CN108733946A - A kind of analogy method to develop for electron cyclotron Current profile in tokamak - Google Patents
A kind of analogy method to develop for electron cyclotron Current profile in tokamak Download PDFInfo
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Abstract
The invention discloses a kind of analogy methods to develop for electron cyclotron Current profile in tokamak.In numerical simulation tokamak device in electron cyclotron wave driving current section evolutionary process, drive current source is described using Gaussian function first, then evolution of the driving current under the shape of specific magnetic fields position is calculated according to the convection equation determined by Fei Shi-Bu Zeer theories, then the magnetic field configuration under driving current amendment is calculated, continue the evolution of calculating driving current with this magnetic field configuration, it calculates repeatedly, reaches the simulation effect to develop for a long time.The present invention realizes electron cyclotron wave driving current section and develops under true three-dimension magnetic field configuration, it can obtain the driving current section of any time, the convection equation determined simultaneously by Fei Shi-Bu Zeer theories can more accurately describe the space distribution situation of driving current, computational efficiency is high, numerical stability is strong, is a kind of method for numerical simulation of stability and high efficiency.
Description
Technical field
The present invention relates to the numerical simulations of magnetic confinement controllable nuclear fusion field tokamak device electric discharge, more particularly to a kind of
Three-dimensional simulation method for electron cyclotron Current profile nonlinear Evolution in tokamak.
Background technology
One serious problem of whole world facing --- energy crisis at present.People's production and living are relied on main
The energy is fossil energy.And the problems such as fossil energy reserves are limited, and the combusts fossil energy also will produce environmental pollution.Scientist's phase
Believe that nuclear fusion energy is most to be hopeful fundamentally to solve the problems, such as one of the approach of energy shortage.In numerous controllable nuclear fusion schemes
In, magnetic confinement method is considered as current most viable method.Therefore, in order to solve this problem, 7 states including China
Family has initiated International Thermal-Nuclear Experimental Reactor (ITER) plan jointly.In order to realize magnetic confinement controllable nuclear fusion, first have to solve
In reaction unit tokamak under quasi-steady running plasma stability problem.In order to control various unstability, science
Many methods have been invented by family, including electron cyclotron wave driving current method.By injecting electronics in the tokamak to electric discharge
The mode of cyclotron wave generates driving current, to inhibit various unstability.However due to experiment electric discharge somewhat expensive, test simultaneously
Misoperation causes experimental provision damage that will also cause huge economic loss, therefore for the numerical simulation of Tokamak discharge
It is particularly important.
At present to the simulation of electron cyclotron wave driving current mainly using the method for fixed driving current section, this method
Although the effect of driving current can be simulated substantially, experiment demand can not be met, the magnetic field configuration in experiment is not
It is fixed, and the function and effect of electron cyclotron wave driving current and magnetic field configuration are closely bound up, therefore urgent need one kind can simulate drive
Streaming current is according to the true three-dimension magnetic field configuration analogy method that self consistent nonlinear develops at any time.And method proposed by the present invention is just
This demand, while the convection equation determined using Fei Shi-Bu Zeer theories can be met well, can more accurately describe to drive
The space distribution situation of streaming current, computational efficiency is high, and numerical stability is strong, is a kind of method for numerical simulation of accurate high speed.
Invention content
Purpose of the present invention is to solve existing method to use the strategy of fixed driving current section, lead to analog result not
The problem of true Current profile evolutionary process can be embodied.Realize electron cyclotron wave driving current section in true three-dimension field bit
Under shape from be in harmony ground nonlinear Evolution.
