2009年2月21日THEMIS-C卫星在磁尾X=-15.7RE(RE为地球半径,1RE=6371km)观测到典型的磁通量绳事件.采用Grad-Shafranov重构技术研究该磁通量绳的特性、内部磁场和电流结构.研究表明,磁通量绳不变轴位于GSM(geocentric solar magnetospher...2009年2月21日THEMIS-C卫星在磁尾X=-15.7RE(RE为地球半径,1RE=6371km)观测到典型的磁通量绳事件.采用Grad-Shafranov重构技术研究该磁通量绳的特性、内部磁场和电流结构.研究表明,磁通量绳不变轴位于GSM(geocentric solar magnetospheric coordinates)坐标为(-0.3975,0.8905,0.2213)的方向,基本位于晨昏方向;通量绳的横截面尺度约为2RE,内部轴向磁通量为1.3×106Wb.与经验模型相比,在对磁通量绳几何形状不做约束的情况下,重构出磁尾X=-15.7RE处磁通量绳横截面上的磁场、电流强度分布图像.通量绳核心部位具有无力场位形结构,而随着径向距离的增加,磁场在偏离轴对称分布的区域逐渐表现为非无力位形.展开更多
We review and summarize the applications of the Grad-Shafranov(GS) reconstruction technique to space plasma structures in the Earth's magnetosphere and in the interplanetary space. We organize our presentations fo...We review and summarize the applications of the Grad-Shafranov(GS) reconstruction technique to space plasma structures in the Earth's magnetosphere and in the interplanetary space. We organize our presentations following the branches of the "academic family tree" rooted on Prof. Bengt U. ? Sonnerup, the inventor of the GS method. Special attentions are paid to validations of the GS reconstruction results via(1) the direct validation by co-spatial in-situ measurements among multiple spacecraft, and(2) indirect validation by implications and interpretations of the physical connection between the structures reconstructed and other related processes. For the latter, the inter-comparison and interconnection between the large-scale magnetic flux ropes(i.e., Magnetic Clouds) in the solar wind and their solar source properties are presented. In addition, we also summarize various GS-type(or-like) reconstruction and an extension of the GS technique to toroidal geometry. In particular,we point to a possible advancement with added complexity of "helical symmetry" and mixed helicity, in the hope of stimulating interest in future development. We close by offering some thoughts on appreciating the scientific merit of GS reconstruction in general.展开更多
In this work,several key scaling laws of the quasi-static magnetic compression of field reversed configuration(FRC)plasma(Spencer et al 1983 Phys.Fluids 261564)are amended from a series of two-dimensional FRC MHD equi...In this work,several key scaling laws of the quasi-static magnetic compression of field reversed configuration(FRC)plasma(Spencer et al 1983 Phys.Fluids 261564)are amended from a series of two-dimensional FRC MHD equilibriums numerically obtained using the Grad–Shafranov equation solver NIMEQ.Based on the new scaling for the elongation and the magnetic fields at the separatrix and the wall,the empirically stable limits for the compression ratio,the fusion gain,and the neutron yield are evaluated,which may serve as a more accurate estimate for the upper ceiling of performance from the magnetic compression of FRC plasma as a potential fusion energy as well as neutron source devices.展开更多
The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inv...The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace＇s equation. In the first place, the variational regularization method is used to deal with the ill- posedness of the Cauchy problem for Laplace＇s equation. Then, the ＇L-Curve＇ principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10-1, the order of the approximate result error can reach 10-3.展开更多
To achieve real-time control of tokamak plasmas, the equilibrium reconstruction has to be completed sufficiently quickly. For the case of an EAST tokamak experiment, real-time equilibrium reconstruction is generally r...To achieve real-time control of tokamak plasmas, the equilibrium reconstruction has to be completed sufficiently quickly. For the case of an EAST tokamak experiment, real-time equilibrium reconstruction is generally required to provide results within 1ms. A graphic processing unit（GPU） parallel Grad–Shafranov（G-S） solver is developed in P-EFIT code,which is built with the CUDA？ architecture to take advantage of massively parallel GPU cores and significantly accelerate the computation. Optimization and implementation of numerical algorithms for a block tri-diagonal linear system are presented. The solver can complete a calculation within 16 μs with 65×65 grid size and 27 μs with 129×129 grid size, and this solver supports that P-EFIT can fulfill the time feasibility for real-time plasma control with both grid sizes.展开更多
It is difficult to obtain the asymmetrical factor along the observation direction parallel to the plasma mid-plane when the detected radiation is also in the mid-plane. This paper considers the magnetic surfaces and G...It is difficult to obtain the asymmetrical factor along the observation direction parallel to the plasma mid-plane when the detected radiation is also in the mid-plane. This paper considers the magnetic surfaces and Grad-Shafranov shift, and develops a new method for inverse asymmetric electron density information, during magnetic equilibrium configuration in a tokamak.展开更多
