For an electron-electron collision with characteristic scale length larger than the relative gyro-radius of the two colliding electrons, when the initial relative parallel kinetic energy cannot surmount the Coulomb re...For an electron-electron collision with characteristic scale length larger than the relative gyro-radius of the two colliding electrons, when the initial relative parallel kinetic energy cannot surmount the Coulomb repulsive potential, reflection will occur with interchange of the parallel velocities of the two electrons after the collision. The Fokker–Planck approach is employed to derive the electron collision term C_R describing parallel velocity scattering due to the reflections for a magnetized plasma where the average electron gyro-radius is much smaller than the Debye length but much larger than the Landau length. The electron parallel velocity friction and diffusion coefficients due to the reflections are evaluated, which are found not to depend on the electron perpendicular velocity. By studying the temporal evolution of the H quantity due to CR, it is found that C_R eventually makes the system relax to a state in which the electron parallel velocity distribution is decoupled from the perpendicular velocity distribution.展开更多
Rutherford scattering formula plays an important role in plasma classical transport.It is urgent to investigate influence of magnetic field on the Rutherford scattering since the high magnetic field has been widely us...Rutherford scattering formula plays an important role in plasma classical transport.It is urgent to investigate influence of magnetic field on the Rutherford scattering since the high magnetic field has been widely used in nowadays magnetic confinement fusion,inertial confinement fusion,and magneto-inertial fusion.In order to elucidate the magnetic field effect in a concise manner,we study the electron-ion collisions transverse to the magnetic field.The scattering angle is defined using the directions of electron velocity before and after collision,which is obtained analytically.It is found that the scattering angle can be influenced by finite magnetic field significantly.The theoretical results agree well with numerical calculation by checking the dependence of scattering angle on the magnetic field.展开更多
Understanding and modeling fast-ion stabilization of ion-temperature-gradient(ITG)driven microturbulence have profound implications for designing and optimizing future fusion reactors.In this work,an analytic model is...Understanding and modeling fast-ion stabilization of ion-temperature-gradient(ITG)driven microturbulence have profound implications for designing and optimizing future fusion reactors.In this work,an analytic model is presented,which describes the effect of fast ions on ITG mode.This model is derived from a bounce-average gyro-kinetic equation for trapped fast ions and ballooning transformation for ITG mode.In addition to dilution,strong wave-fast-ion resonant interaction is involved in this model.Based on numerical calculations,the effects of the main physical parameters are studied.The increasing density of fast ions will strengthen the effects of fast ions.The effect of wave-particle resonance strongly depends on the temperature of fast ions.Furthermore,both increasing density gradient and the ratio of the temperature and density gradients can strengthen the stabilization of fast ions in ITG mode.Finally,the influence of resonance broadening of wave-particle interaction is discussed.展开更多
The analytical approaches for nonlinear tearing mode have been reviewed.It is shown that Rutherford＇s model has triggered numerous studies on the nonlinear tearing mode.Its physical picture is clear meanwhile its mat...The analytical approaches for nonlinear tearing mode have been reviewed.It is shown that Rutherford＇s model has triggered numerous studies on the nonlinear tearing mode.Its physical picture is clear meanwhile its mathematical method is ingenious but still puzzling to understand.It is trying to find how the ＇nonlinear behavior＇ resulted from the linear equation by a nonlinear transform.It is indicated that Li＇s model for the tearing mode includes the linear growth,Rutherford＇s behavior and the new behavior.It was found that the quasilinear modification of magnetic field provided a new damping mechanism for nonlinear growth.The new behavior w~ t1/2 becomes dominant if the mode is weakly unstable.It is shown that many analytical methods have been developed to calculate the criterion parameter D＇ of the tearing mode.Li＇s instability criterion can cover the previous results in the limit cases.展开更多
We analytically investigate nonlinear tearing modes with the anomalous electron viscosity or,as it is normally called,hyper-resistivity.In contrast to the flux average method used by previous work,we employ the standa...We analytically investigate nonlinear tearing modes with the anomalous electron viscosity or,as it is normally called,hyper-resistivity.In contrast to the flux average method used by previous work,we employ the standard singular perturbation technique and a quasilinear method to obtain the time evolution equation of tearing modes.The result that the magnetic flux grows with time in a scaling as t^（2/3）demonstrates that nonlinear tearing modes with the hyper-resistivity effect alone have a weaker dependence on time than that of the corresponding resistive case.展开更多
A trajectory integrator is developed based on a particle's guiding center Hamiltonian.It is verified by a series of benchmarks,which are in good accordance with theoretical prediction.This integrator can be used a...A trajectory integrator is developed based on a particle's guiding center Hamiltonian.It is verified by a series of benchmarks,which are in good accordance with theoretical prediction.This integrator can be used as the guiding center trajectory integrator of a particle-in-cell simulation platform,such as the newly developed VirtEx.It can also be used as a stand-alone tool to investigate particle dynamics in a given background field.展开更多
基金Supported by the National MCF Energy R&D Program under Grant No 2018YFE0311300the National Natural Science Foundation of China under Grant Nos 11875067,11835016,11705275,11675257 and 11675256+2 种基金the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No XDB16010300the Key Research Program of Frontier Science of Chinese Academy of Sciences under Grant No QYZDJ-SSW-SYS016the External Cooperation Program of Chinese Academy of Sciences under Grant No 112111KYSB20160039
文摘For an electron-electron collision with characteristic scale length larger than the relative gyro-radius of the two colliding electrons, when the initial relative parallel kinetic energy cannot surmount the Coulomb repulsive potential, reflection will occur with interchange of the parallel velocities of the two electrons after the collision. The Fokker–Planck approach is employed to derive the electron collision term C_R describing parallel velocity scattering due to the reflections for a magnetized plasma where the average electron gyro-radius is much smaller than the Debye length but much larger than the Landau length. The electron parallel velocity friction and diffusion coefficients due to the reflections are evaluated, which are found not to depend on the electron perpendicular velocity. By studying the temporal evolution of the H quantity due to CR, it is found that C_R eventually makes the system relax to a state in which the electron parallel velocity distribution is decoupled from the perpendicular velocity distribution.