Technical scheme of the present invention：
A kind of analogy method to develop for electron cyclotron Current profile in tokamak, steps are as follows：
Step 1：Core high-temperature plasma body region during Tokamak discharge is tested carries out mesh generation, electron cyclotron
The current function value and magnetic flux functional value obtained in wave driving current evolutionary process is carried out by the node obtained by mesh generation
Storage；
Step 2：The radio frequency system type used in being tested according to Tokamak discharge constructs corresponding mathematical function, uses
In description electron cyclotron wave drive current source Jec；According to the physical size of antenna in radio frequency system and the transmitting work(of radio frequency system
Rate initializes electron cyclotron wave driving current relevant parameter, including the spatially distributed functions of current source, amplitude and Fei Shi-cloth
Basic parameter in the convection equation that Ze Er theories determine, while obtaining initial time electron cyclotron wave driving current jec (0)；
Step 3：Initial magnetic field position shape information is measured using magnetic spy circle and flux ring in Tokamak discharge experiment, and is passed through
Numerical fitting obtains initial magnetic flux function ψ(0), and be stored in grid node；
Step 4：According to the convection equation determined by Fei Shi-Bu Zeer theories, calculate electron cyclotron wave driving current along
The evolution of the magnetic field configuration at this moment at any time, and obtain the driving current j of subsequent timeec (1)；It is as follows：
Step 4.1：Two opposite electron cyclotron driving currents of direction are calculated separately at any time using fourth-order Runge-Kutta method
Between evolution, and obtain develop a unit interval after driving current jec1 (1)And jec2 (1)；
Include two opposite electron cyclotron wave driving currents of direction according to the convection equation that Fei Shi-Bu Zeer theories determine
jec1 (0)And jec2 (0)；Independently Temporal Evolution, then summation are and always drive two electron cyclotron wave driving current electric currents
Electric current；Wherein, the computation scheme of fourth-order Runge-Kutta method is：
K1=Δ tf (tn,jec* n)
K4=Δ tf (tn+Δt,jec* n+K3)
Wherein, f (t, jec*) be driving current to the partial derivative function of time, jec*Refer to jec1And jec2；
Driving current asks the expression formula of partial derivative to be the time：
Wherein, r, θ, z be respectively radial, pole to circumferential coordinate, t is time, μ1And μ2Two electronics are respectively formed to return
Revolve the electron collision frequency of wave driving current, vp,rFor parallel resonance velocity of electrons,It is parallel for the gradient operator of parallel direction
Direction is the positive direction along the magnetic line of force；
Step 4.2：It is theoretical according to Fei Shi-Bu Zeer, by jec1 (1)And jec2 (1)It is added, obtains the unit time step that develops
Total driving current j after lengthec (1), i.e. jec (1)=jec1 (1)+jec2 (1)；
Step 5：According to modified Ohm's law, electron cyclotron wave driving current is coupled into MHD EQUATIONS IN, is calculated
The magnetic flux for the unit interval step-length that develops, and the magnetic flux ψ after being developed(1), calculating process is as follows：
The time stepping method that magnetic flux is carried out using fourth-order Runge-Kutta method is calculated；Wherein, the meter of fourth-order Runge-Kutta method
Calculating format is：
D1=Δ tg (tn,ψn)
D4=Δ tg (tn+Δt,ψn+D3)
Wherein g (t, ψ) is partial derivative function of the magnetic flux to the time；Wherein, it is coupled into electron cyclotron wave driving current
Magnetic flux is to the partial derivative equation of time：
Wherein, r, θ, z be respectively radial, pole to circumferential coordinate, t is the time, and ψ is magnetic flux, and φ is potential, by bright
Miao Er probes measure, and η is plasma resistance rate, and j is plasma total current, can be obtained by balanced cross section inverting；
Step 6：By electron cyclotron wave driving current jecThree-dimensional spatial distribution information be output in file；
Step 7：According to the magnetic flux obtained in step 5, the magnetic field configuration at current time is calculated, then repeats to walk
Rapid 4-7 is to obtain the final product to the electron cyclotron wave driving current j of any timeec (n)。
Beneficial effects of the present invention：The present invention realizes electron cyclotron wave driving current section in given true field bit
From ground nonlinear Evolution is in harmony under shape, the driving current section of any time can be obtained, solve existing method can only use it is solid
The strategy for determining driving current section, is adopted at the problem of causing analog result that cannot embody true Current profile evolutionary process simultaneously
Evolutionary process is realized with the convection equation of Fei Shi-Bu Zeer theories determination, can more accurately describe the sky of driving current
Between distribution situation, computational efficiency is high, and numerical stability is strong, is a kind of method for numerical simulation of efficient stable.
Description of the drawings
The true magnetic field configuration of three-dimensional for the Tokamak that Fig. 1 present invention is applicable in.
Fig. 2 present invention is used to simulate the initial magnetic field position tee section figure for calculating and using.
Fei Shi-Bu Zeer theoretical principle the schematic diagrames that Fig. 3 present invention uses.
The analog result sectional view that Fig. 4 electron cyclotron wave driving currents of the present invention develop.
Fig. 5 present invention, which is used to simulate, calculates the broad flow diagram that electron cyclotron wave driving current develops.
