Exploration of microscopic physical processes of Z-pinch by a modified electrostatic direct implicit particle-in-cell algorithm

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.

Particle-in-cell simulations of EUV-induced hydrogen plasma in the vicinity of a reflective mirror

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.

Implementation of a particle-in-cell method for the energy solver in 3D spherical geodynamic modeling

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.

Modes decomposition in particle-in-cell software CEMPIC

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.

霍尔推进器等离子体鞘层特性的Particle-in-Cell模拟

霍尔(Hall)等离子体推进器鞘层特性对推进器的性能具有重要影响。针对Hall推进器鞘层区域建立物理模型,采用粒子模拟方法(PIC),通过求解泊松方程得到粒子位置产生的电场,确定边界条件,研究了不同磁感应强度和方向、不同推进工质和粒子权重对推进器鞘层电势及壁面二次电子发射系数的影响规律。结果表明:当磁感应强度为0.04T时,随着磁场方位角的增大,鞘层电势绝对值升高,壁面二次电子发射系数降低,变化量在10-3量级;磁场大小对鞘层电势及壁面二次电子发射系数影响较小;对于氩、氪和氙3种工质,鞘层电势和二次电子发射系数依次降低;而当粒子权重大于106时,等离子体鞘层振荡明显,推进器的稳定性降低。

Particle-in-Cell等离子体模拟方法的优化研究

由于PIC(Particle-in-Cell)方法在模拟GEO轨道上等离子体与航天器相互作用时计算量较大,因此限制了该方工程上的应用。文章分析了PIC方法在航天器充放电效应模拟中的计算效率问题,针对占用时间最多的泊松方程求解步骤提出了改进方法,并通过模拟验证了该方法的有效性。

5千瓦霍尔推力器磁场优化及Particle-in-Cell性能仿真

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。

Particle-in-Cell/Monte Carlo Collision simulation of planar DC magnetron sputtering

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.

On the energy conservation electrostatic particle-in-cell/Monte Carlo simulation: Benchmark and application to the radio frequency discharges

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.

不同品系杜洛克、PIC与加系二元母猪杂交后代生长性能及经济效益分析

为了研究猪场引进和选育终端父本以及筛选出符合市场需求的商品猪组合,该试验选取不同品系/品种包括D系杜洛克、F系杜洛克、M系杜洛克和PIC公猪与2~4胎加系长大二元母猪进行杂交,测定母猪繁殖性能、育肥猪日增重、采食量、料肉比、死淘率以及经济效益等指标。结果显示:(1)在繁殖性能方面,D系杜洛克组(DC)总产仔数和产健仔数均显著高于M系杜洛克组(MC)(P<0.05);F系杜洛克组(FC)初生健仔窝重显著高于MC(P<0.05);MC组初生头均重显著高于PIC组(PC)(P<0.05)。(2)商品猪生长性能方面,DC组达校正100 kg日龄最短;MC组170日龄料肉比显著高于PC组(P<0.05);DC组170日龄日增重显著PC组(P<0.05)。DC组出栏重显著高于其他3组(P<0.05);平均日增重显著高于PC组(P<0.05)。MC组出栏料肉比显著高于PC组(P<0.05);FC组出栏死淘率最低为2%。可见,在同等条件下,DC组产仔数最高且在生长速度方面具有明显优势,经济效益最好。

Effects of electron trapping on nonlinear electron-acoustic waves excited by an electron beam via particle-in-cell simulations

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.

Electromagnetic Particle-in-Cell Simulations of Electron Holes Formed During the Electron Two-Stream Instability

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.

Implicit electrostatic particle-in-cell/Monte Carlo simulation for the magnetized plasma:Algorithms and application in gas-inductive breakdown

An implicit electrostatic particle-in-cell/Monte Carlo （PIC/MC） algorithm is developed for the magnetized discharging device simulation. The inductive driving force can be considered. The direct implicit PIC algorithm （DIPIC） and energy conservation scheme are applied together and the grid heating can be eliminated in most cases. A tensor-susceptibility Poisson equation is constructed. Its discrete form is made up by a hybrid scheme in one-dimensional （1D） and two- dimensional （2D） cylindrical systems. A semi-coarsening multigrid method is used to solve the discrete system. The algorithm is applied to simulate the cylindrical magnetized target fusion （MTF） pre-ionization process and get qualitatively correct results. The potential application of the algorithm is discussed briefly.

Spontaneous growth of the reconnection electric field during magnetic reconnection with a guide field:A theoretical model and particle-in-cell simulations

Reconnection electric field is a key element of magnetic reconnection.It quantifies the change of magnetic topology and the dissipation of magnetic energy.In this work,two-dimensional(2D)particle-in-cell(PIC)simulations are performed to study the growth of the reconnection electric field in the electron diffusion region(EDR)during magnetic reconnection with a guide field.At first,a seed electric field is produced due to the excitation of the tearing-mode instability.Then,the reconnection electric field in the EDR,which is dominated by the electron pressure tensor term,suffers a spontaneous growth stage and grows exponentially until it saturates.A theoretical model is also proposed to explain such a kind of growth.The reconnection electric field in the EDR is found to be directly proportional to the electron outflow speed.The time derivative of electron outflow speed is proportional to the reconnection electric field in the EDR because the outflow is formed after the inflow electrons are accelerated by the reconnection electric field in the EDR and then directed away along the outflow direction.This kind of reinforcing process at last leads to the exponential growth of the reconnection electric field in the EDR.

