Many magnetohydrodynamic stability analyses require generation of a set of equilibria with a fixed safety factor q-profile while varying other plasma parameters.A neural network(NN)-based approach is investigated that...Many magnetohydrodynamic stability analyses require generation of a set of equilibria with a fixed safety factor q-profile while varying other plasma parameters.A neural network(NN)-based approach is investigated that facilitates such a process.Both multilayer perceptron(MLP)-based NN and convolutional neural network(CNN)models are trained to map the q-profile to the plasma current density J-profile,and vice versa,while satisfying the Grad–Shafranov radial force balance constraint.When the initial target models are trained,using a database of semianalytically constructed numerical equilibria,an initial CNN with one convolutional layer is found to perform better than an initial MLP model.In particular,a trained initial CNN model can also predict the q-or J-profile for experimental tokamak equilibria.The performance of both initial target models is further improved by fine-tuning the training database,i.e.by adding realistic experimental equilibria with Gaussian noise.The fine-tuned target models,referred to as fine-tuned MLP and fine-tuned CNN,well reproduce the target q-or J-profile across multiple tokamak devices.As an important application,these NN-based equilibrium profile convertors can be utilized to provide a good initial guess for iterative equilibrium solvers,where the desired input quantity is the safety factor instead of the plasma current density.展开更多
Interpreting experimental diagnostics data in tokamaks,while considering non-ideal effects,is challenging due to the complexity of plasmas.To address this challenge,a general synthetic diagnostics(GSD)platform has bee...Interpreting experimental diagnostics data in tokamaks,while considering non-ideal effects,is challenging due to the complexity of plasmas.To address this challenge,a general synthetic diagnostics(GSD)platform has been established that facilitates microwave imaging reflectometry and electron cyclotron emission imaging.This platform utilizes plasma profiles as input and incorporates the finite-difference time domain,ray tracing and the radiative transfer equation to calculate the propagation of plasma spontaneous radiation and the external electromagnetic field in plasmas.Benchmark tests for classical cases have been conducted to verify the accuracy of every core module in the GSD platform.Finally,2D imaging of a typical electron temperature distribution is reproduced by this platform and the results are consistent with the given real experimental data.This platform also has the potential to be extended to 3D electromagnetic field simulations and other microwave diagnostics such as cross-polarization scattering.展开更多
Variational principle for the neoclassical theory has been developed by including a momentum restoring term in the electron-electron collisional operator, which gives an additional free parameter maximizing the heat p...Variational principle for the neoclassical theory has been developed by including a momentum restoring term in the electron-electron collisional operator, which gives an additional free parameter maximizing the heat production rate. All transport coefficients are obtained including the bootstrap current. The essential feature of the study is that the aspect ratio affects the function of the electron-electron collision operator through a geometrical factor. When the aspect ratio approaches to unity, the fraction of circulating particles goes to zero and the contribution to particle flux from the electron-electron collision vanishes. The resulting diffusion coefficient is in rough agreement with Hazeltine. When the aspect ratio approaches to infinity, the results are in agreement with Rosenbluth. The formalism gives the two extreme cases a connection. The theory is particularly important for the calculation of bootstrap current in spherical tokamaks and the present tokamaks, in which the square root of the inverse aspect ratio, in general, is not small.展开更多
Based on a linearized MHD model, the effect of equilibrium current profiles on external kink modes in tokamaks is studied by MARS code. Three types of equilibrium current profiles are adopted in this work. Firstly, a ...Based on a linearized MHD model, the effect of equilibrium current profiles on external kink modes in tokamaks is studied by MARS code. Three types of equilibrium current profiles are adopted in this work. Firstly, a set of parabolic equilibrium current profiles are chosen. In these profiles the maximum current values in the center of the plasma are fixed, and the currents have different gradient and jump at the plasma boundary. The effects of the current gradient and jump on the growth rate of external kink mode are investigated. It is found that the current jump which causes the q profiles to change plays an important role in the externM kink modes in tokamaks. Secondly, a set of step equilibrium current profiles with different jump positions are chosen. The effect of jump position on external kink modes is discussed. Thirdly, a set of parabolic equilibrium current profiles with current bumps are chosen for the case of off-axis heating. The effects of height~ width and position of the current bumps on external kink modes are analyzed. The fiat equilibrium current profiles are disadvantageous for the MHD stabilities of tokamaks, because of the large current jump at the plasma edge. The peaked equilibrium current profiles and a large and localized current bump near the plasma edge benefit the MHD stabilities of tokamaks.展开更多