Specific implementation mode
Below in conjunction with attached drawing and technical solution, the specific implementation mode that further illustrates the present invention.
The magnetic field of tokamak device is made of nested magnetic surface, as shown in Fig. 1,Indicate big ring direction coordinate.?
In Tokamak discharge experiment, the effect of electron cyclotron wave driving current mainly inhibits magnetic island, therefore initial magnetic field position shape is logical
It is commonly present magnetic island, as shown in Fig. 2, for field line reconnection at magnetic island structure, wherein r is minor radius coordinate, and θ is pole to coordinate.Electricity
Sub- cyclotron wave general action is in magnetic island center.Electron cyclotron wave driving current can carry out being in harmony non-certainly along given magnetic field configuration
It is linear to develop, finally reach steady-state distribution in space.The present embodiment describes electron cyclotron wave driving using Gaussian function first
Current source.Experimentally generally use gyrotron generates electron cyclotron wave, and Gaussian function can preferably describe the driving of its excitation
Current source；Then, cyclotron wave driving current is initialized, driving electricity is calculated according to the convection equation that Fei Shi-Bu Zeer theories determine
Flow the nonlinear Evolution along the given magnetic line of force.Wherein, Fei Shi-Bu Zeer theoretical principles schematic diagram is as shown in Fig. 3, by penetrating
Display system injects electron cyclotron wave in high-temperature plasma, generates driving current in resonance zone, while driving current can edge
Magnetic line of force propagation, the evolution of driving current follows the convection equation of Fei Shi-Bu Zeer theories determination；Followed by modified
Driving current after evolution is coupled into electromagnetic fluid equation group by Ohm's law, calculates driving current to last moment magnetic field
It corrects, and obtains revised magnetic field；Finally driving current is calculated using revised magnetic field as the magnetic field configuration at current time
Nonlinear Evolution, repeat before the step of it is multiple, final electron cyclotron wave driving current reaches steady-state distribution in space, such as
Shown in attached drawing 4.
Specific implementation step is as follows：
Step 1：Core high-temperature plasma body region during Tokamak discharge is tested carries out mesh generation, electron cyclotron
The current function value that is obtained in wave driving current evolutionary process and magnetic flux functional value by the node that is obtained by mesh generation into
Row storage；
Step 2：Electron cyclotron wave is described according to the suitable mathematical function of radio frequency system type structure used in experiment to drive
Streaming current source Jec.Experimentally generally use gyrotron generates electron cyclotron wave, therefore this example describes it using Gaussian function
The drive current source of excitation.Concrete form is
Wherein, r is radial coordinate, ξ be spiral angular direction coordinate (according to the helical structure in tokamak magnetic field, pole to θ and
Circumferential z can be converted into helical angle ξ), jd0For driving current amplitude, can be calculated according to radio frequency system transmission power, r0With
ξ0The respectively radial position of the rf wave zone of action and helical angle direction position, Δ rdWith Δ ξdRespectively radial effect width
With spiral angular direction active width.
Electronics is initialized according to experiment parameters such as the transmission powers of the physical size of radio frequency system antenna and radio frequency system
Cyclotron wave driving current relevant parameter obtains initial time electron cyclotron wave driving current jec (0)；
Step 3：The device measurings initial magnetic fields such as magnetic spy circle and flux ring position shape information is experimentally used, and quasi- by numerical value
The mathematical computations such as conjunction obtain initial magnetic flux function ψ(0)And it is stored in grid node.This example use initial magnetic field position shaped like
Shown in attached drawing 2.
