A recent satellite observation has revealed the presence of energy conversion in the separatrix region(SR)of magnetotail reconnection,driven by perpendicular components.We investigated this phenomenon by means of part...A recent satellite observation has revealed the presence of energy conversion in the separatrix region(SR)of magnetotail reconnection,driven by perpendicular components.We investigated this phenomenon by means of particle-in-cell simulations in two-dimensional(2D)and three-dimensional(3D)systems.Our result indicates that in the 2D simulation,energy conversion in the SR is dominated by parallel components,with the main influencing factor being the parallel electric field,which is not consistent with the observation.However,a case that is similar to the observation is found in the 3D simulation,suggesting that the observation result may be attributed to the 3D characteristics.Our findings provide a potential explanation for the satellite observation.展开更多
Previous studies have shown that there is an obvious coupling relationship between the installation location of the external cathode and the magnetic separatrix in the plume region of a Hall thruster.In this paper,the...Previous studies have shown that there is an obvious coupling relationship between the installation location of the external cathode and the magnetic separatrix in the plume region of a Hall thruster.In this paper,the particle-in-cell simulation method is used to compare the thruster discharge process under the conditions of different position relationships between the cathode and the magnetic separatrix.By comparing the distribution of electron conduction,potential,plasma density and other microscopic parameters,we try to explain the formation mechanism of the discharge difference.The simulation results show that the cathode inside and outside the magnetic separatrix has a significant effect on the distribution of potential and plasma density.When the cathode is located on the outer side of the magnetic separatrix,the potential above the plume region is relatively low,and there is a strong potential gradient above the plume region.This potential gradient is more conducive to the radial diffusion of ions above the plume,which is the main reason for the strong divergence of the plume.The distribution of ion density is also consistent with the distribution of potential.When the cathode is located on the outer side of the magnetic separatrix,the radial diffusion of ions in the plume region is enhanced.Meanwhile,by comparing the results of electron conduction,it is found that the traiectories of electrons emitted from the cathode are significantly different between the inner and outer sides of the magnetic separatrix.This is mainly because the electrons are affected by the magnetic mirror effect of the magnetic tip,which makes it difficult for the electrons to move across the magnetic separatrix.This is the main reason for the difference in potential distribution.In this paper,the simulation results of macroscopic parameters under several conditions are also compared,and they are consistent with the experimental results.The cathode is located on the inner side of the magnetic separatrix,which can effectively reduce the plume divergence angle and improve the thrust.In this paper,the cathode moves from R=50 mm to R=35 mm along the radial direction,the thrust increases by 3.6 mN and the plume divergence angle decreases by 23.77%.Combined with the comparison of the ionization region and the peak ion density,it is found that the main reason for the change in thrust is the change in the radial diffusion of ions in the plume region.展开更多
For a given system, by using the Tkachev method which concerned with the proof of the stability of a multiple limit cycle, the exact computation formula of the third separatrix values named by Leontovich for the multi...For a given system, by using the Tkachev method which concerned with the proof of the stability of a multiple limit cycle, the exact computation formula of the third separatrix values named by Leontovich for the multiple limit cycle bifurcation was given, which was one of the main criterions for the number of limit cycles bifurcated from a homoclinic orbit and the stability of the homoclinic loop, and a computation formula for higher separatrix values was conjectured.展开更多
The waves in a magnetic null could play important roles during 3D magnetic reconnection.Some preliminary clues in this paper show that the ion Bernstein wave(IBW)may be closely related to transport process in magnetic...The waves in a magnetic null could play important roles during 3D magnetic reconnection.Some preliminary clues in this paper show that the ion Bernstein wave(IBW)may be closely related to transport process in magnetic null region.The magnetic null configuration experiment reported here is set up in a linear helicon plasma device,Peking University plasma test device(PPT).The wave modes with frequencies between the first and third harmonics of local ion cyclotron frequency(w_(ci))are observed in the separatrix of magnetic null,which are identified as the IBW based on the dispersion relation.Further analysis shows that IBW could drive substantial particle flux across the magnetic separatrix.The theoretical radial particle flux driven by IBW and the measured parallel flow in PPT device are almost on the same order,which shows that IBW may play an important role during 3D reconnection process.展开更多
It is generally accepted that during collisionless magnetic reconnection, electrons flow toward the X line in the separatrix region, and then an electron depletion layer is formed.In this paper, with two-dimensional(2...It is generally accepted that during collisionless magnetic reconnection, electrons flow toward the X line in the separatrix region, and then an electron depletion layer is formed.In this paper, with two-dimensional(2 D) particle-in-cell(PIC)simulation, we investigate the characteristics of the separatrix region during magnetic reconnection.In addition to the electron depletion layer, we find that there still exists an electric field parallel to the magnetic field in the separatrix region.Because a reduced ion-to-electron mass ratio and light speed are usually used in PIC simulation models, we also change these parameters to analyze the characteristics of the separatrix region.It is found that the increase in the ion-to-electron mass ratio makes the electron depletion layer and the parallel electric field more obvious, while the influence of light speed is less pronounced.展开更多
A sufficient and necessary condition of the existence of clam shaped curve solution for the cubic system is given in this paper. Again the author gives a sufficient and necessary condition of the existence of clam sha...A sufficient and necessary condition of the existence of clam shaped curve solution for the cubic system is given in this paper. Again the author gives a sufficient and necessary condition of the existence of clam shaped curve separatrix cycle for a special type of cubic system and obtains their accurate domain in parameter space.展开更多
In this paper, we give the necessary and sufficient condition for the coexistence of a class of cubic curve separatrix cycles and limit cycles to the cubic system, and study their topological structures.