Fundamental characteristics of charging of a dust particle and its dynamics in SOL/divertor plasma in tokamaks are studied. According to the OML （orbit motion limited） theory, the charging process is extremely faste...Fundamental characteristics of charging of a dust particle and its dynamics in SOL/divertor plasma in tokamaks are studied. According to the OML （orbit motion limited） theory, the charging process is extremely faster, with a charging time of nanoseconds, than the dynamics process of the dust particle in SOL/divertor plasma, with a characteristic time of mil- liseconds, which means that the local charge state can be taken as the equilibrium charge state. It was clarified that the equilibrium charge Zd, eq can be determined in the form of Zd, eq/RdTe, which is a function of both the normalized relative speed of plasma ion flow with respect to the velocity of the dust particle and the plasma temperature ratio. After the investigation of domi- nant forces acting on dust particles, the friction forces due to the plasma ion absorption and ion Coulomb scattering are found of the same order for the case of low relative speed. The critical radius of a dust particle, for which the gravity is larger than the friction forces due to plasma ions, is obtained.展开更多
Shaping effects of the E-fishbone in tokamaks are investigated. Coordinates related to the Solov＇ev configuration are used to calculate the precession frequency and kinetic contribu- tion. It is shown that elongation...Shaping effects of the E-fishbone in tokamaks are investigated. Coordinates related to the Solov＇ev configuration are used to calculate the precession frequency and kinetic contribu- tion. It is shown that elongation does not change the precession frequency and the kinetic energy. Growth rates of the E-fishbone vary with elongation which essentially has destabilizing effects. For elongated tokamaks, triangularity has a stabilizing effect on the modes which play a compensative role. The results may apply to Sunist.展开更多
Joint experiments(JEs)on small tokamaks have been regularly performed between 2005 and 2015 under the framework of the International Atomic Energy Agency(IAEA)coordinated research projects(CRPs).This paper describes t...Joint experiments(JEs)on small tokamaks have been regularly performed between 2005 and 2015 under the framework of the International Atomic Energy Agency(IAEA)coordinated research projects(CRPs).This paper describes the background and the rationale for these experiments,how they were organized and executed,main areas of research covered during these experiments,main results,contributions to mainstream fusion research,and discusses lessons learned and outcomes from these activities.We underline several of the most important scientific outputs and also specific outputs in the education of young scientists and scientists from developing countries and their importance.展开更多
A criterion of an ideal internal kink mode is derived for a shaped tokamak configuration in which q-profile is very flat in the core region. A combining criterion is obtained including the necessary criterion of Merci...A criterion of an ideal internal kink mode is derived for a shaped tokamak configuration in which q-profile is very flat in the core region. A combining criterion is obtained including the necessary criterion of Mercier and the sufficient criterion of Lortz. The new criterion makes progress compared with the necessary criterion of Mercier. In the elongated plasma, a poloidal beta can cause instability, while the triangularity has a stabilizing effect. The result is applicable for DIII-D and SUNIST.展开更多
Neoclassical transport for the shaped tokamak with X point is investigated using Hamiltonian formalism. For a set of Soloveev's configurations, the neoclassical diffusion coefficient is rigorously derived for the ...Neoclassical transport for the shaped tokamak with X point is investigated using Hamiltonian formalism. For a set of Soloveev's configurations, the neoclassical diffusion coefficient is rigorously derived for the plateau regime which is inversely proportional to the connection length. When an X point appears on plasma boundary, the diffusion coefficient is greatly reduced by a much longer connection length compared with a circular cross-section plasma. Since the formalism is not limited for aspect ratio, for A = 1.3, it may be valid in a very narrow range of collisionality, 0.8 < V*i < 1.0, at / o = 0.95. In the range of collisionality, the detrapping rate is very high.展开更多