Step 4：Electron cyclotron wave driving current is calculated along this according to the convection equation determined by Fei Shi-Bu Zeer theories
The evolution at any time of the magnetic field configuration at moment simultaneously obtains the driving current j of subsequent timeec (1), wherein Fei Shi-Bu Zeer are theoretical former
It is as shown in Fig. 3 to manage schematic diagram.It is as follows：
Step 4.1：Two opposite electron cyclotron driving currents of direction are calculated separately at any time using fourth-order Runge-Kutta method
Between evolution, and obtain develop a unit interval after driving current jec1 (1)And jec2 (1)。
Here, include that two opposite electron cyclotron waves of direction drive according to the convection equation that Fei Shi-Bu Zeer theories determine
Streaming current jec1 (0)And jec2 (0).Two electric currents independently Temporal Evolution, then summation is total driving current.Wherein, four
The computation scheme of rank Runge-Kutta method is：
K1=Δ tf (tn,jec* n)
K4=Δ tf (tn+Δt,jec* n+K3)
Wherein f (t, jec*) be driving current to the partial derivative function of time, jec*Refer to jec1And jec2。
Driving current asks the expression formula of partial derivative to be the time：
Wherein, r, θ, z be respectively radial, pole to circumferential coordinate, t is time, μ1And μ2Respectively form two driving electricity
The electron collision frequency of stream, vp,rFor parallel resonance velocity of electrons,For the gradient operator of parallel direction, parallel direction be along
The positive direction of the magnetic line of force；
Step 4.2：It is theoretical according to Fei Shi-Bu Zeer, by jec1 (1)And jec2 (1)Addition can obtain a unit interval of developing
Total driving current j after step-lengthec (1), i.e. jec (1)=jec1 (1)+jec2 (1)；
Step 5：Electron cyclotron wave driving current is coupled into MHD EQUATIONS IN according to modified Ohm's law, calculating is drilled
Magnetic flux ψ after changing the magnetic flux of a unit interval step-length and being developed(1), calculating process is as follows：
The time stepping method that magnetic flux is carried out using fourth-order Runge-Kutta method is calculated.Wherein, the meter of fourth-order Runge-Kutta method
Calculating format is：
D1=Δ tg (tn,ψn)
D4=Δ tg (tn+Δt,ψn+D3)
Wherein g (t, ψ) is partial derivative function of the magnetic flux to the time；Wherein, it is coupled into electron cyclotron wave driving current
Magnetic flux is to the partial derivative equation of time：
Wherein, r, θ, z be respectively radial, pole to circumferential coordinate, t is the time, and ψ is magnetic flux, and φ is potential, can be passed through
Langmuir probe measures, and η is plasma resistance rate, and j is plasma total current, can be obtained by balanced cross section inverting；
Step 6：By electron cyclotron wave driving current jecThree-dimensional spatial distribution information be output in file；
Step 7：The magnetic field configuration at current time is calculated according to the magnetic flux obtained in step 5, then repeats to walk
Rapid 4-7 can be obtained the electron cyclotron wave driving current j of any timeec (n)。
Develop by long-time, final electron cyclotron wave driving current reaches steady-state distribution in space, such as 5 institute of attached drawing
Show.
The above content is combine optimal technical scheme to the present invention done further description, and it cannot be said that invention
Specific implementation is only limitted to these explanations.For general technical staff of the technical field of the invention, the present invention is not being departed from
Design under the premise of, can also make it is simple deduce and replace, all should be considered as protection scope of the present invention.
Claims (1)
1. a kind of analogy method to develop for electron cyclotron Current profile in tokamak, which is characterized in that steps are as follows：
Step 1：Core high-temperature plasma body region during Tokamak discharge is tested carries out mesh generation, and electron cyclotron wave drives
The current function value and magnetic flux functional value obtained in streaming current evolutionary process, is stored up by the node obtained by mesh generation
It deposits；
Step 2：The radio frequency system type used in being tested according to Tokamak discharge, constructs corresponding mathematical function, for retouching
State electron cyclotron wave drive current source Jec；According to the physical size of antenna in radio frequency system and the transmission power of radio frequency system,
Initialize electron cyclotron wave driving current relevant parameter, including the spatially distributed functions of current source, amplitude and Fei Shi-Bu Zeer
Basic parameter in the convection equation that theory determines, while obtaining initial time electron cyclotron wave driving current jec (0)；
Step 3：Initial magnetic field position shape information is measured using magnetic spy circle and flux ring in Tokamak discharge experiment, and passes through numerical value
Fitting obtains initial magnetic flux function ψ(0), and be stored in grid node；
Step 4：According to the convection equation determined by Fei Shi-Bu Zeer theories, electron cyclotron wave driving current is calculated along at this time
