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
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
A simple and direct theoretical method has been proposed to investigate the so- called ion-banana-orbit-width （IBW） effect on the bootstrap current in the region of magnetic islands generated by the neoclassical tea...A simple and direct theoretical method has been proposed to investigate the so- called ion-banana-orbit-width （IBW） effect on the bootstrap current in the region of magnetic islands generated by the neoclassical tearing mode （NTM）. The result shows that, when the IBW approaches the island width, the （ion） bootstrap current can be partly restored inside the island while the pressure profile is flattened. This can lead to the reduction of the bootstrap current drive on the NTM. The strength of the IBW effect on the NTM is related to the safety factor and the inverse aspect ratio on the rational surface.展开更多
In this paper we work with a special theory of gravity|the Novello-Di Lorenci-Luciane (hereby called NDL theory) which extends the Feynman-Deser standard theoretical-fi eld approach to General Relativity. In the so-ca...In this paper we work with a special theory of gravity|the Novello-Di Lorenci-Luciane (hereby called NDL theory) which extends the Feynman-Deser standard theoretical-fi eld approach to General Relativity. In the so-called NDL theory, matter interacts universally with gravity in accordance with the Weak Equivalence Principle, while gravitons have a nonlinear self-interaction. Our main aim in this work is to show that, though the NDL theory does not admit a Schwarzschild solution, the Jebsen-Birkhoff theorem is still valid in this framework.展开更多
Mitigation of ELMs by electrostatic field is studied. The perpendicular heating in cyclotron waves tends to pile up the resonant particles toward the low magnetic field side in which a electrostatic field may result [...Mitigation of ELMs by electrostatic field is studied. The perpendicular heating in cyclotron waves tends to pile up the resonant particles toward the low magnetic field side in which a electrostatic field may result [J. Y. Hsu, V. S. Chan, R. W. Harvey, R. Prater, and S. K. Wong, Phys. Rev. Lett. 53, 564 (1984)]. The electrostatic field can make circulating particles trapped or make trapped particles circulating depending on the field direction. The trapped- particle population and bootstrap current change accordantly. Modulating bootstrap current, mitigation of type-1 ELM by the electrostatic field is possible. The electrostatic potential needed for the mitigation is quantitatively estimated. Experiments by either ECRH or biasing are being prepared to verify the theory.展开更多
研究了在托卡马克装置中中性束注入时快离子自举电流的产生。利用快离子分布函数在两小增量δ=ρp/a(ρp是极向拉莫尔半径,a是小半径)和δ*=τB/τs(τB是俘获粒子反弹周期,τs是慢化时间)下进行展开的方法求解漂移动力学方程;给出了快...研究了在托卡马克装置中中性束注入时快离子自举电流的产生。利用快离子分布函数在两小增量δ=ρp/a(ρp是极向拉莫尔半径,a是小半径)和δ*=τB/τs(τB是俘获粒子反弹周期,τs是慢化时间)下进行展开的方法求解漂移动力学方程;给出了快离子自举电流的一般表达式。计算了圆截面大纵横比托卡马克中快离子自举电流密度分布和总的快离子自举电流的大小,研究表明:在中性束垂直注入时快离子自举电流约占总电流的10%;自举电流的大小既敏感地依赖于中性束注入的角度——平行注入时较小、接近垂直时迅速增大,同时也较强的依赖于快离子的产生速度与临界速度的比值,即v b vc,而v b2∝E(束能量);自举电流的大小随注入束能量的增加而迅速增大。展开更多
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(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.
基金supported by the National Magnetic Confinement Fusion Science Program of China(Nos.2011GB105002 and 2010GB106006)National Natural Science Foundation of China(No.11175057)
文摘A simple and direct theoretical method has been proposed to investigate the so- called ion-banana-orbit-width （IBW） effect on the bootstrap current in the region of magnetic islands generated by the neoclassical tearing mode （NTM）. The result shows that, when the IBW approaches the island width, the （ion） bootstrap current can be partly restored inside the island while the pressure profile is flattened. This can lead to the reduction of the bootstrap current drive on the NTM. The strength of the IBW effect on the NTM is related to the safety factor and the inverse aspect ratio on the rational surface.
文摘In this paper we work with a special theory of gravity|the Novello-Di Lorenci-Luciane (hereby called NDL theory) which extends the Feynman-Deser standard theoretical-fi eld approach to General Relativity. In the so-called NDL theory, matter interacts universally with gravity in accordance with the Weak Equivalence Principle, while gravitons have a nonlinear self-interaction. Our main aim in this work is to show that, though the NDL theory does not admit a Schwarzschild solution, the Jebsen-Birkhoff theorem is still valid in this framework.
文摘Mitigation of ELMs by electrostatic field is studied. The perpendicular heating in cyclotron waves tends to pile up the resonant particles toward the low magnetic field side in which a electrostatic field may result [J. Y. Hsu, V. S. Chan, R. W. Harvey, R. Prater, and S. K. Wong, Phys. Rev. Lett. 53, 564 (1984)]. The electrostatic field can make circulating particles trapped or make trapped particles circulating depending on the field direction. The trapped- particle population and bootstrap current change accordantly. Modulating bootstrap current, mitigation of type-1 ELM by the electrostatic field is possible. The electrostatic potential needed for the mitigation is quantitatively estimated. Experiments by either ECRH or biasing are being prepared to verify the theory.
文摘研究了在托卡马克装置中中性束注入时快离子自举电流的产生。利用快离子分布函数在两小增量δ=ρp/a(ρp是极向拉莫尔半径,a是小半径)和δ*=τB/τs(τB是俘获粒子反弹周期,τs是慢化时间)下进行展开的方法求解漂移动力学方程;给出了快离子自举电流的一般表达式。计算了圆截面大纵横比托卡马克中快离子自举电流密度分布和总的快离子自举电流的大小,研究表明:在中性束垂直注入时快离子自举电流约占总电流的10%;自举电流的大小既敏感地依赖于中性束注入的角度——平行注入时较小、接近垂直时迅速增大,同时也较强的依赖于快离子的产生速度与临界速度的比值,即v b vc,而v b2∝E(束能量);自举电流的大小随注入束能量的增加而迅速增大。
