Particle‐in‐cell/Monte Carlo simulation of electron and ion currents to cylindrical Langmuir probe

Electron and ion currents to a cylindrical Langmuir (electrostatic) probe were calculated using the particle‐in‐cell/Monte Carlo (PIC/MC) self‐consistent simulation for a neutral gas in the pressure range 2–3,000 Pa. The simulation enables us to calculate the probe currents even at high neutral gas pressures when the collisions of collected charged particles with neutral gas particles near the probe are important. The main aim of this paper is the calculation of probe currents at such high gas pressures and the comparison of the results with experimentally measured probe currents. Simulations were performed for two cases: (a) probes with varying radii in a non‐thermal plasma with high electron temperature at low neutral gas pressure of 2 Pa (in order to verify the correctness of our simulations), and (b) probe with the radius of 10 μm in the afterglow plasma with low electron temperature and a higher neutral gas pressure (up to 3,000 Pa). The electron probe currents obtained in case (a) show good agreement with those predicted by the orbital motion limited current (OMLC) theory for probes with radii up to 100 μm for the given plasma conditions. At larger probe radii and/or at higher probe voltages, the OMLC theory incorrectly predicts too high an electron probe current for the plasma parameters studied. Additionally, a formula describing the spatial dependence of the electron density in the presheath in the collisionless case is derived. The simulation at higher neutral gas pressures, i.e. case (b), shows a decrease of the electron probe current with increasing gas pressure and the creation of a large presheath around the probe. The simulated electron probe currents are compared with those of measurements by other authors, and the differences are discussed.     

Monte Carlo Simulations of the Influence of Ion‐Neutral Collisions on the Ion Currents Collected by Electrostatic Probes

We have carried out Monte Carlo simulation of the motion of Ar⁺ ions in the space charge sheath surrounding a cylindrical Langmuir probe. The ion currents to the probe have been calculated from these simulations and the percentages of ions crossing the sheath boundary that are collected by the probe have been determined. It has been shown that the collisions of ions with neutral helium gas atoms in the sheath increase the percentage of ions collected by the probe above that predicted by collisionless orbital motion limited current (OMLC) theory at lower helium pressure and decrease this percentage below the OMLC theory prediction at higher helium pressure. It has been shown also that the ion current almost does not depend on probe radius at higher helium pressures. The results of the simulations have been compared with recent Langmuir probe measurements made in flowing afterglow plasmas and with other probe theories.     

Electrostatic simulations of the radio frequency heating of a non‐neutral plasma in an electron trap

The electrostatic simulations of the radio frequency (RF) heating mechanism, excitations, and ionization process of an electron plasma are carried out using a two‐dimensional (2D) particle‐in‐cell (PIC) code. RF drives with excitation frequencies of 1–15 MHz and amplitudes of 5 and 10 V were applied at two different axial positions, to the centre and to one end on the electrode stack of the ELTRAP device, at ultra‐high vacuum conditions. It is observed that the axial kinetic energy (eV) profile of the confined electrons increases with an increase of the RF excitation amplitudes, and densities from 5 × 10⁷ to 10¹² m^?3 for all cases under consideration. The simulation results indicate that with continuous RF excitations, the electron heating in the beginning is higher at the trap wall of the device and extends towards the central region of the trap over a simulation time of up to 100 µs. These results on the electron heating are in good agreement with the experimental findings (optical diagnostics of ELTRAP). The heating effect is larger when the RF power is applied from the position close to one end of the trap in comparison to the central position. Monte–Carlo PIC simulations with hydrogen as a background gas are also performed to evaluate the ionization process at pressures of 10^?8, 10^?7, and 10^?6 torr using the same electron plasma densities. The results show that at increasing pressures, the electron‐neutral collisions rate increases linearly with the background gas pressure. Increased collision frequency is obtained at higher RF drive amplitudes, which proportionally increases electron temperature, so that more ionization and secondary electrons are generated.     

Längsfeldstärke,Elektronentemperatur, mittlere Neutralgasdichte,Ionenstromdichte auf die Wand und mittlere Entladungsstromdichte in der Freifallsäule bei hohem Ionisationsgrad

On the basis of a foregoing paper new theoretical results for the positive column at low pressure and strong ionization, especially for discharges in noble gas ion lasers, are given. The mean velocity v_n0 of the neutral atoms reemitted from the wall is taken into account. The electric conductivity is calculated for an argon plasma. The formulas connecting the electron temperature, the mean neutral gas density, and the electric field strength are derived. The electron temperature, the axial electric field intensity, the degree of ionization, the axial electron drift velocity, the ion flux to the wall, and the force density causing the main part of gas pumping along the column are calculated as functions of the product of the mean current density and the tube radius, and of v_n0 for argon. The axial drift velocity of the electrons is still smaller than the mean thermal electron velocity for high discharge currents, except at very low gas pressures. In general, the ion flux to the wall is not directly proportional to the discharge current. The factor for the determination of the charged particle density by means of probe measurements at the wall is discussed. The self-magnetic field affects the discharge only at high electron temperature, high degree of ionization, and relatively large tube radius, i.e. at high current density and low gas pressure in not too narrow discharge channels.     