The evolution of the magnetic field configuration at quarter at any time, and obtain the driving current j of subsequent timeec (1)；It is as follows：
Step 4.1：Two opposite electron cyclotron driving currents of direction are calculated separately at any time using fourth-order Runge-Kutta method
Develop, and obtains the driving current j after one unit interval of evolutionec1 (1)And jec2 (1)；
Include two opposite electron cyclotron wave driving current j of direction according to the convection equation that Fei Shi-Bu Zeer theories determineec1 (0)And jec2 (0)；Independently Temporal Evolution, then summation as always drive electricity to two electron cyclotron wave driving current electric currents
Stream；Wherein, the computation scheme of fourth-order Runge-Kutta method is：
Wherein,It is driving current to the partial derivative function of time,Refer to jec1And jec2；
Driving current asks the expression formula of partial derivative to be the time：
Wherein, r, θ, z be respectively radial, pole to circumferential coordinate, t is time, μ1And μ2Respectively form two electron cyclotron waves
The electron collision frequency of driving current, vp,rFor parallel resonance velocity of electrons,For the gradient operator of parallel direction, parallel direction
For along the positive direction of the magnetic line of force；
Step 4.2：It is theoretical according to Fei Shi-Bu Zeer, by jec1 (1)And jec2 (1)Be added, obtain developing unit interval step-length it
Total driving current j afterwardsec (1), i.e. jec (1)=jec1 (1)+jec2 (1)；
Step 5：According to modified Ohm's law, electron cyclotron wave driving current is coupled into MHD EQUATIONS IN, calculates and develops
The magnetic flux of one unit interval step-length, and the magnetic flux ψ after being developed(1), calculating process is as follows：
The time stepping method that magnetic flux is carried out using fourth-order Runge-Kutta method is calculated；Wherein, the calculating lattice of fourth-order Runge-Kutta method
Formula is：
D1=Δ tg (tn,ψn)
D4=Δ tg (tn+Δt,ψn+D3)
Wherein g (t, ψ) is partial derivative function of the magnetic flux to the time；Wherein, it is coupled into the magnetic flux of electron cyclotron wave driving current
It measures and is to the partial derivative equation of time：
Wherein, r, θ, z be respectively radial, pole to circumferential coordinate, t is the time, and ψ is magnetic flux, and φ is potential, passes through Langmuir
Probe measures, and η is plasma resistance rate, and j is plasma total current, can be obtained by balanced cross section inverting；
Step 6：By electron cyclotron wave driving current jecThree-dimensional spatial distribution information be output in file；
Step 7：According to the magnetic flux obtained in step 5, the magnetic field configuration at current time is calculated, then repeats step 4-
7 to obtain the final product to the electron cyclotron wave driving current j of any timeec (n)。
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| CN111259599A (en) * | 2020-01-07 | 2020-06-09 | 大连理工大学 | Test particle simulation method for analyzing constraint performance of high-energy particles in tokamak |
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| CN112966453A (en) * | 2021-03-15 | 2021-06-15 | 大连理工大学 | Simulation method for EAST tokamak radio frequency waveguide induced electronic temperature evolution |
| CN113283135A (en) * | 2021-05-17 | 2021-08-20 | 核工业西南物理研究院 | Method for extracting electromagnetic simulation plasma current data of tokamak vacuum chamber |
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| WO2022193041A1 (en) * | 2021-03-15 | 2022-09-22 | 大连理工大学 | Method for simulating electron temperature evolution caused by east tokamak radio frequency wave |
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| CN110232205A (en) * | 2019-04-28 | 2019-09-13 | 大连理工大学 | The analogy method of neo-classicial tearing mode is controlled for the magnetic disturbance that resonates in tokamak |
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| CN111259599A (en) * | 2020-01-07 | 2020-06-09 | 大连理工大学 | Test particle simulation method for analyzing constraint performance of high-energy particles in tokamak |
| CN111259599B (en) * | 2020-01-07 | 2022-09-20 | 大连理工大学 | Test particle simulation method for analyzing constraint performance of high-energy particles in tokamak |
| CN112966453A (en) * | 2021-03-15 | 2021-06-15 | 大连理工大学 | Simulation method for EAST tokamak radio frequency waveguide induced electronic temperature evolution |
| CN112966453B (en) * | 2021-03-15 | 2022-09-20 | 大连理工大学 | Simulation method for EAST tokamak radio frequency waveguide induced electronic temperature evolution |
| WO2022193041A1 (en) * | 2021-03-15 | 2022-09-22 | 大连理工大学 | Method for simulating electron temperature evolution caused by east tokamak radio frequency wave |
| CN113283135A (en) * | 2021-05-17 | 2021-08-20 | 核工业西南物理研究院 | Method for extracting electromagnetic simulation plasma current data of tokamak vacuum chamber |
| CN113468789A (en) * | 2021-09-06 | 2021-10-01 | 广东电网有限责任公司中山供电局 | Temperature rise simulation method for ground wire-wire clamp assembly under lightning stroke effect |
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