In this paper we present a coupled Finite Element Method–Boundary Element Method(FEM-BEM)approach for the solution of the free-boundary axi-symmetric plasma equilibrium problem.The proposed method,obtained from an i...In this paper we present a coupled Finite Element Method–Boundary Element Method(FEM-BEM)approach for the solution of the free-boundary axi-symmetric plasma equilibrium problem.The proposed method,obtained from an improvement of the Hagenow-Lackner coupling method,allows to efficiently model the equilibrium problem in unbounded domains by discretizing only the plasma region;the external conductors can be modelled either as 2D or 3D models,according to the problem of interest.The paper explores different iterative methods for the solution of the nonlinear Grad-Shafranov equation,such as Picard,Newton-Raphson and Newton-Krylov,in order to provide a robust and reliable tool,able to handle large-scale problems(e.g.high resolution equilibria).This method has been implemented in the FRIDA code(FReeboundary Integro-Differential Axisimmetric–https://github.om/matteobonotto/FRIDA),together with a suitable Adaptive Integration Technique(AIT)for the computation of the source term.FRIDA has been successfully tested and validated against experimental data from RFX-mod device,and numerical equilibria of an ITER-like device.展开更多
Cluster spacecraft observed an earthward flowing plasmoid along with a travelling compression region(TCR)structure in southern plasma sheet boundary layer(PSBL)at 21:09 UT of September 19,2001.We have reconstructed th...Cluster spacecraft observed an earthward flowing plasmoid along with a travelling compression region(TCR)structure in southern plasma sheet boundary layer(PSBL)at 21:09 UT of September 19,2001.We have reconstructed the two-dimensional topology of the magnetic field structure observed by C1 using Grad-Shafranov reconstruction method.Results show that C1passed through part of a plasmoid,which compressed the lobe magnetic field and formed a TCR.The size of the whole plasmoid structure in X direction is estimated to be about 3 RE.Furthermore,using multi-spacecraft observations,we have found some detailed information about this structure.First,C1 observed bi-streaming electron components,which supports our suggestion that the spacecraft passed through closed field lines.Second,a small magnetic field perturbation within this plasmoid accompanied by slight decrease in electron flux suggests that a flux rope core might exist at the center of the plasmoid.展开更多
We studied the compressional wave event in Pc5 frequency range observed in the dawn-side magnetic equator on 9 March 1998 by Grad-Shafranov(GS) reconstruction method for the first time. To test the effectiveness of ap...We studied the compressional wave event in Pc5 frequency range observed in the dawn-side magnetic equator on 9 March 1998 by Grad-Shafranov(GS) reconstruction method for the first time. To test the effectiveness of application of GS method on Pc5 compressional wave, we benchmarked our procedure by applying it to a one-dimensional current sheet model first. Excluding the left-hand corners, the average error magnitude was less than 10%. The reconstruction of actual data showed that we obtained the 2-D map of compressional wave without suffering model constraints for the first time. The magnetic filed lines density cyclical changed, and the wavelength was about 2-4 times earth radius. The reconstructed magnetic topology had a shape very similar to the empirical 2-dimensional standing wave model proposed by the former workers. Besides, we also recovered the plasma thermal pressure and current density of the wave quantitatively.展开更多
Solutions of Grad-Shafranov(GS) equation with Reversed Current Density(RCD) profiles present magnetic islands when the magnetic flux is explicitly dependent on the poloidal angle.In this work it is shown that a typica...Solutions of Grad-Shafranov(GS) equation with Reversed Current Density(RCD) profiles present magnetic islands when the magnetic flux is explicitly dependent on the poloidal angle.In this work it is shown that a typical cylindrical(large aspect-ratio) RCD equilibrium configuration perturbed by the magnetic field of a circular loop(simulating a divertor) is capable of generate magnetic islands,due to the poloidal symmetry break of the GS equilibrium solution.展开更多
文摘2009年2月21日THEMIS-C卫星在磁尾X=-15.7RE(RE为地球半径,1RE=6371km)观测到典型的磁通量绳事件.采用Grad-Shafranov重构技术研究该磁通量绳的特性、内部磁场和电流结构.研究表明,磁通量绳不变轴位于GSM(geocentric solar magnetospheric coordinates)坐标为(-0.3975,0.8905,0.2213)的方向,基本位于晨昏方向;通量绳的横截面尺度约为2RE,内部轴向磁通量为1.3×106Wb.与经验模型相比,在对磁通量绳几何形状不做约束的情况下,重构出磁尾X=-15.7RE处磁通量绳横截面上的磁场、电流强度分布图像.通量绳核心部位具有无力场位形结构,而随着径向距离的增加,磁场在偏离轴对称分布的区域逐渐表现为非无力位形.