The principle of minimum dissipation rate is applied to tokamak plasmas with energy and helicity balances imposed as two constraints. The analytical solution on toroidal current distribution are derived from the resul...The principle of minimum dissipation rate is applied to tokamak plasmas with energy and helicity balances imposed as two constraints. The analytical solution on toroidal current distribution are derived from the resulting Euler-Lagrangian equation. Three typical forms of current profiles are found for low-aspect-ratio tokamaks like NSTX. One of them decreases with r on equatorial plane, the second peaks in the inner half part on equatorial plane and the third may have a hole or reverse in the central part.展开更多
Compact toroidal magnetized plasmas are an important part of the world’s magnetic fusion and plasma science efforts. These devices can play an integral role in the development of magnetic fusion as a viable commercia...Compact toroidal magnetized plasmas are an important part of the world’s magnetic fusion and plasma science efforts. These devices can play an integral role in the development of magnetic fusion as a viable commercial energy source, and in our understanding of plasma instabilities, particle and energy transport, and magnetic field transport. In this paper, we are developing a numerical program to study the magnetic dynamo or relaxation of CT’s characterized by arbitrary tight aspect ratio (major to minor radii of tokamak) and arbitrary cross-sections (Multi-pinch and D-Shaped). The lowest ZFE’s has been calculated through the Taylor’s relaxed state (force-free) toroidal plasmas equation. For ZFE’s, we use the toroidal flux vanishing boundary condition along the whole boundary of tokamaks. Several runs of the program for various wave numbers showed that ZFE was very insensitive to the choice of wave numbers. Besides, the CT’s poloidal magnetic field topologies are well represented. It was very interesting to check our methods for the cases when aspect ratio tends to unity (zero tokamak whole). A good fulfillment of the boundary condition is achieved.展开更多
The control of turbulence at tokamaks is very complex problem.The idea is to apply the fuzzy Markovian processes and fuzzy Brownian motions as good approximation of general robust drift kinetic equation. It is obtaine...The control of turbulence at tokamaks is very complex problem.The idea is to apply the fuzzy Markovian processes and fuzzy Brownian motions as good approximation of general robust drift kinetic equation. It is obtained by using the artificial neural networks for solving of appropriate advanced control problem. The proof of the appropriate theorem is shown.展开更多
The effect of plasma with toroidal rotation on the resistive wall modes in tokamaks is studied numerically. An eigenvalue method is adopted to calculate the growth rate of the modes for changing plasma resistivity and...The effect of plasma with toroidal rotation on the resistive wall modes in tokamaks is studied numerically. An eigenvalue method is adopted to calculate the growth rate of the modes for changing plasma resistivity and plasma density distribution, as well as the diffusion time of magnetic field through the resistive wall. It is found that the resistive wall mode can be suppressed by the toroidal rotation of the plasma. Also, the growth rate of the resistive wall mode decreases when the edge plasma density is the same as the core plasma density, but it only changes slightly with the plasma resistivity.展开更多
The alpha-particle effects on high-n toroidal shear Alfven mode are investigated analytically.The mode can be driven to unstable when the alpha-particles have an anisotropic distribution function due to ripple losses ...The alpha-particle effects on high-n toroidal shear Alfven mode are investigated analytically.The mode can be driven to unstable when the alpha-particles have an anisotropic distribution function due to ripple losses in tokamaks.The growth rates of the instability in both“fast”and "slow"plasma heating cases are calculated,and the conditions for the excitation of the modes are also studied.展开更多
There are a series of serious mistakes in the paper cited,1 making the whole analysis and result incorrect.A fundamental mistake is the argument that the formation of the rotation or rotation shear layer is equivalent...There are a series of serious mistakes in the paper cited,1 making the whole analysis and result incorrect.A fundamental mistake is the argument that the formation of the rotation or rotation shear layer is equivalent to a“heat sink”in a steady-state tokamak plasma.This is a mistake because the authors made a confusion between energy and power.展开更多
A simple model,rotation-inducing local cooling,for the mechanism on the formation of thermal transport barrier and the increase in rotation velocity is presented.It is shown that the sheared rotation can make electron...A simple model,rotation-inducing local cooling,for the mechanism on the formation of thermal transport barrier and the increase in rotation velocity is presented.It is shown that the sheared rotation can make electron temperature profile T_(e)(r)steepen near the rotation layer and▽T_(e)>0 on some location inside it,in agreement with the experimental observations in tokamaks,such as JT-60U with(poloidal or toroidal)sheared rotation and HL-1M with a biased electrode.Such temperature profile can remarkably improve the energy confinement in tokamaks.展开更多
