Wall Recombination in Glow Discharges

We derived a model describing the radial distribution of the ion and electron densities and the radial electric field strength in the positive column of a glow discharge. The set of equations related to the plasma consists of the equations for particle and momentum conservation for the ions and electrons and the Poisson-equation. In a novel approach, the necessary boundary conditions in our model result from a system of balance equations for the charge carriers on the insulated wall surrounding the positive column.     

Radial Distributions of Dusty Plasma Parameters in a DC Glow Discharge

A non‐stationary non‐local kinetic model for radial distributions of dusty plasma parameters based on the solution of Boltzmann equation for electron energy distribution function is presented. Electrons and ions production in ionizing collisions and their recombination on dust particle surface were taken into account. The drift‐diffusion approximation for ions was used. To obtain the self‐consistent radial distribution of electric potential the Poisson equation was used. It is shown that at high dust particle density the recombination of electrons and ions can exceed their production in ionization collisions in the region of dusty cloud. In this case the non‐monotonous radial distribution of the electric field is formed, the radial electric field becomes reversed and the radial electron and ion fluxes change their direction toward the center of the tube (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Calculations of the Concentrations,of the Radial Distributions,and of the Radial Particle Currents of Excited and of Doubly Charged Ions in Low Pressure Discharges

A system of differential equations describing the radial profiles of the number densities and of the radial drift velocities of the ions and of the electrons in positive columns at low pressure containing several species of ions is derived. Excited ions and doubly charged ions, generated in two-step processes by electron impacts, the inertia of the ions and space charge effects are taken into account. For the excited ions de-excitation processes by electron collisions and by spontaneous emission are regarded. A set of nonlinear equations to determine the population densities and the initial values of the differential equations and corresponding boundary conditions are put up. Numerical solutions are given for discharges in argon under free-fall conditions similiar to argon ion lasers. One notices that without stepwise processes via excited ion levels the concentration of double charged ions remains small. In some cases the radial drift of the ions considerably reduces the population of the metastable ion levels. The radial density profiles of the double charged ions and of long-living excited ions considerably deviate from the squared radial profile of the electron density. In addition, for low degrees of ionization the theory of the free-fall column given by Tonks and Langmuir is extended to plasmas containing two species of ions.     

Theoretical Description of the Radial Distributions of the Ions and of the Electrons in the Subnormal Positive Column

A relatively simple set of differential equations describing the radial profiles of the number densities and of the radial drift velocities of the ions and the electrons and of the radial electric field intensity in the subnormal positive column is derived. The inertia of the ions is taken into consideration, but the ion temperature is supposed to be zero. Corresponding boundary conditions are used. For discharges in argon under diffusion and under free-fall conditions numerical solutions are given.     

The Theory of the Low Pressure Discharge in the Strong Ionization Regime

A system of integro-differential equations describing the velocity distribution functions of the neutral atoms and of the ions and the radial profiles of the electric potential and the particle densities in the positive column at low pressures and high degrees of ionization is derived. This system is solved for a simplified, but self-consistent, plane model. Both the initial velocity of the ions and the neutral gas depletion caused by the ionization processes are taken into account. For a cylindrical model a solution is obtained for the region near the axis. With rising neutral gas temperature the radial ion flux density is slightly increasing. The pressure tensor, the heat flux tensor, and several components of the corresponding tensor of the fourth order for the ion gas are calculated. It is shown that on the axis the radial and the azimuthal ion temperatures are smaller than the neutral gas temperature because the ions generated out of neutral atoms are retarded during the flight to the axis.     

Numerical Simulation of a DC-Glow-Discharge in an Electronegative Gas

A one-dimensional continuum model is presented for a dc-glow-discharge in an electronegative gas between parallel plates. It is based on the local balance equations for particle densities and fluxes of electrons, positive and negative ions, the local electron energy balance and the Poisson equation for the self-consistent electric field. These equations are supplemented by suitably chosen boundary conditions and are solved by the finite difference procedure HEMODES (HEnyey Method Ordinary Differential Equation Solver) which, in particular, can successfully handle the singular point occuring if the inertia term in the ion momentum balance equation is taken into account. Since not all data needed within this treatment for the simulation of realistic electronegative gases were available, a fictitious argon-like gas has been considered which nevertheless can demonstrate the characteristic features of such a discharge. In particular, the influence of variations of the attachment and the ion-ion recombination coefficients on the physical variables has been studied.     

A self-consistent model for the production and growth of nanoparticles in low-temperature plasmas

A theoretical global model is presented for describing the kinetics of generation and growth of clusters and nanoparticles in low-pressure plasmas, where important processes for clusters and grains are collisions with monomers, electrons, and ions and particle coagulation and loss because of diffusion and gas flow drag. Simple equations are given for calculations of monomer density, particle-size distribution function, critical cluster size, the rate of particle production and particle density and mean size, and plasma characteristics (the densities and average energies of “cold” and “hot” electrons and the density of positively charged ions). The model is self-consistent; that is, the above-mentioned properties of clusters, nanoparticles, electrons, and ions are calculated jointly from coupled equations as functions of a small number of radio frequency (RF) discharge parameters (discharge geometry; absorbed electric power; voltage across the RF sheath; gas pressure; composition; and flow rate). Comparisons are made with the experimental data on SiH₄-Ar mixtures. Published in Russian in Khimicheskaya Fizika, 2008, Vol. 27, No. 4, pp. 79–93. The article was translated by the authors.     

