring mutual inductance among the plasma grid points, the poloidal field coils and the magnetic probes, plasma grid areas and division accuracy, and expansion orders of the polynomial current model.
S2, selecting and loading balance data of the tokamak device as an initial balance configuration;
s3, setting an iteration error, determining an error value, and then solving the equilibrium configuration of the Tokamak plasma, wherein the method specifically comprises the following steps:
in a particular embodiment, the starting point for the calculation is the Grad-Shafranov equation (i.e., the G-S equation) describing the Tokamak plasma equilibrium, which is calculated as:
Figure BDA0003655019440000041
where ψ is a magnetic flux, R is a large radius, Z is a vertical coordinate, μ 0 Is a vacuum permeability, J φ Is a plasma current;
firstly, setting an iteration error, wherein the iteration error is smaller than a threshold value K; specifically, the iteration error is usually less than 1e-3, in this embodiment, 1e-4 is selected as an example for description of the method;
constructing a plasma current equation, wherein the plasma current equation is as follows:
Figure BDA0003655019440000042
in the formula (I), the compound is shown in the specification,
Figure BDA0003655019440000043
and
Figure BDA0003655019440000044
the expansion of (a) is:
Figure BDA0003655019440000045
Figure BDA0003655019440000046
wherein R is a horizontal coordinate, Z is a vertical coordinate, P is a plasma pressure, and F is RB t ，B t Is the circumferential magnetic induction intensity, psi is the magnetic flux, mu 0 Is vacuum permeability,. psi N To normalize the magnetic flux, a n And gamma n Is the expansion coefficient, n p And n F The highest order of the expansion;
wherein P is plasma pressure，F＝RB φ ，B φ Is the circumferential component of the magnetic induction. Psi N The value range is (0,1) for normalizing the magnetic flux.
In the formula of alpha n And gamma n Is the undetermined coefficient. Once the value of the undetermined coefficient is determined, the plasma current J can be obtained φ Distribution of (2).
Wherein the expansion order is n p ＝2,n F When the plasma current distribution is 1, the expression of the plasma current distribution is as follows:
Figure BDA0003655019440000051
constructing a response matrix gamma according to a Green function table for measuring mutual inductance among the plasma grid points, the polar field coils and the magnetic probes;
solving plasma current distribution J using electromagnetic measurement signals using a response matrix φ ；
Solving the plasma current based on the electromagnetic diagnostic data and the response matrix, wherein the relation is as follows:
F·D＝(F·Γ)×U；
wherein F is a matrix formed by weighted values, D represents a matrix of electromagnetic diagnostic data, and U represents a matrix of plasma current;
based on the obtained plasma current distribution, a Picard iteration format is utilized to solve a Grad-Shafranov equation for describing the Tokamak plasma balance, and the magnetic flux distribution obtained in the step (n + 1) is as follows:
Figure BDA0003655019440000052
where ψ is a magnetic flux, R is a large radius, Z is a vertical coordinate, μ 0 Is a vacuum permeability, J φ For the plasma current, n and n +1 both represent the number of iteration steps;
the magnetic flux values of the X point and the magnetic axis position are optimized, and the X point and the magnetic axis position are easy to have larger numerical errors, so that the calculation result is inaccurate, and therefore, the X point and the magnetic axis position need to be optimized in a targeted manner, and the calculation precision is improved.
S4, outputting results after iterative convergence, and displaying the balance configuration, wherein the method specifically comprises the following steps:
comparing the difference value of the iteration result and the last iteration result;
if the difference value is larger than the iteration error, continuing the iteration step, otherwise outputting the current magnetic flux distribution as a result;
and simultaneously, storing the result in a discharge experiment database, and carrying out graphic visual display and output.
As shown in fig. 3, a diagram is presented showing the visualization of the results of the reconstruction method.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents, which should be construed as being within the scope of the invention.