A new theoretical model,which includes density and temperature gradients and impurity radiation effects,for the edge turbulence in high-and low-density tokamaks is established on the magnetohydrodynamics.The different...A new theoretical model,which includes density and temperature gradients and impurity radiation effects,for the edge turbulence in high-and low-density tokamaks is established on the magnetohydrodynamics.The different drive effects in the turbulent evolution are discussed and the mechanism of nonlinear saturation is investigated.The fluctuation levels and the associated diffusion coefficients at the turbulent saturation state are analytically given.The theoretical results are in agreement with the experimental observations on both high-and low-density tokamaks.展开更多
Numerical simulation on the resonant magnetic perturbation penetration is carried out by the newly-updated initial value code MDC(MHD@Dalian Code).Based on a set of two-fluid fourfield equations,the bootstrap current,...Numerical simulation on the resonant magnetic perturbation penetration is carried out by the newly-updated initial value code MDC(MHD@Dalian Code).Based on a set of two-fluid fourfield equations,the bootstrap current,parallel,and perpendicular transport effects are included appropriately.Taking into account the bootstrap current,a mode penetration-like phenomenon is found,which is essentially different from the classical tearing mode model.To reveal the influence of the plasma flow on the mode penetration process,E×B drift flow and diamagnetic drift flow are separately applied to compare their effects.Numerical results show that a sufficiently large diamagnetic drift flow can drive a strong stabilizing effect on the neoclassical tearing mode.Furthermore,an oscillation phenomenon of island width is discovered.By analyzing it in depth,it is found that this oscillation phenomenon is due to the negative feedback regulation of pressure on the magnetic island.This physical mechanism is verified again by key parameter scanning.展开更多
A cylindrical model of linear MHD instabilities in tokamaks is presented. In the model, the cylindrical plasma is surrounded by a vacuum which is divided into inner and outer vacuum areas by a conducting wall. Lineari...A cylindrical model of linear MHD instabilities in tokamaks is presented. In the model, the cylindrical plasma is surrounded by a vacuum which is divided into inner and outer vacuum areas by a conducting wall. Linearized resistivity MHD equations with plasma viscosity are adopted to describe our model, and the equations are solved numerically as an initial value problem. Some of the results are used as benchmark tests for the code, and then a series of equilibrium current profiles are used to simulate the bootstrap current profiles in actual experiments with a bump on tail. Thus the effects of these kinds of profiles on MHD instabilities in tokamaks are revealed. From the analysis of the numerical results, it is found that more plasma can be confined when the center of the current bump is closer to the plasma surface, and a higher and narrower current bump has a better stabilizing effect on the MHD instabilities.展开更多
In this letter,a model on inducing H-mode by biased electrode in tokamaks is put forward,it successfully explains the experiments in CCT,TEXTOR,and HL-1 with bias.
基金supported by National Natural Science Foundation of China (Nos. 12205033, 12105317, 11905022 and 11975062)Dalian Youth Science and Technology Project (No. 2022RQ039)+1 种基金the Fundamental Research Funds for the Central Universities (No. 3132023192)the Young Scientists Fund of the Natural Science Foundation of Sichuan Province (No. 2023NSFSC1291)
文摘Many magnetohydrodynamic stability analyses require generation of a set of equilibria with a fixed safety factor q-profile while varying other plasma parameters.A neural network(NN)-based approach is investigated that facilitates such a process.Both multilayer perceptron(MLP)-based NN and convolutional neural network(CNN)models are trained to map the q-profile to the plasma current density J-profile,and vice versa,while satisfying the Grad–Shafranov radial force balance constraint.When the initial target models are trained,using a database of semianalytically constructed numerical equilibria,an initial CNN with one convolutional layer is found to perform better than an initial MLP model.In particular,a trained initial CNN model can also predict the q-or J-profile for experimental tokamak equilibria.The performance of both initial target models is further improved by fine-tuning the training database,i.e.by adding realistic experimental equilibria with Gaussian noise.The fine-tuned target models,referred to as fine-tuned MLP and fine-tuned CNN,well reproduce the target q-or J-profile across multiple tokamak devices.As an important application,these NN-based equilibrium profile convertors can be utilized to provide a good initial guess for iterative equilibrium solvers,where the desired input quantity is the safety factor instead of the plasma current density.