基金supported by National Aeronautics and Space Administration (NASA) and National Science Foundation (NSF) (Grants Nos. AGS-1062050, NNG04GF47G, NNG06GD41G, NNX12AF97G, NNX12AH50G, NNH13ZDA001N, and NNX14AF41G)
文摘We review and summarize the applications of the Grad-Shafranov(GS) reconstruction technique to space plasma structures in the Earth's magnetosphere and in the interplanetary space. We organize our presentations following the branches of the "academic family tree" rooted on Prof. Bengt U. ? Sonnerup, the inventor of the GS method. Special attentions are paid to validations of the GS reconstruction results via(1) the direct validation by co-spatial in-situ measurements among multiple spacecraft, and(2) indirect validation by implications and interpretations of the physical connection between the structures reconstructed and other related processes. For the latter, the inter-comparison and interconnection between the large-scale magnetic flux ropes(i.e., Magnetic Clouds) in the solar wind and their solar source properties are presented. In addition, we also summarize various GS-type(or-like) reconstruction and an extension of the GS technique to toroidal geometry. In particular,we point to a possible advancement with added complexity of "helical symmetry" and mixed helicity, in the hope of stimulating interest in future development. We close by offering some thoughts on appreciating the scientific merit of GS reconstruction in general.
基金supported by the National Magnetic Confinement Fusion Program of China (No. 2017YFE0301805)National Natural Science Foundation of China (No. 51821005)+3 种基金the Fundamental Research Funds for the Central Universities at Huazhong University of Science and Technology (No. 2019kfy XJJS193)the U.S. Department of Energy (Nos. DE-FG02-86ER53218 and DE-SC0018001)the supports from the NIMROD teamthe support from the Chinese Government Scholarship.
文摘In this work,several key scaling laws of the quasi-static magnetic compression of field reversed configuration(FRC)plasma(Spencer et al 1983 Phys.Fluids 261564)are amended from a series of two-dimensional FRC MHD equilibriums numerically obtained using the Grad–Shafranov equation solver NIMEQ.Based on the new scaling for the elongation and the magnetic fields at the separatrix and the wall,the empirically stable limits for the compression ratio,the fusion gain,and the neutron yield are evaluated,which may serve as a more accurate estimate for the upper ceiling of performance from the magnetic compression of FRC plasma as a potential fusion energy as well as neutron source devices.
基金Project supported by the National Natural Science Foundation of China(Grant No.41175025)
文摘The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace＇s equation. In the first place, the variational regularization method is used to deal with the ill- posedness of the Cauchy problem for Laplace＇s equation. Then, the ＇L-Curve＇ principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10-1, the order of the approximate result error can reach 10-3.