Claims (5)

1. A lightweight reconstruction method for Tokamak plasma equilibrium configuration is characterized by comprising the following specific steps:
s1, acquiring various types of electromagnetic measurement data, and presetting model constant parameters;
s2, selecting and loading balance data of the tokamak device as an initial balance configuration;
s3, setting an iteration error, determining an error value, and then solving the equilibrium configuration of the Tokamak plasma;
and S4, outputting the result after iterative convergence, and displaying the balance configuration.
2. The method according to claim 1, wherein the plurality of types of electromagnetic measurement data comprise plasma current, magnetic field, and magnetic flux.
3. The method as claimed in claim 1, wherein the model constant parameters include a Green function table, a plasma mesh region and partition precision, and an expansion order of the polynomial current model.
4. The method of claim 1, wherein the S3 sets an iteration error, and the specific step of solving the tokamak plasma equilibrium configuration after determining the error value includes:
firstly, setting an iteration error, wherein the iteration error is smaller than a threshold value K;
constructing a plasma current equation, wherein the plasma current equation is as follows:
Figure FDA0003655019430000011
in the formula (I), the compound is shown in the specification,
Figure FDA0003655019430000012
and
Figure FDA0003655019430000013
the expansion of (a) is:
Figure FDA0003655019430000014
Figure FDA0003655019430000015
wherein R is a horizontal coordinate, Z is a vertical coordinate, P is a plasma pressure, and F is RB t ，B t Is the circumferential magnetic induction intensity, psi is the magnetic flux, mu 0 Is vacuum permeability,. psi N To normalize the magnetic flux, a n And gamma n To be unfoldedCoefficient n p And n F The highest order of the expansion;
constructing a response matrix gamma according to the Green function table;
and solving the plasma current based on the electromagnetic diagnostic data and the response matrix, wherein the relation is as follows:
F·D＝(F·Γ)×U；
in the formula, F is a matrix formed by weighted values, D represents a matrix of electromagnetic diagnostic data, and U represents a matrix of plasma current;
based on the obtained plasma current distribution, a Picard iteration format is utilized to solve a Grad-Shafranov equation for describing the Tokamak plasma balance, and the magnetic flux distribution obtained in the step (n + 1) is as follows:
Figure FDA0003655019430000021
where ψ is a magnetic flux, R is a large radius, Z is a vertical coordinate, μ 0 Is a vacuum permeability, J φ For the plasma current, n and n +1 represent the number of iteration steps;
the magnetic flux values for the X point and the magnetic axis position are optimized.
5. The method for lightweight reconstruction of the equilibrium configuration of the tokamak plasma according to claim 1 or 4, wherein the step of outputting the result after iterative convergence of S4 and performing the display of the equilibrium configuration comprises the following specific steps:
comparing the difference value of the iteration result and the last iteration result;
if the difference value is larger than the iteration error, continuing the iteration step, otherwise outputting the current magnetic flux distribution as a result;
and simultaneously, storing the result in a discharge experiment database, and carrying out graphic visual display and output.
CN202210550935.1A 2022-05-20 2022-05-20 Light-weight reconstruction method for Tokamak plasma equilibrium configuration Pending CN114996631A (en)

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116167247A (en) * 2023-04-21 2023-05-26 中国科学院合肥物质科学研究院 GS equation numerical calculation method based on Fengha Gnoff method
CN117010314A (en) * 2023-09-28 2023-11-07 中国科学院合肥物质科学研究院 Implementation method, device, equipment and medium of magnetic confinement reaction device
CN117371299A (en) * 2023-12-08 2024-01-09 安徽大学 Machine learning method for Tokamak new classical circumferential viscous torque

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116167247A (en) * 2023-04-21 2023-05-26 中国科学院合肥物质科学研究院 GS equation numerical calculation method based on Fengha Gnoff method
CN117010314A (en) * 2023-09-28 2023-11-07 中国科学院合肥物质科学研究院 Implementation method, device, equipment and medium of magnetic confinement reaction device
CN117010314B (en) * 2023-09-28 2024-01-16 中国科学院合肥物质科学研究院 Implementation method, device, equipment and medium of magnetic confinement reaction device
CN117371299A (en) * 2023-12-08 2024-01-09 安徽大学 Machine learning method for Tokamak new classical circumferential viscous torque
CN117371299B (en) * 2023-12-08 2024-02-27 安徽大学 Machine learning method for Tokamak new classical circumferential viscous torque

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