基金supported by the National Magnetic Confinement Fusion Energy Program of China(No.2019YFE03020001)the Collaborative Innovation Program of Hefei Science Center,CAS(No.2021HSC-CIP010)the Fundamental Research Funds for the Central Universities。
文摘Interpreting experimental diagnostics data in tokamaks,while considering non-ideal effects,is challenging due to the complexity of plasmas.To address this challenge,a general synthetic diagnostics(GSD)platform has been established that facilitates microwave imaging reflectometry and electron cyclotron emission imaging.This platform utilizes plasma profiles as input and incorporates the finite-difference time domain,ray tracing and the radiative transfer equation to calculate the propagation of plasma spontaneous radiation and the external electromagnetic field in plasmas.Benchmark tests for classical cases have been conducted to verify the accuracy of every core module in the GSD platform.Finally,2D imaging of a typical electron temperature distribution is reproduced by this platform and the results are consistent with the given real experimental data.This platform also has the potential to be extended to 3D electromagnetic field simulations and other microwave diagnostics such as cross-polarization scattering.
基金The project supported by the National Nature Science Fundation of China(No.19885006 and No.10175020)
文摘Variational principle for the neoclassical theory has been developed by including a momentum restoring term in the electron-electron collisional operator, which gives an additional free parameter maximizing the heat production rate. All transport coefficients are obtained including the bootstrap current. The essential feature of the study is that the aspect ratio affects the function of the electron-electron collision operator through a geometrical factor. When the aspect ratio approaches to unity, the fraction of circulating particles goes to zero and the contribution to particle flux from the electron-electron collision vanishes. The resulting diffusion coefficient is in rough agreement with Hazeltine. When the aspect ratio approaches to infinity, the results are in agreement with Rosenbluth. The formalism gives the two extreme cases a connection. The theory is particularly important for the calculation of bootstrap current in spherical tokamaks and the present tokamaks, in which the square root of the inverse aspect ratio, in general, is not small.
基金supported by National Natural Science Foundation of China(Nos.11275041 and 11105065)
文摘Based on a linearized MHD model, the effect of equilibrium current profiles on external kink modes in tokamaks is studied by MARS code. Three types of equilibrium current profiles are adopted in this work. Firstly, a set of parabolic equilibrium current profiles are chosen. In these profiles the maximum current values in the center of the plasma are fixed, and the currents have different gradient and jump at the plasma boundary. The effects of the current gradient and jump on the growth rate of external kink mode are investigated. It is found that the current jump which causes the q profiles to change plays an important role in the externM kink modes in tokamaks. Secondly, a set of step equilibrium current profiles with different jump positions are chosen. The effect of jump position on external kink modes is discussed. Thirdly, a set of parabolic equilibrium current profiles with current bumps are chosen for the case of off-axis heating. The effects of height~ width and position of the current bumps on external kink modes are analyzed. The fiat equilibrium current profiles are disadvantageous for the MHD stabilities of tokamaks, because of the large current jump at the plasma edge. The peaked equilibrium current profiles and a large and localized current bump near the plasma edge benefit the MHD stabilities of tokamaks.
基金supported in part by the JSPS-CAS Core-University Program in tile field of Plasma and Nuclear Fusion, the Grant-in-Aid for scientific research from Ministry of Education, Science and Culture of Japan (No. 19055005)tile Chinese National Magnetic Confinement Fusion Science Program (No. 2009GB106006)
文摘Fundamental characteristics of charging of a dust particle and its dynamics in SOL/divertor plasma in tokamaks are studied. According to the OML （orbit motion limited） theory, the charging process is extremely faster, with a charging time of nanoseconds, than the dynamics process of the dust particle in SOL/divertor plasma, with a characteristic time of mil- liseconds, which means that the local charge state can be taken as the equilibrium charge state. It was clarified that the equilibrium charge Zd, eq can be determined in the form of Zd, eq/RdTe, which is a function of both the normalized relative speed of plasma ion flow with respect to the velocity of the dust particle and the plasma temperature ratio. After the investigation of domi- nant forces acting on dust particles, the friction forces due to the plasma ion absorption and ion Coulomb scattering are found of the same order for the case of low relative speed. The critical radius of a dust particle, for which the gravity is larger than the friction forces due to plasma ions, is obtained.
基金supported by National Natural Science Foundation of China (Nos. 11261140327, 11005035, 11175058)National Magnetic Confinement Fusion Science Program of China (No. 2009GB105002)
文摘Shaping effects of the E-fishbone in tokamaks are investigated. Coordinates related to the Solov＇ev configuration are used to calculate the precession frequency and kinetic contribu- tion. It is shown that elongation does not change the precession frequency and the kinetic energy. Growth rates of the E-fishbone vary with elongation which essentially has destabilizing effects. For elongated tokamaks, triangularity has a stabilizing effect on the modes which play a compensative role. The results may apply to Sunist.