A contribution to the assessment of the influence of collisions on the measurements with Langmuir probes in the thick sheath working regime

In the present work we investigate theoretically and experimentally the influence of elastic collisions in a probe sheath on a cylindrical Langmuir probe. The analysed probe working regime covers conditions under which the following probe characteristic parameters are comparable: the probe radius, the Debye length and both the ion and electron mean free paths.The preliminary investigations under almost collisionless conditions show good agreement between theoretical and experimental values of the ion saturation currents and of the floating potentials only when the ion currents for the studied working regime of the cylindrical Langmuir probe are calculated according to the theory of Chen (Plasma Phys.7 (1965)47). These collisionless currents form the basis for the calculation of the collision-corrected probe characteristics according to the presented procedure by Talbot and Chou (Rarefied Gas Dynamics, Academic Press, New York, 1966, p. 1723).The applied theoretical analysis covers the influence of the collisions on the electron and ion current of the single probe characteristic and on the estimation of the space potential. The results of the calculations are presented in graphical overviews for the series of cases of practical importance. The other working regimes can be covered using the calculating procedure presented.For comparison of the calculated collision-corrected characteristics with those from an experiment we used the positive column plasma of the He glow discharge where the electron density is known and the space potential can be experimentally estimated from the lowest excitation potential of He. The comparison was carried out for the ion and electron currents, the floating potential and the zero-cross of the probe characteristic second derivative.The estimation of the secondary electron current contribution to the total probe current shows that it limits the applicability of the collision-corrected probe characteristic to the plasma diagnostic in the transition to the collision-determined working regime.     

Performance evaluation of self-breakdown-based single-gap plasma cathode electron gun

This paper presents the experimental studies on self-breakdown-based single-gap plasma cathode electron (PCE) gun (5–20 kV/50–160 A) in argon, gas atmosphere and its performance evaluation based on particle-in-cell (PIC) simulation code ‘OOPIC-Pro’. The PCE-Gun works in conducting phase (low energy, high current) of pseudospark discharge. It produces intense electron beam, which can propagate more than 200 mm in the drift space region without external magnetic field. The profile of this beam in the drift space region at different breakdown conditions (i.e., gas pressures and applied voltages) has been studied and the experimental results are compared with simulated values. It is demonstrated that ～30% beam current is lost during the propagation possibly due to space charge neutralization and collisions with neutral particles and walls.     

基于负氢离子源的全三维PIC/MCC模拟算法研究

在分析负氢离子源中等离子体物理机理基础下, 研究并优化粒子模拟算法, 设计高效的粒子存储方法. 研究并运用粒子碰撞蒙特卡罗方法, 考虑等离子体势以及带电粒子间库仑碰撞, 研制了全三维粒子模拟/蒙特卡罗算法(PIC/MCC). 采用磁荷模型, 运用时域有限差分方法计算多峰磁场, 并结合国外负氢离子源JT-60U, 考虑负氢离子源中主要反应, 对全三维PIC/MCC模拟算法模拟验证.     

一种补偿时间步长限制的粒子模拟-蒙特卡罗碰撞模型

 从碰撞次数的概率分布出发,推导出一种补偿蒙特卡罗碰撞模型,采用以正态分布计算得到的平均碰撞次数作为碰撞概率,来补偿传统方法中忽略的多次碰撞。通过模拟不同折合电场强度条件下He气放电产生电子的运动规律,验证了补偿蒙特卡罗碰撞模型的正确性。计算结果表明:补偿蒙特卡罗碰撞模型可以有效地提高计算效率,特别适用于高气压气体放电现象的粒子模拟。     

Particle-in-cell charged-particle simulations, plus Monte Carlocollisions with neutral atoms, PIC-MCC

Many-particle charged-particle plasma simulations using spatial meshes for the electromagnetic field solutions, particle-in-cell (PIC) merged with Monte Carlo collision (MCC) calculations, are coming into wide use for application to partially ionized gases. The author emphasizes the development of PIC computer experiments since the 1950s starting with one-dimensional (1-D) charged-sheet models, the addition of the mesh, and fast direct Poisson equation solvers for 2-D and 3-D. Details are provided for adding the collisions between the charged particles and neutral atoms. The result is many-particle simulations with many of the features met in low-temperature collision plasmas; for example, with applications to plasma-assisted materials processing, but also related to warmer plasmas at the edges of magnetized fusion plasmas     

