For investigating efficiently the stagnation kinetic-process of Z-pinch,we develop a novel modified electrostatic implicit particle-in-cell algorithm in radial one-dimension for Z-pinch simulation in which a small-ang...For investigating efficiently the stagnation kinetic-process of Z-pinch,we develop a novel modified electrostatic implicit particle-in-cell algorithm in radial one-dimension for Z-pinch simulation in which a small-angle cumulative binary collision algorithm is used.In our algorithm,the electric field in z-direction is solved by a parallel electrode-plate model,the azimuthal magnetic field is obtained by Ampere’s law,and the term for charged particle gyromotion is approximated by the cross product of the averaged velocity and magnetic field.In simulation results of 2 MA deuterium plasma shell Zpinch,the mass-center implosion trajectory agrees generally with that obtained by one-dimensional MHD simulation,and the plasma current also closely aligns with the external current.The phase space diagrams and radial-velocity probability distributions of ions and electrons are obtained.The main kinetic characteristic of electron motion is thermal equilibrium and oscillation,which should be oscillated around the ions,while that of ion motion is implosion inwards.In the region of stagnation radius,the radial-velocity probability distribution of ions transits from the non-equilibrium to equilibrium state with the current increasing,while of electrons is basically the equilibrium state.When the initial ion density and current peak are not high enough,the ions may not reach their thermal equilibrium state through collisions even in its stagnation phase.展开更多
Particle-In-Cell(PIC)simulations were performed in this work to study the dynamics of the EUVinduced hydrogen plasma.The Monte-Carlo Collision(MCC)model was employed to deal with the collisions between charged particl...Particle-In-Cell(PIC)simulations were performed in this work to study the dynamics of the EUVinduced hydrogen plasma.The Monte-Carlo Collision(MCC)model was employed to deal with the collisions between charged particles and background gas molecules.The dynamic evolution of the plasma sheath,as well as the flux and energy distribution of ions impacting on the mirror surface,was discussed.It was found that the emission of secondary electrons under the EUV irradiation on the ruthenium mirror coating creates a positively charged wall and then prevents the ions from impacting on the mirror and therefore changes the flux and energy distribution of ions reaching the mirror.Furthermore,gas pressure has a notable effect on the plasma sheath and the characteristics of the ions impinging on the mirrors.With greater gas pressure,the sheath potential decreases more rapidly.The flux of ions received by the mirror grows approximately linearly and at the same time the energy corresponding to the peak flux decreases slightly.However,the EUV source intensity barely changes the sheath potential,and its influence on the ion impact is mainly limited to the approximate linear increase in ion flux.展开更多
The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences.However,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially i...The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences.However,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially in the presence of sharp thermal gradients,such as when modeling subducting slabs and rising plumes.This phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic processes.After examining several approaches for removing these numerical oscillations,we show that the Lagrangian method provides an ideal way to solve this problem.In this study,we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems,as well as in a global spherical simulation with data assimilation.We have implemented this method in the open-source finite-element code CitcomS,which features a spherical coordinate system,distributed memory parallel computing,and data assimilation algorithms.展开更多
The direct implicit particle-in-cell is a powerful kinetic method for researching plasma characteristics.However,it is time-consuming to obtain the future electromagnetic field in such a method since the field equatio...The direct implicit particle-in-cell is a powerful kinetic method for researching plasma characteristics.However,it is time-consuming to obtain the future electromagnetic field in such a method since the field equations contain time-dependent matrix coefficients.In this work,we propose to explicitly push particles and obtain the future electromagnetic field based on the information about the particles in the future.The new method retains the form of implicit particle pusher,but the future field is obtained by solving the traditional explicit equation.Several numerical experiments,including the motion of charged particle in electromagnetic field,plasma sheath,and free diffusion of plasma into vacuum,are implemented to evaluate the performance of the method.The results demonstrate that the proposed method can suppress finite-grid-instability resulting from the coarse spatial resolution in electron Debye length through the strong damping of high-frequency plasma oscillation,while accurately describe low-frequency plasma phenomena,with the price of losing the numerical stability at large time-step.We believe that this work is helpful for people to research the bounded plasma by using particle-in-cell simulations.展开更多