基金supported by funding by the IAEA technical contracts within IAEA Coordinated Research Projects on‘Joint Research Using Small Tokamaks’and on‘Utilisation of a Network of Small Magnetic Confinement Fusion Devices for Mainstream Fusion Research’funded by Russian Science Foundation,Project 19-12-00312+3 种基金partly supported by the Competitiveness Program of NRNU MEPhIthe partial financial support from MEPhI and NRU MPEI in the framework of the Russian Academic Excellence Projectsupported by Tokamak Energy LtdOxford Instruments(UK)。
文摘Joint experiments(JEs)on small tokamaks have been regularly performed between 2005 and 2015 under the framework of the International Atomic Energy Agency(IAEA)coordinated research projects(CRPs).This paper describes the background and the rationale for these experiments,how they were organized and executed,main areas of research covered during these experiments,main results,contributions to mainstream fusion research,and discusses lessons learned and outcomes from these activities.We underline several of the most important scientific outputs and also specific outputs in the education of young scientists and scientists from developing countries and their importance.
基金This work was supported by National Natural Science Foundation of China No.19885006,No.10175020 Nuclear Science Foundation of China No.Y7100C0301.
文摘A criterion of an ideal internal kink mode is derived for a shaped tokamak configuration in which q-profile is very flat in the core region. A combining criterion is obtained including the necessary criterion of Mercier and the sufficient criterion of Lortz. The new criterion makes progress compared with the necessary criterion of Mercier. In the elongated plasma, a poloidal beta can cause instability, while the triangularity has a stabilizing effect. The result is applicable for DIII-D and SUNIST.
文摘Neoclassical transport for the shaped tokamak with X point is investigated using Hamiltonian formalism. For a set of Soloveev's configurations, the neoclassical diffusion coefficient is rigorously derived for the plateau regime which is inversely proportional to the connection length. When an X point appears on plasma boundary, the diffusion coefficient is greatly reduced by a much longer connection length compared with a circular cross-section plasma. Since the formalism is not limited for aspect ratio, for A = 1.3, it may be valid in a very narrow range of collisionality, 0.8 < V*i < 1.0, at / o = 0.95. In the range of collisionality, the detrapping rate is very high.
文摘The principle of minimum dissipation rate is applied to tokamak plasmas with energy and helicity balances imposed as two constraints. The analytical solution on toroidal current distribution are derived from the resulting Euler-Lagrangian equation. Three typical forms of current profiles are found for low-aspect-ratio tokamaks like NSTX. One of them decreases with r on equatorial plane, the second peaks in the inner half part on equatorial plane and the third may have a hole or reverse in the central part.
文摘Compact toroidal magnetized plasmas are an important part of the world’s magnetic fusion and plasma science efforts. These devices can play an integral role in the development of magnetic fusion as a viable commercial energy source, and in our understanding of plasma instabilities, particle and energy transport, and magnetic field transport. In this paper, we are developing a numerical program to study the magnetic dynamo or relaxation of CT’s characterized by arbitrary tight aspect ratio (major to minor radii of tokamak) and arbitrary cross-sections (Multi-pinch and D-Shaped). The lowest ZFE’s has been calculated through the Taylor’s relaxed state (force-free) toroidal plasmas equation. For ZFE’s, we use the toroidal flux vanishing boundary condition along the whole boundary of tokamaks. Several runs of the program for various wave numbers showed that ZFE was very insensitive to the choice of wave numbers. Besides, the CT’s poloidal magnetic field topologies are well represented. It was very interesting to check our methods for the cases when aspect ratio tends to unity (zero tokamak whole). A good fulfillment of the boundary condition is achieved.
文摘The control of turbulence at tokamaks is very complex problem.The idea is to apply the fuzzy Markovian processes and fuzzy Brownian motions as good approximation of general robust drift kinetic equation. It is obtained by using the artificial neural networks for solving of appropriate advanced control problem. The proof of the appropriate theorem is shown.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11275041, 11105065, 11095015, and 10675029)the National Basic Research Program of China (Grant Nos. 2008CB717801, 2008CB787103, 2009GB105004, and 2010GB106002)
文摘The effect of plasma with toroidal rotation on the resistive wall modes in tokamaks is studied numerically. An eigenvalue method is adopted to calculate the growth rate of the modes for changing plasma resistivity and plasma density distribution, as well as the diffusion time of magnetic field through the resistive wall. It is found that the resistive wall mode can be suppressed by the toroidal rotation of the plasma. Also, the growth rate of the resistive wall mode decreases when the edge plasma density is the same as the core plasma density, but it only changes slightly with the plasma resistivity.