基于MPI+CUDA的DSMC/PIC耦合模拟异构并行及性能优化研究

DSMC/PIC耦合模拟是一类重要的高性能计算应用,大规模DSMC/PIC耦合模拟计算量巨大,需要实现高效并行计算。由于粒子动态注入、迁移等操作,基于MPI并行的DSMC/PIC耦合模拟往往通信开销较大且难以实现负载均衡。针对自主研发的DSMC/PIC耦合模拟软件,在原有MPI并行优化版本上设计实现了高效的MPI+CUDA异构并行算法,结合GPU体系结构和DSMC/PIC计算特点,开展了GPU访存优化、GPU线程工作负载优化、CPU-GPU数据传输优化及DSMC/PIC数据冲突优化等一系列性能优化。在北京北龙超级云HPC系统的NVIDIA V100和A100 GPU上,针对数亿粒子规模的脉冲真空弧等离子体羽流应用,开展了大规模DSMC/PIC耦合异构并行模拟,相比原有纯MPI并行,GPU异构并行大幅缩短了模拟时间,两块GPU卡较192核的CPU加速比达到550%,同时具有更好的强可扩展性。

Particle-in-cell simulation for effect of anode temperature on discharge characteristics of a Hall effect thruster

Propellant gas flow has an important impact on the ionization and acceleration process of Hall effect thrusters （HETs）. In this paper, a particle-in-cell numerical method is used to study the effect of the anode temperature, i.e., the flow speed of the propellant gas, on the discharge characteristics of a HET. The simulation results show that, no matter the magnitude of the discharge voltage, the calculated variation trends of performance parameters with the anode temperature are in good agreement with the experimental ones presented in the literature. Further mechanism analysis indicates that the magnitude of the electron temperature is responsible for the two opposing variation laws found under different discharge voltages. When the discharge voltage is low, the electron temperature is low, and so is the intensity of the propellant ionization; the variation of the thruster performance with the anode temperature is thereby determined by the variation of the neutral density that affects the propellant utilization efficiency. When the discharge voltage is high, the electron temperature is large enough to guarantee a high degree of the propellant utilization no matter the magnitude of the anode temperature. The change of the thruster performance with the anode temperature is thus dominated by the change of the electron temperature and consequently the electron-neutral collisions as well as the electron cross-field mobility that affect the current utilization efficiency.

Particle-in-Cell Simulation Study on the Floating Potential of Spacecraft in the Low Earth Orbit

In order to further understand the characteristics of the floating potential of low earth orbit spacecraft,the effects of the electron current collection area,background electron temperature,photocurrent emission,spacecraft wake,and the shape of spacecraft on spacecraft floating potential were studied here by particle-in-cell simulation in the low earth orbit.The simulation results show that the electron current collection area and background electron temperature impact on the floating potential by changing the electron current collection of spacecraft.By increasing the electron current collection area or background electron temperature,the spacecraft will float at a lower electric potential with respect to the surrounding plasma.However,the spacecraft wake affects the floating potential by increasing the ion current collected by spacecraft.The emission of the photocurrent from the spacecraft surface,which compensates for the electrons collected from background plasma,causes the floating potential to increase.The shape of the spacecraft is also an important factor influencing the floating potential.

Particle-in-cell simulation for the effect of magnetic cusp on discharge characteristics in a cylindrical Hall thruster

The cylindrical Hall thruster has the good prospect of serving as a miniaturized electric propulsion device.A 2 D-3 V particle-in-cell plus Monte Carlo（PIC-MCC） method is used to study the effect of the magnetic cusp on discharge characteristics of a cylindrical Hall thruster.The simulation results show that the main ionization region and the main potential drop of the thruster are located at the upstream of the discharge channel.When the magnetic cusp moves toward the anode side,the main ionization region is compressed and weakened,moving upstream correspondingly.The ionization near the cusp is enhanced,and the interaction between the plasma and the wall increases.The simulation results suggest that the magnetic cusp should be located near the channel exit.

Particle-in-cell simulation for different magnetic mirror effects on the plasma distribution in a cusped field thruster

Magnetic mirror used as an efficient tool to confine plasma has been widely adopted in many different areas especially in recent cusped field thrusters. In order to check the influence of magnetic mirror effect on the plasma distribution in a cusped field thruster, three different radii of the discharge channel(6 mm, 4 mm, and 2 mm) in a cusped field thruster are investigated by using Particle-in-Cell Plus Monte Carlo(PIC-MCC) simulated method, under the condition of a fixed axial length of the discharge channel and the same operating parameters. It is found that magnetic cusps inside the small radius discharge channel cannot confine electrons very well. Thus, the electric field is hard to establish. With the reduction of the discharge channel’s diameter, more electrons will escape from cusps to the centerline area near the anode due to a lower magnetic mirror ratio. Meanwhile, the leak width of the cusped magnetic field will increase at the cusp. By increasing the magnetic field strength in a small radius model of a cusped field thruster, the negative effect caused by the weak magnetic mirror effect can be partially compensated. Therefore, according to engineering design, the increase of magnetic field strength can contribute to obtaining a good performance, when the radial distance between the magnets and the inner surface of the discharge channel is relatively big.

Analysis of microwave propagation in a time-varying plasma slab with particle-in-cell simulations

Continuous microwave propagation through a time-varying plasma and frequency up-conversion has been demonstrated by particle-in-cell (PIC) simulation. In principle, it is possible to transform a 2.45 GHz source radiation to an arbitrary larger frequency radiation. The energy conversion is also obtained by the theoretical analysis and has been testified by PIC simulation. The source wave was propagating in a parallel plate waveguide locally filled with the ionized gas. In this paper we would discuss the effects of the rise time, the plasma length, the switching time and the collision frequency on the energy conversion, and the methods to improve the upshift wave energy are proposed. We also put forward the new concept of the critical values of the rise time and the source wave amplitude to provide a theoretical basis for the selection of parameters in the experiments.