在大气压介质阻挡放电的实际应用中,空气介质阻挡放电具有极其广泛的工业化应用前景。目前,空气均匀放电的获得仍比较困难,且诊断均匀性的依据缺乏可信的依据。文章采用粒子云网格法(Particle in Cell,PIC)与蒙特卡罗碰撞(Monte Carlo C...在大气压介质阻挡放电的实际应用中,空气介质阻挡放电具有极其广泛的工业化应用前景。目前,空气均匀放电的获得仍比较困难,且诊断均匀性的依据缺乏可信的依据。文章采用粒子云网格法(Particle in Cell,PIC)与蒙特卡罗碰撞(Monte Carlo Collision,MCC)方法模拟了放电过程中粒子的运动情况,研究大气压下空气介质阻挡放电的发展过程,然后讨论介质厚度、电源频率对形成均匀放电的影响,并研究这两种因素对等离子体密度的影响。模拟结果表明:介质厚度在d≥1.5 mm时可获得没有放电细丝的电流波形;电源频率高于2.5 kHz时,放电细丝是难以避免的。在能够形成均匀放电的条件下,将介质厚度适当的调整在1.5 mm附近,提高电源频率,将产生更高的等离子体密度。展开更多
The numerical method of modes analysis and decomposition of the output signal in 3D electromagnetic particle-in-cell simulation is presented. By the method, multiple modes can be resolved at one time using a set of di...The numerical method of modes analysis and decomposition of the output signal in 3D electromagnetic particle-in-cell simulation is presented. By the method, multiple modes can be resolved at one time using a set of diagnostic data, the amplitudes and the phases of the specified modes can all be given separately. Based on the method, the output signals of one X-band tri-bend mode converter used for one high power microwave device, with ionization process in the device due to the strong normal electric field, are analyzed and decomposed.展开更多
为了提升兰州空间技术物理研究所研制的一种5 k W霍尔推力器LHT—140的性能,采用ANSOFT软件进行了磁场优化设计,将磁场径向分量的轴向梯度提高了47%,相同励磁激励下放电通道中的磁场强度提高了38%。建立了一个R-Z平面内的二维particle-i...为了提升兰州空间技术物理研究所研制的一种5 k W霍尔推力器LHT—140的性能,采用ANSOFT软件进行了磁场优化设计,将磁场径向分量的轴向梯度提高了47%,相同励磁激励下放电通道中的磁场强度提高了38%。建立了一个R-Z平面内的二维particle-in-cell(PIC)等离子体模型,对磁场优化后推力器的性能进行了仿真分析,预估其在300~800 V放电电压、10~15 mg/s流率范围内,推力提升了9.6%~22.1%,效率提升了8.7%~19.3%。性能验证试验表明磁场优化后在相同放电电压与流率下,性能提升的测试值高于仿真值。展开更多
In this paper a numerical simulation of a planar DC magnetron discharge is performed with the Particle-in Cell/Monte Carlo Collision (PIC/MCC) method. The magnetic field used in the simulation is calculated with fin...In this paper a numerical simulation of a planar DC magnetron discharge is performed with the Particle-in Cell/Monte Carlo Collision (PIC/MCC) method. The magnetic field used in the simulation is calculated with finite element method according to experimental configuration. The simulation is carried out under the condition of gas pressure of 0.665 Pa and voltage magnitude of 400V. Typical results such as the potential distribution, charged particle densities, the discharge current density and ion flux onto the target are calculated. The erosion profile from the simulation is compared with the experimental data. The maximum erosion position corresponds to the place where the magnetic field lines are parallel to the target surface.展开更多
We benchmark and analyze the error of energy conservation (EC) scheme in particle-in-cell/Monte Carlo (PIC/MC) algorithms by simulating the radio frequency discharge. The plasma heating behaviors and electron dist...We benchmark and analyze the error of energy conservation (EC) scheme in particle-in-cell/Monte Carlo (PIC/MC) algorithms by simulating the radio frequency discharge. The plasma heating behaviors and electron distributing functions obtained by one-dimensional (1D) simulation are analyzed. Both explicit and implicit algorithms are checked. The results showed that the EC scheme can eliminated the self-heating with wide grid spacing in both cases with a small reduction of the accuracies. In typical parameters, the EC implicit scheme has higher precision than EC explicit scheme. Some "numerical cooling" behaviors are observed and analyzed. Some other errors are also analyzed. The analysis showed that the EC implicit scheme can be used to qualitative estimation of some discharge problems with much less computational resource cost without much loss of accuracies.展开更多
By performing one-dimensional particle-in-cell simulations, the nonlinear effects of electronacoustic(EA) waves are investigated in a multispecies plasma, whose constituents are hot electrons, cold electrons, and beam...By performing one-dimensional particle-in-cell simulations, the nonlinear effects of electronacoustic(EA) waves are investigated in a multispecies plasma, whose constituents are hot electrons, cold electrons, and beam electrons with immobile neutralized positive ions. Numerical analyses have identified that EA waves with a sufficiently large amplitude tend to trap cold electrons. Because EA waves are dispersive, where the wave modes with different wavenumbers have different phase velocities, the trapping may lead to the mixing of cold electrons. The cold electrons finally get thermalized or heated. The investigation also shows that the excited EA waves give rise to a broad range of wave frequencies, which may be helpful for understanding the broadband-electrostatic-noise spectrum in the Earth’s auroral region.展开更多