基金supported by NSFC,APSC and UNESCO grant SC/RP 231322.7.
文摘The alpha-particle effects on high-n toroidal shear Alfven mode are investigated analytically.The mode can be driven to unstable when the alpha-particles have an anisotropic distribution function due to ripple losses in tokamaks.The growth rates of the instability in both“fast”and "slow"plasma heating cases are calculated,and the conditions for the excitation of the modes are also studied.
文摘There are a series of serious mistakes in the paper cited,1 making the whole analysis and result incorrect.A fundamental mistake is the argument that the formation of the rotation or rotation shear layer is equivalent to a“heat sink”in a steady-state tokamak plasma.This is a mistake because the authors made a confusion between energy and power.
基金Supported by the National Natural Science Foundation of China under Grant No.59472026Shanghai Foundation of Natural Science under Grant No.95ZE14007。
文摘A simple model,rotation-inducing local cooling,for the mechanism on the formation of thermal transport barrier and the increase in rotation velocity is presented.It is shown that the sheared rotation can make electron temperature profile T_(e)(r)steepen near the rotation layer and▽T_(e)>0 on some location inside it,in agreement with the experimental observations in tokamaks,such as JT-60U with(poloidal or toroidal)sheared rotation and HL-1M with a biased electrode.Such temperature profile can remarkably improve the energy confinement in tokamaks.
文摘A new theoretical model,which includes density and temperature gradients and impurity radiation effects,for the edge turbulence in high-and low-density tokamaks is established on the magnetohydrodynamics.The different drive effects in the turbulent evolution are discussed and the mechanism of nonlinear saturation is investigated.The fluctuation levels and the associated diffusion coefficients at the turbulent saturation state are analytically given.The theoretical results are in agreement with the experimental observations on both high-and low-density tokamaks.
基金supported by the National Key R&D Program of China(No.2022YFE03040001)National Natural Science Foundation of China(Nos.11925501 and 12075048)+1 种基金Chinese Academy of Sciences,Key Laboratory of Geospace Environment,University of Science&Technology of China(No.GE2019-01)Fundamental Research Funds for the Central Universities(No.DUT21GJ204)。
文摘Numerical simulation on the resonant magnetic perturbation penetration is carried out by the newly-updated initial value code MDC(MHD@Dalian Code).Based on a set of two-fluid fourfield equations,the bootstrap current,parallel,and perpendicular transport effects are included appropriately.Taking into account the bootstrap current,a mode penetration-like phenomenon is found,which is essentially different from the classical tearing mode model.To reveal the influence of the plasma flow on the mode penetration process,E×B drift flow and diamagnetic drift flow are separately applied to compare their effects.Numerical results show that a sufficiently large diamagnetic drift flow can drive a strong stabilizing effect on the neoclassical tearing mode.Furthermore,an oscillation phenomenon of island width is discovered.By analyzing it in depth,it is found that this oscillation phenomenon is due to the negative feedback regulation of pressure on the magnetic island.This physical mechanism is verified again by key parameter scanning.
基金supported by National Natural Science Foundation of China(No.10675029)National Basic Research Program of China(Nos.2008CB717801,2008CB787103,2009GB105004,2010GB106002)
文摘A cylindrical model of linear MHD instabilities in tokamaks is presented. In the model, the cylindrical plasma is surrounded by a vacuum which is divided into inner and outer vacuum areas by a conducting wall. Linearized resistivity MHD equations with plasma viscosity are adopted to describe our model, and the equations are solved numerically as an initial value problem. Some of the results are used as benchmark tests for the code, and then a series of equilibrium current profiles are used to simulate the bootstrap current profiles in actual experiments with a bump on tail. Thus the effects of these kinds of profiles on MHD instabilities in tokamaks are revealed. From the analysis of the numerical results, it is found that more plasma can be confined when the center of the current bump is closer to the plasma surface, and a higher and narrower current bump has a better stabilizing effect on the MHD instabilities.
文摘In this letter,a model on inducing H-mode by biased electrode in tokamaks is put forward,it successfully explains the experiments in CCT,TEXTOR,and HL-1 with bias.