Modelling of the Positive Column in an Argon-Hexamethyl-disiloxane dc Glow Discharge

A model is presented of the positive column of a dc glow discharge in argon with small admixtures of hexamethyldisiloxane (HMDS). The axial electric field, the ion production rates for direct-, stepwise-, pair-, and Penning ionization, the densities of metastable Ar atoms and of electrons, and the wall current of HMDS ions are calculated in dependence on HMDS admixture and discharge current density. For the calculations particle balance equations were used for a diffusion determined plasma in a mixture of two gaseous components. The reaction rates for the electron collision processes were determined applying the electron distribution function calculated for pure argon. Taking into account PENNING ionization of HMDS molecules by metastable argon atoms the decrease of electric field for increasing HMDS admixtures is according to the experimen-tally measured values. Also ion wall currents and electron densities are compared with experimen-tal values for thin film formation rate and results of probe measurements.     

Analysis of dusty plasma in the positive column of glow discharges

The radial distributions of ions,electrons and dust particles in the positive colum of glow discharges are investigated in a tripled-pole diffusion model.The dust particles are mainly trapped in the region around the column axis where the electrostatic potential is the highest.The presence of the dust particles results in the ion density increasing and the electron density decreasiung in the dust-trapped region.The dust-trapped region is wider for a higher dust temperature or a smaller particulate redius.The ions and electrons in the dust-free region away from the column axis are in ambipolar diffusion.     

Scaling laws for the spatial distributions of the plasma parameters in the positive column of a dc oxygen discharge

Comprehensive self-consistent simulations of the positive column plasma of a dc oxygen discharge are performed with the help of commercial CFDRC software (), which enables one to carry out computations in an arbitrary 3D geometry using fluid equations for heavy components and a kinetic equation for electrons. The main scaling laws for the spatial distributions of charged particles are determined. These scaling laws are found to be quite different in the parameter ranges that are dominated by different physical processes. At low pressures, both the electrons and negative ions in the inner discharge region obey a Boltzmann distribution; as a result, a flat profile of the electron density and a parabolic profile of the ion density are established there. In the ion balance, transport processes prevail, so that ion heating in an electric field dramatically affects the spatial distribution of the charged particles. At elevated pressures, the volume processes prevail in the balance of negative ions and the profiles of the charged particle densities in the inner region turn out to be similar to each other.     

激光等离子体二维相对论电磁粒子模拟

研制了激光等离子体二维相对论电磁粒子模拟程序(2DCIC)。追踪几万甚至百万个模拟粒子在外加激光场和自洽场中运动,自洽地计算电荷和电流密度,求解完全的Maxwel方程,电子的相对论运动方程和离子的牛顿运动方程,辅以灵活的诊断研究波-波,波-粒子相互作用的发生、发展和饱和的细节以及时间演化规律。激光可以正入射,也可以斜入射;等离子体可以是均匀密度,也可以具有密度梯度;为了节约机时,还发展了并行运算。物理模型参数可调,既适用于研究激光聚变等离子体相互作用,也适用于超短脉冲超强激光等离子体相互作用和其它等离子体问题。经过多次试算检验,对等离子体平衡态进行了计算研究,对于超短脉冲超强激光的传播也进行了初步模拟计算。     

Simulation of laser–plasma interactions and fast-electron transport in inhomogeneous plasma

A new framework is introduced for kinetic simulation of laser–plasma interactions in an inhomogeneous plasma motivated by the goal of performing integrated kinetic simulations of fast-ignition laser fusion. The algorithm addresses the propagation and absorption of an intense electromagnetic wave in an ionized plasma leading to the generation and transport of an energetic electron component. The energetic electrons propagate farther into the plasma to much higher densities where Coulomb collisions become important. The high-density plasma supports an energetic electron current, return currents, self-consistent electric fields associated with maintaining quasi-neutrality, and self-consistent magnetic fields due to the currents. Collisions of the electrons and ions are calculated accurately to track the energetic electrons and model their interactions with the background plasma. Up to a density well above critical density, where the laser electromagnetic field is evanescent, Maxwell’s equations are solved with a conventional particle-based, finite-difference scheme. In the higher-density plasma, Maxwell’s equations are solved using an Ohm’s law neglecting the inertia of the background electrons with the option of omitting the displacement current in Ampere’s law. Particle equations of motion with binary collisions are solved for all electrons and ions throughout the system using weighted particles to resolve the density gradient efficiently. The algorithm is analyzed and demonstrated in simulation examples. The simulation scheme introduced here achieves significantly improved efficiencies.     