基金supported by the National Magnetic Confinement Fusion Research Program of China(Grant No.2014GB103000)the National Natural Science Foundation of China(Grant No.11575245)the National Natural Science Foundation of China for Youth(Grant No.11205191)
文摘To achieve real-time control of tokamak plasmas, the equilibrium reconstruction has to be completed sufficiently quickly. For the case of an EAST tokamak experiment, real-time equilibrium reconstruction is generally required to provide results within 1ms. A graphic processing unit（GPU） parallel Grad–Shafranov（G-S） solver is developed in P-EFIT code,which is built with the CUDA？ architecture to take advantage of massively parallel GPU cores and significantly accelerate the computation. Optimization and implementation of numerical algorithms for a block tri-diagonal linear system are presented. The solver can complete a calculation within 16 μs with 65×65 grid size and 27 μs with 129×129 grid size, and this solver supports that P-EFIT can fulfill the time feasibility for real-time plasma control with both grid sizes.
文摘It is difficult to obtain the asymmetrical factor along the observation direction parallel to the plasma mid-plane when the detected radiation is also in the mid-plane. This paper considers the magnetic surfaces and Grad-Shafranov shift, and develops a new method for inverse asymmetric electron density information, during magnetic equilibrium configuration in a tokamak.
文摘In this paper we present a coupled Finite Element Method–Boundary Element Method(FEM-BEM)approach for the solution of the free-boundary axi-symmetric plasma equilibrium problem.The proposed method,obtained from an improvement of the Hagenow-Lackner coupling method,allows to efficiently model the equilibrium problem in unbounded domains by discretizing only the plasma region;the external conductors can be modelled either as 2D or 3D models,according to the problem of interest.The paper explores different iterative methods for the solution of the nonlinear Grad-Shafranov equation,such as Picard,Newton-Raphson and Newton-Krylov,in order to provide a robust and reliable tool,able to handle large-scale problems(e.g.high resolution equilibria).This method has been implemented in the FRIDA code(FReeboundary Integro-Differential Axisimmetric–https://github.om/matteobonotto/FRIDA),together with a suitable Adaptive Integration Technique(AIT)for the computation of the source term.FRIDA has been successfully tested and validated against experimental data from RFX-mod device,and numerical equilibria of an ITER-like device.
基金supported by the National Natural Science Foundation of China(Grant No.375 41150110579)the Research Funding Project Thales/HNSWRN,NSRF(Grant No.339868)
文摘Cluster spacecraft observed an earthward flowing plasmoid along with a travelling compression region(TCR)structure in southern plasma sheet boundary layer(PSBL)at 21:09 UT of September 19,2001.We have reconstructed the two-dimensional topology of the magnetic field structure observed by C1 using Grad-Shafranov reconstruction method.Results show that C1passed through part of a plasmoid,which compressed the lobe magnetic field and formed a TCR.The size of the whole plasmoid structure in X direction is estimated to be about 3 RE.Furthermore,using multi-spacecraft observations,we have found some detailed information about this structure.First,C1 observed bi-streaming electron components,which supports our suggestion that the spacecraft passed through closed field lines.Second,a small magnetic field perturbation within this plasmoid accompanied by slight decrease in electron flux suggests that a flux rope core might exist at the center of the plasmoid.
文摘We studied the compressional wave event in Pc5 frequency range observed in the dawn-side magnetic equator on 9 March 1998 by Grad-Shafranov(GS) reconstruction method for the first time. To test the effectiveness of application of GS method on Pc5 compressional wave, we benchmarked our procedure by applying it to a one-dimensional current sheet model first. Excluding the left-hand corners, the average error magnitude was less than 10%. The reconstruction of actual data showed that we obtained the 2-D map of compressional wave without suffering model constraints for the first time. The magnetic filed lines density cyclical changed, and the wavelength was about 2-4 times earth radius. The reconstructed magnetic topology had a shape very similar to the empirical 2-dimensional standing wave model proposed by the former workers. Besides, we also recovered the plasma thermal pressure and current density of the wave quantitatively.
文摘Solutions of Grad-Shafranov(GS) equation with Reversed Current Density(RCD) profiles present magnetic islands when the magnetic flux is explicitly dependent on the poloidal angle.In this work it is shown that a typical cylindrical(large aspect-ratio) RCD equilibrium configuration perturbed by the magnetic field of a circular loop(simulating a divertor) is capable of generate magnetic islands,due to the poloidal symmetry break of the GS equilibrium solution.