A sufficient and necessary condition of the existence to a double bun curve solution for axial symmetry cubic system is given in this paper. The global topological structure of its trajectories in the phase space is a...A sufficient and necessary condition of the existence to a double bun curve solution for axial symmetry cubic system is given in this paper. The global topological structure of its trajectories in the phase space is also given.展开更多
基金The 3D simulation was carried out by the K computer at the RIKEN Advanced Institute for Computational Science through the HPCI Research project(hp140129,hp150123)supported by the National Natural Science Foundation of China under Grant Nos.42350710793,41874189 and 41821003。
文摘A recent satellite observation has revealed the presence of energy conversion in the separatrix region(SR)of magnetotail reconnection,driven by perpendicular components.We investigated this phenomenon by means of particle-in-cell simulations in two-dimensional(2D)and three-dimensional(3D)systems.Our result indicates that in the 2D simulation,energy conversion in the SR is dominated by parallel components,with the main influencing factor being the parallel electric field,which is not consistent with the observation.However,a case that is similar to the observation is found in the 3D simulation,suggesting that the observation result may be attributed to the 3D characteristics.Our findings provide a potential explanation for the satellite observation.
基金supported by the Shanghai 2022 Science and Technology Innovation Action Plan(No.22YF1446800)。
文摘Previous studies have shown that there is an obvious coupling relationship between the installation location of the external cathode and the magnetic separatrix in the plume region of a Hall thruster.In this paper,the particle-in-cell simulation method is used to compare the thruster discharge process under the conditions of different position relationships between the cathode and the magnetic separatrix.By comparing the distribution of electron conduction,potential,plasma density and other microscopic parameters,we try to explain the formation mechanism of the discharge difference.The simulation results show that the cathode inside and outside the magnetic separatrix has a significant effect on the distribution of potential and plasma density.When the cathode is located on the outer side of the magnetic separatrix,the potential above the plume region is relatively low,and there is a strong potential gradient above the plume region.This potential gradient is more conducive to the radial diffusion of ions above the plume,which is the main reason for the strong divergence of the plume.The distribution of ion density is also consistent with the distribution of potential.When the cathode is located on the outer side of the magnetic separatrix,the radial diffusion of ions in the plume region is enhanced.Meanwhile,by comparing the results of electron conduction,it is found that the traiectories of electrons emitted from the cathode are significantly different between the inner and outer sides of the magnetic separatrix.This is mainly because the electrons are affected by the magnetic mirror effect of the magnetic tip,which makes it difficult for the electrons to move across the magnetic separatrix.This is the main reason for the difference in potential distribution.In this paper,the simulation results of macroscopic parameters under several conditions are also compared,and they are consistent with the experimental results.The cathode is located on the inner side of the magnetic separatrix,which can effectively reduce the plume divergence angle and improve the thrust.In this paper,the cathode moves from R=50 mm to R=35 mm along the radial direction,the thrust increases by 3.6 mN and the plume divergence angle decreases by 23.77%.Combined with the comparison of the ionization region and the peak ion density,it is found that the main reason for the change in thrust is the change in the radial diffusion of ions in the plume region.
文摘For a given system, by using the Tkachev method which concerned with the proof of the stability of a multiple limit cycle, the exact computation formula of the third separatrix values named by Leontovich for the multiple limit cycle bifurcation was given, which was one of the main criterions for the number of limit cycles bifurcated from a homoclinic orbit and the stability of the homoclinic loop, and a computation formula for higher separatrix values was conjectured.
基金supported by National Natural Science Foundation of China(No.11975038)the National MCF Energy R&D Program of China(Nos.2017YFE0300601 and 2018YFE0311400).
文摘The waves in a magnetic null could play important roles during 3D magnetic reconnection.Some preliminary clues in this paper show that the ion Bernstein wave(IBW)may be closely related to transport process in magnetic null region.The magnetic null configuration experiment reported here is set up in a linear helicon plasma device,Peking University plasma test device(PPT).The wave modes with frequencies between the first and third harmonics of local ion cyclotron frequency(w_(ci))are observed in the separatrix of magnetic null,which are identified as the IBW based on the dispersion relation.Further analysis shows that IBW could drive substantial particle flux across the magnetic separatrix.The theoretical radial particle flux driven by IBW and the measured parallel flow in PPT device are almost on the same order,which shows that IBW may play an important role during 3D reconnection process.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.41774169,41527804,and 41804159)the Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.QYZDJ-SSW-DQC010)the Youth Innovation Promotion Association of the Chinese Academy of Sciences(Grant No.2016395)
文摘It is generally accepted that during collisionless magnetic reconnection, electrons flow toward the X line in the separatrix region, and then an electron depletion layer is formed.In this paper, with two-dimensional(2 D) particle-in-cell(PIC)simulation, we investigate the characteristics of the separatrix region during magnetic reconnection.In addition to the electron depletion layer, we find that there still exists an electric field parallel to the magnetic field in the separatrix region.Because a reduced ion-to-electron mass ratio and light speed are usually used in PIC simulation models, we also change these parameters to analyze the characteristics of the separatrix region.It is found that the increase in the ion-to-electron mass ratio makes the electron depletion layer and the parallel electric field more obvious, while the influence of light speed is less pronounced.
文摘A sufficient and necessary condition of the existence of clam shaped curve solution for the cubic system is given in this paper. Again the author gives a sufficient and necessary condition of the existence of clam shaped curve separatrix cycle for a special type of cubic system and obtains their accurate domain in parameter space.
文摘In this paper, we give the necessary and sufficient condition for the coexistence of a class of cubic curve separatrix cycles and limit cycles to the cubic system, and study their topological structures.
文摘A sufficient and necessary condition of the existence to a double bun curve solution for axial symmetry cubic system is given in this paper. The global topological structure of its trajectories in the phase space is also given.