气体电离的全三维电磁粒子模拟/蒙特卡罗数值研究

深入研究电子束对中性气体电离的物理机理,在粒子模拟(PIC)软件CHIPIC的基础上,设计了蒙特卡罗(MCC)电离碰撞模块,并对电子与离子同时进行了跟踪,成功研制了全三维电磁PIC/MCC代码.通过该软件对填充氦气相对论返波管的模拟,对全三维电磁PIC/MCC代码进行验证.模拟结果显示:填充气体可以中和空间电荷限制效应,有效提高电流大小;填充适量的气体可提高功率峰值,扩展脉冲宽度;过量的气体则会缩短脉冲宽度、降低峰值功率.     

Particle-in-Cell Simulation of the Focusing Properties of High Energy Electron Beam in Plasma Ion Channel

The focusing properties of high energy electron beam in ion channel is investigated in the paper. The collisions of electrons with the neutral gas and the ionization resulted are considered to study the formation of ion channels with PIC method. The effects of various parameters on the beam focusing are analyzed.     

潘宁源放电的全三维电磁粒子模拟/蒙特卡罗碰撞数值算法研究

深入研究潘宁放电的物理机制, 研制了全三维高品质算法粒子模拟软件(PIC), 设计并添加了相应物理情景的蒙特卡罗碰撞模块(MCC), 并对电子、氢分子离子(H₂⁺)、氢正离子(H⁺)、氢三正离子(H₃⁺)同时进行了跟踪, 成功研制了全三维电磁PIC/MCC数值算法. 结合国内研究较热的潘宁放电模型, 对该算法进行模拟验证. 模拟结果显示: 采用有效的滤波算法能抑制电磁数值噪声, 电子能量呈麦克斯韦分布, 由于电子的径向漂移和加速导致离子源顶端H₂⁺产量较大. 关键词： 潘宁离子源 高品质算法 粒子模拟/蒙特卡罗     

Orbital motion of dust particles in an rf magnetron discharge. Ion drag force or neutral atom wind force

Microparticles with sizes up to 130 μm have been confined and the velocity and diameter of particles in a plasma trap of an rf magnetron discharge with an arc magnetic field have been simultaneously measured. The motion of the gas induced by electron and ion cyclotron currents has been numerically simulated using the Navier-Stokes equation. The experimental and numerical results confirm the mechanism of the orbital motion of dust particles in the magnetron discharge plasma that is associated with the orbital motion of the neutral gas accelerated by electron and ion drift flows in crossed electric and magnetic fields.     

The Influence of Collisions in the Space Charge Sheath on the Ion current Collected by a Langmuir Probe

The current/voltage characteristics of a cylindrical Langmuir probe have been studied in Ar⁺/electron afterglow plasmas in helium carrier gas under truly thermal conditions at 300 K using our flowing afterglow/Langmuir probe (FALP) apparatus. The orbital motion limited (oml) ion and electron current regions of the probe characteristics have been explored over a wide range of the reduced probe voltage (up to ～ 100) and over a wide range of electron (n_e) and ion (n₊) number densities (1.6 × 10⁷ to 1.5 × 10¹⁰ cm^?3) at a constant pressure of the He carrier gas of 1.2 Torr. The observed increase of the probe ion currents above those predicted by collisionless oml theory, resulting in an apparent increase of the measured ion number density above n_e in the plasma, is explained by the enhancement in the ion current collection efficiency due to collisions of ions with neutral gas atoms in the space charge sheath surrounding the probe. The continuous change in the exponent, χ, of the power-law dependence,i₊ ∞ V of the ion current, i₊, on the probe voltage, V_p from 0.5 at the highest n₊ (smallest sheath) towards 1.0 at the lowest n₊ (large sheath) indicates that the ion current collection from the plasma changes from the oml current regime at the high n₊ to the continuum regime at the low n₊ when the ions undergo multiple collisions with the helium atoms in the space charge sheath and thus “drift” towards the probe.     

The Influence of Ion – Neutral Collisions in the Plasma Sheath on the Ion Current to an Electrostatic Probe: Monte Carlo Simulation

We have carried out Monte Carlo simulation of the motion of Ar⁺ ions in the space charge sheath surrounding a cylindrical Langmuir probe. From these simulations the percentage of ions crossing the sheath boundary that are collected by the probe have been determined and thus the ion currents to the probe have been calculated. It is shown that the collisions of ions with neutral helium gas atoms in the sheath increase the percentage of ions collected by the probe above that predicted by collisionless orbital motion limited current (OMLC) theory and that the exponent, χ, of the power law dependence, i₊～U, of the ion current, i₊, on the probe voltage, U_p, increases above the value 0.5 predicted by OMLC theory. The results of the simulations are compared with recent Langmuir probe measurements made in flowing afterglow plasmas.     