电磁辐照金属铝膜材料释气效应研究

为研究空间环境中通用航天器表面覆盖的热控层电磁辐照效应,采用粒子模拟(PIC)和蒙特卡罗(MC)模拟相结合方法,建立了真空环境下电磁辐照航天器热控材料模型,模拟了场致电子发射、次级电子倍增、释气雪崩电离的全过程,并讨论了释气密度对热防护材料表面产生释气电离现象的影响。通过对比不同释气密度下该过程产生的电子和离子情况,获得热防护材料表面释气产生雪崩电离的阈值。模拟结果表明,当铝膜表面气体密度较小时,由于材料表面释气碰撞电离概率偏低而不会发生雪崩电离;只有当释气密度超过阈值时,材料表面释气碰撞电离过程加强,材料表面发生雪崩电离生成等离子体,等离子体吸收电磁波能量,其离子和电子总能量提升,可能对金属铝膜材料造成损伤。     

Zur Radialstruktur der diffusionsbestimmten positiven Säule der Sauerstoff-Entladung bei niederen Gasdrucken

The radial distribution of the electrons, negative and positive ions in the cylindrical positive column of the direct current discharge in 0₂ has been calculated. The negative ions are formed by dissociative attachment (0₂ + e →^? + 0), the destruction of negative ions is effected by the reverse process (0^? + 0 0₂ + e). The pressure is assumed to be low enough that the radial variation of 0-concentration can be neglected. By use of the condition of the quasineutrality and the ambipolarity for the radial current from the balance equations of the electrons and the negative ions two differential equations of second order are derived, which has been solved numerically for different values of the ratio z_j/z_a and β[0]. Numerical results show that the radial distributions of the charge carriers are not-proportional. If z_j ≈? z_a the radial distribution of the electron density is enlarged, compared to a Bessel distribution. The radial distribution of the negative ions is also enlarged in the centre of the column, but near the wall of the tube a lack in the density exists. The effective diffusion coefficient of the negative ions is negative, i.e., they are moving from the wall of the tube to the centre of the discharge. The enlargement of the radial distributions of the charge carriers, which results in an improvement of the economy of the balance of electrons, increases if z_j/z_a and β/[0] are decreased.     

Theoretical analysis for transmission of Gaussian and sine time irradiance of electromagnetic beam in collisional dusty plasmas

A theoretical model of propagation of Gaussian and Sine time irradiance of an electromagnetic beam in collisional dusty plasma has been done in the present analysis. It contains equilibrium of dust charge, particle density, and energy of plasma ingredients having charge neutrality. Ionization of neutral particles, recombination of free electrons with ions, adsorption and emission of electrons from dust grain surface, and binary collisions between plasma components are also considered in this treatment. Time varying behaviour of modified electron temperature and collision frequency has been illustrated numerically as a function of dust densities. Also, the comparative analyses of variation of beam waist parameter with the dimensionless length of transmission for both the Gaussian and Sine time irradiance are involved in this model as a function of distinguishable time width, collision frequencies, and dust densities under the condition that the size of dust nebulous is greater than the electrons mean free path for the adsorption on the dust grain surface. The observed results are significant for the applications in industry and astrophysics.     

Numerical investigation of the plasma processes for propellant heating in electrothermal plasma thruster for nanosatellites

Numerical investigation of the plasma processes in a cylindrical chamber with small dimensions of a novel microwave electrothermal plasma thruster for nanosatellites has been conducted. The absorbed microwave power from the electrons in the plasma column of the surface wave discharge is included in the computational model as a heat source with Gaussian distribution. The computational model takes into account the elastic and inelastic collisions of the electrons with the atoms in the ground state and two excited states (−s, −p) and the processes of recombination and deactivation of the plasma species in the volume and on the walls of the chamber. The computational model includes the flow of neutral gas and the processes in the plasma for effective heating of neutral particles by collisions not only with electrons but also with ions. Selected combinations of input power and propellant mass flow rates are used as initial parameters for the numerical investigation. The results show that at higher mass flow rates the heating of the neutral gas is more effective and at power levels of 4 W and propellant mass flow rate of 3 mg/s the electrothermal plasma thruster demonstrates effective performance and thrust levels in the order of 1 mN.     

Screening of a charged dust particle within a nonlocal charging theory

We study the influence of the nonlocality of the electron energy distribution function on the dust particle charge screening in a two-component plasma of various inert gases and nitrogen at atmospheric pressure. For our analytical and numerical calculations, we have chosen the point sink model in the diffusion-drift approximation, which, in addition to the bulk production and loss of electrons and ions, also includes the heterogeneous processes of their absorption by a dust particle. We have established that the dust particle potential distribution in the problem under consideration is a superposition of three Debye exponentials with three different screening constants. The first constant practically coincides with the inverse Debye length. The second constant is determined by the inverse length travelled by the electrons and ions in the ambipolar diffusion process in the characteristic recombination time. The third constant coincides with the inverse characteristic distance of electron energy transfer through heat conduction in the characteristic time of electron energy establishment in the processes of heating by a beam of fast electrons and energy losses in elastic and inelastic collisions. We compare our numerical calculations of the screening constants with the analytical estimates obtained in the ambipolar diffusion approximation.