Previous electrostatic particle-in-cell (PIC) simulations have pointed out that elec- tron phase-space holes (electron holes) can be formed during the nonlinear evolution of the electron two-stream instability. Th...Previous electrostatic particle-in-cell (PIC) simulations have pointed out that elec- tron phase-space holes (electron holes) can be formed during the nonlinear evolution of the electron two-stream instability. The parallel cuts of the parallel and perpendicular electric field have bipolar and unipolar structures in these electron holes, respectively. In this study, two-dimensional (2D) electromagnetic PIC simulations are performed in the x - y plane to investigate the evolution of the electron two-stream instability, with the emphasis on the magnetic structures associated with these electron holes in different plasma conditions. In the simulations, the background magnetic field (Bo = Boer) is along the x direction. In weakly magnetized plasma (Ωe 〈ωpe, where Ωe and ωpe are the electron gyrofrequency and electron plasma frequency, respectively), several 2D electron holes are formed. In these 2D electron holes, the parallel cut of the fluctuating magnetic field δBx and δBz has unipolar structures, while the fluctuating magnetic field δBy has bipolar structures. In strongly magnetized plasma (Ωe 〉 ωpe), several quasi-lD electron holes are formed. The electrostatic whistler waves with streaked structures of Ey are excited. The fluctuating mag- netic field δBx and δBz also have streaked structures. The fluctuating magnetic field δBx and δBy are produced by the current in the z direction due to the electric field drift of the trapped elec- trons, while the fluctuating magnetic field δBz can be explained by the Lorentz transformation of a moving quasielectrostatic structure. The influences of the initial temperature anisotropy on the magnetic structures of the electron holes are also analyzed. The electromagnetic whistler waves are found to be excited in weakly magnetized plasma. However, they do not have any significant effects on the electrostatic structures of the electron holes.展开更多
基金the graduated students Zhixing Feng,Xiaoqiang Zhang,and Deli Fang for their excellent works to develop the PIC simulation codes of Z-pinch.This research was partly supported by the National Natural Science Foundation of China(Grant Nos.11675025 and 11135007)the Innovation Project of China Academy of Engineering Physics(Grant No.CX2019030).
文摘For investigating efficiently the stagnation kinetic-process of Z-pinch,we develop a novel modified electrostatic implicit particle-in-cell algorithm in radial one-dimension for Z-pinch simulation in which a small-angle cumulative binary collision algorithm is used.In our algorithm,the electric field in z-direction is solved by a parallel electrode-plate model,the azimuthal magnetic field is obtained by Ampere’s law,and the term for charged particle gyromotion is approximated by the cross product of the averaged velocity and magnetic field.In simulation results of 2 MA deuterium plasma shell Zpinch,the mass-center implosion trajectory agrees generally with that obtained by one-dimensional MHD simulation,and the plasma current also closely aligns with the external current.The phase space diagrams and radial-velocity probability distributions of ions and electrons are obtained.The main kinetic characteristic of electron motion is thermal equilibrium and oscillation,which should be oscillated around the ions,while that of ion motion is implosion inwards.In the region of stagnation radius,the radial-velocity probability distribution of ions transits from the non-equilibrium to equilibrium state with the current increasing,while of electrons is basically the equilibrium state.When the initial ion density and current peak are not high enough,the ions may not reach their thermal equilibrium state through collisions even in its stagnation phase.
基金supported by National Natural Science Foundation of China(Nos.12172356,U23B20110)the Interdisciplinary and Collaborative Teams of CAS。
文摘Particle-In-Cell(PIC)simulations were performed in this work to study the dynamics of the EUVinduced hydrogen plasma.The Monte-Carlo Collision(MCC)model was employed to deal with the collisions between charged particles and background gas molecules.The dynamic evolution of the plasma sheath,as well as the flux and energy distribution of ions impacting on the mirror surface,was discussed.It was found that the emission of secondary electrons under the EUV irradiation on the ruthenium mirror coating creates a positively charged wall and then prevents the ions from impacting on the mirror and therefore changes the flux and energy distribution of ions reaching the mirror.Furthermore,gas pressure has a notable effect on the plasma sheath and the characteristics of the ions impinging on the mirrors.With greater gas pressure,the sheath potential decreases more rapidly.The flux of ions received by the mirror grows approximately linearly and at the same time the energy corresponding to the peak flux decreases slightly.However,the EUV source intensity barely changes the sheath potential,and its influence on the ion impact is mainly limited to the approximate linear increase in ion flux.