沿面闪络流体模型电离参数粒子模拟确定方法

介绍了粒子模拟确定高功率微波介质沿面闪络击穿流体模型相关电离参数的方法.对粒子模拟方法 (包括带电粒子动力学方程、次级电子发射以及蒙特卡罗碰撞模型)和流体整体模型方法 (包括连续性方程和能量守恒方程)做了简介.基于自编的1D3V粒子模拟-蒙特卡罗碰撞程序给出了在高(低)气压、不同气体种类以及不同微波场强和微波频率下流体模型电离参数的粒子模拟结果,包括电离频率、击穿时间、平均电子能量、电子能量分布函数类型.研究结果表明:平均电子能量与电子能量分布函数类型关系不大;中低气压下,电子能量接近Maxwell分布,电子能量分布函数类型对电离参数几乎没有影响;中高气压下,电子能量分布函数类型对电离参数有重要影响,其依赖系数X趋于高阶形式.不同气体的电子能量分布函数类型不同,需要利用粒子模拟对电子能量分布函数类型进行标定.同时,电子能量分布函数依赖系数与微波场强和频率也有关系,其随微波场强增加而增大,随微波频率增加而减小.在给定考察范围(微波场强在7 MV/m以下,微波频率在40 GHz以内),中低气压下,平均电子能量随微波场强增加而迅速增大,电离频率随微波场强增加先增大后降低,平均电子能量随微波频率增加而降低,电离频率随微波频率增加先增加后降低;高气压下,平均电子能量随微波场强增加而缓慢增大,电离频率随微波场强增加而增大,微波频率对平均电子能量和电离频率影响不大.     

Validity of the two-term Boltzmann approximation employed in the fluid model for high-power microwave breakdown in gas

The electron energy distribution function （EEDF）, predicted by the Boltzmann equation solver BOLSIG＋ based on the two-term approximation, is introduced into the fluid model for simulating the high-power microwave （HPM） breakdown in argon, nitrogen, and air, and its validity is examined by comparing with the results of particle-in-cell Monte Carlo collision （PIC/MCC） simulations as well as the experimental data. Numerical results show that, the breakdown time of the fluid model with the Maxwellian EEDF matches that of the PIC/MCC simulations in nitrogen; however, in argon under high pressures, the results from the Maxwellian EEDF were poor. This is due to an overestimation of the energy tail of the Maxwellian EEDF in argon breakdown. The prediction of the fluid model with the BOLSIG＋ EEDF, however, agrees very well with the PIC/MCC prediction in nitrogen and argon over a wide range of pressures. The accuracy of the fluid model with the BOLSIG＋ EEDF is also verified by the experimental results of the air breakdown.     

Optimization of Operating Parameters of Plasma Antenna

In this work, the operating parameters of the plasma antenna are optimized using a kinetic model based on Particle in Cell‐Monte Carlo Collisions (PIC‐MCC) method. This optimization study is performed via the investigation of variations in the operating parameters of the plasma antenna, i. e., its dimensions, background gas pressure, and the applied voltage frequency and their consequent effects on the plasma frequency, kinetic energy of electrons and plasma current density of plasma antenna. While the antenna performance is improved at higher tube lengths and applied frequencies, it is optimized at a particular tube radius. Moreover, higher background pressures have increasing effects on the plasma antenna operation. Based on this parametric study, the optimum operating parameters of the plasma antenna are established. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

���������ʲ㼰������ײ��΢������̽����ϵ�Ӱ��

针对气压大于133Pa的气体放电时等离子体鞘层及粒子碰撞对微波共振探针密度测量的影响变大的问题,对微波共振探针模型进行了改进,推导了鞘层修正因子和碰撞修正因子,探讨了微波共振探针尺寸对测量等离子体密度的影响。结果表明,针丝半径选择0.2mm,并且选用较大宽度的探针有利于减小测量误差。     

等离子体鞘层及粒子碰撞对微波共振探针诊断的影响

针对气压大于133Pa的气体放电时等离子体鞘层及粒子碰撞对微波共振探针密度测量的影响变大的问题,对微波共振探针模型进行了改进,推导了鞘层修正因子和碰撞修正因子,探讨了微波共振探针尺寸对测量等离子体密度的影响。结果表明,针丝半径选择0.2mm,并且选用较大宽度的探针有利于减小测量误差。