基金supported by the National Natural Science Foundation of China(Grant Nos.11835016 and 11875067)the National MCF Energy R&D Program(Grant No.2018YFE0311300)。
文摘Rutherford scattering formula plays an important role in plasma classical transport.It is urgent to investigate influence of magnetic field on the Rutherford scattering since the high magnetic field has been widely used in nowadays magnetic confinement fusion,inertial confinement fusion,and magneto-inertial fusion.In order to elucidate the magnetic field effect in a concise manner,we study the electron-ion collisions transverse to the magnetic field.The scattering angle is defined using the directions of electron velocity before and after collision,which is obtained analytically.It is found that the scattering angle can be influenced by finite magnetic field significantly.The theoretical results agree well with numerical calculation by checking the dependence of scattering angle on the magnetic field.
基金National Natural Science Foundation of China(Nos.11822505,11835016 and 11675257)the Youth Innovation Promotion Association CAS,the Users with Excellence Program of Hefei Science Center CAS(No.2019HSC-UE013)+1 种基金the Fundamental Research Funds for the Central Universities(No.WK3420000008)the Collaborative Innovation Program of Hefei Science Center CAS(No.2019HSC-CIP014)。
文摘Understanding and modeling fast-ion stabilization of ion-temperature-gradient(ITG)driven microturbulence have profound implications for designing and optimizing future fusion reactors.In this work,an analytic model is presented,which describes the effect of fast ions on ITG mode.This model is derived from a bounce-average gyro-kinetic equation for trapped fast ions and ballooning transformation for ITG mode.In addition to dilution,strong wave-fast-ion resonant interaction is involved in this model.Based on numerical calculations,the effects of the main physical parameters are studied.The increasing density of fast ions will strengthen the effects of fast ions.The effect of wave-particle resonance strongly depends on the temperature of fast ions.Furthermore,both increasing density gradient and the ratio of the temperature and density gradients can strengthen the stabilization of fast ions in ITG mode.Finally,the influence of resonance broadening of wave-particle interaction is discussed.
基金supported by National Natural Science Foundation of Chinathe National Magnetic Confinement Fusion Science Program of China under Grant Nos.11675257 and 2014GB106004+2 种基金the CAS Strategic Priority Research Programthe CAS Key Research Program of Frontier Sciencethe CAS External Cooperation Program of CAS under Grant Nos.XDB16010300,QYZDJ-SSW-SYS016 and 112111KYSB20160039
文摘The analytical approaches for nonlinear tearing mode have been reviewed.It is shown that Rutherford＇s model has triggered numerous studies on the nonlinear tearing mode.Its physical picture is clear meanwhile its mathematical method is ingenious but still puzzling to understand.It is trying to find how the ＇nonlinear behavior＇ resulted from the linear equation by a nonlinear transform.It is indicated that Li＇s model for the tearing mode includes the linear growth,Rutherford＇s behavior and the new behavior.It was found that the quasilinear modification of magnetic field provided a new damping mechanism for nonlinear growth.The new behavior w~ t1/2 becomes dominant if the mode is weakly unstable.It is shown that many analytical methods have been developed to calculate the criterion parameter D＇ of the tearing mode.Li＇s instability criterion can cover the previous results in the limit cases.
基金Supported by the National Natural Science Foundation of China under Grant No 11675257the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No XDB16010300+2 种基金the Key Research Program of Frontier Science of Chinese Academy of Sciences under Grant No QYZDJ-SSW-SYS016the External Cooperation Program of Chinese Academy of Sciences under Grant No 112111KYSB20160039supported by the US Department of Energy,Office of Science,Office of Fusion Energy Sciences,LLNL-JRNL-748586
文摘We analytically investigate nonlinear tearing modes with the anomalous electron viscosity or,as it is normally called,hyper-resistivity.In contrast to the flux average method used by previous work,we employ the standard singular perturbation technique and a quasilinear method to obtain the time evolution equation of tearing modes.The result that the magnetic flux grows with time in a scaling as t^（2/3）demonstrates that nonlinear tearing modes with the hyper-resistivity effect alone have a weaker dependence on time than that of the corresponding resistive case.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11675257,11675256 and 11705275the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No XDB16010300+2 种基金the Key Research Program of Frontier Science of Chinese Academy of Sciences under Grant No QYZDJ-SSW-SYS016the External Cooperation Program of Chinese Academy of Sciences under Grant No 112111KYSB20160039the National Magnetic Confinement Fusion Science Program of China under Grant Nos 2013GB111003 and 2013GB112011
文摘A trajectory integrator is developed based on a particle's guiding center Hamiltonian.It is verified by a series of benchmarks,which are in good accordance with theoretical prediction.This integrator can be used as the guiding center trajectory integrator of a particle-in-cell simulation platform,such as the newly developed VirtEx.It can also be used as a stand-alone tool to investigate particle dynamics in a given background field.