基金the National Supercomputer Center in Tianjin for their patient assistance in providing the compilation environment.We thank the editor,Huajian Yao,for handling the manuscript and Mingming Li and another anonymous reviewer for their constructive comments.The research leading to these results has received funding from National Natural Science Foundation of China projects(Grant Nos.92355302 and 42121005)Taishan Scholar projects(Grant No.tspd20210305)others(Grant Nos.XDB0710000,L2324203,XK2023DXC001,LSKJ202204400,and ZR2021ZD09).
文摘The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences.However,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially in the presence of sharp thermal gradients,such as when modeling subducting slabs and rising plumes.This phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic processes.After examining several approaches for removing these numerical oscillations,we show that the Lagrangian method provides an ideal way to solve this problem.In this study,we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems,as well as in a global spherical simulation with data assimilation.We have implemented this method in the open-source finite-element code CitcomS,which features a spherical coordinate system,distributed memory parallel computing,and data assimilation algorithms.
基金Project supported by the National Key Research and Development Program of China (Grant No.2022YFE03050001)partly by the National Natural Science Foundation of China (Grant No.12175160)the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)。
文摘The direct implicit particle-in-cell is a powerful kinetic method for researching plasma characteristics.However,it is time-consuming to obtain the future electromagnetic field in such a method since the field equations contain time-dependent matrix coefficients.In this work,we propose to explicitly push particles and obtain the future electromagnetic field based on the information about the particles in the future.The new method retains the form of implicit particle pusher,but the future field is obtained by solving the traditional explicit equation.Several numerical experiments,including the motion of charged particle in electromagnetic field,plasma sheath,and free diffusion of plasma into vacuum,are implemented to evaluate the performance of the method.The results demonstrate that the proposed method can suppress finite-grid-instability resulting from the coarse spatial resolution in electron Debye length through the strong damping of high-frequency plasma oscillation,while accurately describe low-frequency plasma phenomena,with the price of losing the numerical stability at large time-step.We believe that this work is helpful for people to research the bounded plasma by using particle-in-cell simulations.
文摘在大气压介质阻挡放电的实际应用中,空气介质阻挡放电具有极其广泛的工业化应用前景。目前,空气均匀放电的获得仍比较困难,且诊断均匀性的依据缺乏可信的依据。文章采用粒子云网格法(Particle in Cell,PIC)与蒙特卡罗碰撞(Monte Carlo Collision,MCC)方法模拟了放电过程中粒子的运动情况,研究大气压下空气介质阻挡放电的发展过程,然后讨论介质厚度、电源频率对形成均匀放电的影响,并研究这两种因素对等离子体密度的影响。模拟结果表明:介质厚度在d≥1.5 mm时可获得没有放电细丝的电流波形;电源频率高于2.5 kHz时,放电细丝是难以避免的。在能够形成均匀放电的条件下,将介质厚度适当的调整在1.5 mm附近,提高电源频率,将产生更高的等离子体密度。
基金Project supported by the fund of the State Key Laboratory of Intense Pulsed Radiation Simulation and Effect (Grant No. SKLIPR1908).
文摘The numerical method of modes analysis and decomposition of the output signal in 3D electromagnetic particle-in-cell simulation is presented. By the method, multiple modes can be resolved at one time using a set of diagnostic data, the amplitudes and the phases of the specified modes can all be given separately. Based on the method, the output signals of one X-band tri-bend mode converter used for one high power microwave device, with ionization process in the device due to the strong normal electric field, are analyzed and decomposed.
文摘为了提升兰州空间技术物理研究所研制的一种5 k W霍尔推力器LHT—140的性能,采用ANSOFT软件进行了磁场优化设计,将磁场径向分量的轴向梯度提高了47%,相同励磁激励下放电通道中的磁场强度提高了38%。建立了一个R-Z平面内的二维particle-in-cell(PIC)等离子体模型,对磁场优化后推力器的性能进行了仿真分析,预估其在300~800 V放电电压、10~15 mg/s流率范围内,推力提升了9.6%~22.1%,效率提升了8.7%~19.3%。性能验证试验表明磁场优化后在相同放电电压与流率下,性能提升的测试值高于仿真值。
基金Project supported by the National Science Found for Distinguished Young Scholars of China (Grant No 50407015)
文摘In this paper a numerical simulation of a planar DC magnetron discharge is performed with the Particle-in Cell/Monte Carlo Collision (PIC/MCC) method. The magnetic field used in the simulation is calculated with finite element method according to experimental configuration. The simulation is carried out under the condition of gas pressure of 0.665 Pa and voltage magnitude of 400V. Typical results such as the potential distribution, charged particle densities, the discharge current density and ion flux onto the target are calculated. The erosion profile from the simulation is compared with the experimental data. The maximum erosion position corresponds to the place where the magnetic field lines are parallel to the target surface.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11275007,11105057,11175023,and 11275039)the Program for Liaoning Excellent Talents in University,China(Grant No.LJQ2012098)
文摘We benchmark and analyze the error of energy conservation (EC) scheme in particle-in-cell/Monte Carlo (PIC/MC) algorithms by simulating the radio frequency discharge. The plasma heating behaviors and electron distributing functions obtained by one-dimensional (1D) simulation are analyzed. Both explicit and implicit algorithms are checked. The results showed that the EC scheme can eliminated the self-heating with wide grid spacing in both cases with a small reduction of the accuracies. In typical parameters, the EC implicit scheme has higher precision than EC explicit scheme. Some "numerical cooling" behaviors are observed and analyzed. Some other errors are also analyzed. The analysis showed that the EC implicit scheme can be used to qualitative estimation of some discharge problems with much less computational resource cost without much loss of accuracies.
基金the support from Chinese Academy of Science(CAS)TWAS for his Ph.D studies at the University of Science and Technology of China in the category of a 2016 CAS-TWAS President’s Fellowship Awardee(Series No.2016-172)+1 种基金partially supported by National Natural Science Foundation of China(Nos.41331067,41774169,and 41527804)the Key Research Program of Frontier Sciences,CAS(QYZDJ-SSW-DQC010)
文摘By performing one-dimensional particle-in-cell simulations, the nonlinear effects of electronacoustic(EA) waves are investigated in a multispecies plasma, whose constituents are hot electrons, cold electrons, and beam electrons with immobile neutralized positive ions. Numerical analyses have identified that EA waves with a sufficiently large amplitude tend to trap cold electrons. Because EA waves are dispersive, where the wave modes with different wavenumbers have different phase velocities, the trapping may lead to the mixing of cold electrons. The cold electrons finally get thermalized or heated. The investigation also shows that the excited EA waves give rise to a broad range of wave frequencies, which may be helpful for understanding the broadband-electrostatic-noise spectrum in the Earth’s auroral region.
基金supported by Ocean Public Welfare Scientific Research Project, State Oceanic Administration People’s Republic of China(No. 201005017)National Natural Science Foundation of China (Nos. 41274144, 41174124, 40931053, 41121003)+1 种基金CAS Key Research Program KZZD-EW-01,973 Program (2012CB825602)the Fundamental Research Funds for the Central Universities(WK2080000010)
文摘Previous electrostatic particle-in-cell (PIC) simulations have pointed out that elec- tron phase-space holes (electron holes) can be formed during the nonlinear evolution of the electron two-stream instability. The parallel cuts of the parallel and perpendicular electric field have bipolar and unipolar structures in these electron holes, respectively. In this study, two-dimensional (2D) electromagnetic PIC simulations are performed in the x - y plane to investigate the evolution of the electron two-stream instability, with the emphasis on the magnetic structures associated with these electron holes in different plasma conditions. In the simulations, the background magnetic field (Bo = Boer) is along the x direction. In weakly magnetized plasma (Ωe 〈ωpe, where Ωe and ωpe are the electron gyrofrequency and electron plasma frequency, respectively), several 2D electron holes are formed. In these 2D electron holes, the parallel cut of the fluctuating magnetic field δBx and δBz has unipolar structures, while the fluctuating magnetic field δBy has bipolar structures. In strongly magnetized plasma (Ωe 〉 ωpe), several quasi-lD electron holes are formed. The electrostatic whistler waves with streaked structures of Ey are excited. The fluctuating mag- netic field δBx and δBz also have streaked structures. The fluctuating magnetic field δBx and δBy are produced by the current in the z direction due to the electric field drift of the trapped elec- trons, while the fluctuating magnetic field δBz can be explained by the Lorentz transformation of a moving quasielectrostatic structure. The influences of the initial temperature anisotropy on the magnetic structures of the electron holes are also analyzed. The electromagnetic whistler waves are found to be excited in weakly magnetized plasma. However, they do not have any significant effects on the electrostatic structures of the electron holes.