Spatially hybrid computations for streamer discharges : II. Fully 3D simulations

We recently have presented first physical predictions of a spatially hybrid model that follows the evolution of a negative streamer discharge in full three spatial dimensions; our spatially hybrid model couples a particle model in the high field region ahead of the streamer with a fluid model in the streamer interior where electron densities are high and fields are low. Therefore the model is computationally efficient, while it also follows the dynamics of single electrons including their possible run-away. Here we describe the technical details of our computations, and present the next step in a systematic development of the simulation code. First, new sets of transport coefficients and reaction rates are obtained from particle swarm simulations in air, nitrogen, oxygen and argon. These coefficients are implemented in an extended fluid model to make the fluid approximation as consistent as possible with the particle model, and to avoid discontinuities at the interface between fluid and particle regions. Then two splitting methods are introduced and compared for the location and motion of the fluid-particle-interface in three spatial dimensions. Finally, we present first results of the 3D spatially hybrid model for a negative streamer in air. Future applications of the hybrid model lie in effects of electron density fluctuations on inception, propagation and branching of streamers, and in accurate calculations of electron energies at and of electron run-away from the streamer head. The last is relevant for hard radiation from streamer-leader systems and possibly for Terrestrial Gamma-Ray Flashes.     

超热电子在稠密等离子体中输运的混合粒子模拟方法

相对论激光等离子体相互作用以及所产生的带电粒子束在高密度等离子体中的输运行为非常重要.该物理问题的数值模拟研究仍面临技术挑战.本文介绍一种粒子/流体混合模拟方法.该方法中超热电子采用动力学方法描述,背景冷的稠密等离子体采用简化的流体方程描述,适合于超热电子密度远小于背景电子密度,超热电子能量远大于背景电子温度.我们的三维并行混合模拟程序HEETS的模拟结果表明：背景材料的电离和电阻率模型至关重要,将严重影响高能电子输运过程的模拟.     

The effects of fluid motion on oscillatory and chaotic fronts

We study oscillatory and chaotic reaction fronts described by the Kuramoto-Sivashinsky equation coupled to different types of fluid motion. We first apply a Poiseuille flow on the fronts inside a two-dimensional slab. We show regions of period doubling transition to chaos for different values of the average speed of Poiseuille flow. We also analyze the effects of a convective flow due to a Rayleigh-Taylor instability. Here the front is a thin interface separating two fluids of different densities inside a two-dimensional vertical slab. Convection is caused by buoyancy forces across the front as the lighter fluid is under a heavier fluid. We first obtain oscillatory and chaotic solutions arising from instabilities intrinsic to the front. Then, we determine the changes on the solutions due to fluid motion.     

Effects of secondary electron emission on plasma characteristics in dual-frequency atmospheric pressure helium discharge by fluid modeling

A one-dimensional(1D) fluid simulation of dual frequency discharge in helium gas at atmospheric pressure is carried out to investigate the role of the secondary electron emission on the surfaces of the electrodes. In the simulation, electrons,ions of He~+ and He_2~+, metastable atoms of He*and metastable molecules of He*_2 are included. It is found that the secondary electron emission coefficient significantly influences plasma density and electric field as well as electron heating mechanisms and ionization rate. The particle densities increase with increasing SEE coefficient from 0 to 0.3 as well as the sheath's electric field and electron source. Moreover, the SEE coefficient also influences the electron heating mechanism and electron power dissipation in the plasma and both of them increase with increasing SEE coefficient within the range from 0 to 0.3 as a result of increasing of electron density.     

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.     

二次发射微波电子枪的模拟计算及其特性分析

 采用URMEL-T程序进行了二次发射微波电子枪的腔内电磁计算和特性分析。同时利用URMEL-T得出的腔内轴向电场及自编程序,模拟电子在该高频场作用下的运动。计算表明二次发射微波电子枪确实具有相位选择性,进而探讨了腔形尺寸、射频电场强度对相位选择性和产生二次倍增的有关条件的影响,以及输出电子的能量稳定性。模拟结果表明,这类电子枪（MPG）可得到高电流密度（5303A/cm²）及短脉冲（3.15~10ps）的电子束。     

Mechanism of branching in negative ionization fronts

When a strong electric field is applied to nonconducting matter, narrow channels of plasma called streamers may form. Branchlike patterns of streamers have been observed in anode directed discharges. We explain a mechanism for branching as the result of a balance between the destabilizing effect of impact ionization and the stabilizing effect of electron diffusion on ionization fronts. The dispersion relation for transversal perturbation of a planar negative front is obtained analytically when the ratio D between the electron diffusion coefficient and the intensity of the externally imposed electric field is small. We estimate the spacing lambda between streamers and deduce a scaling law lambda approximately D(1/3).     

Spin filtering in a hybrid ferromagnetic-semiconductor microstructure

We fabricated a hybrid structure in which cobalt and permalloy micromagnets produce a local in-plane spin-dependent potential barrier for high-mobility electrons at the GaAs/AlGaAs interface. Spin effects are observed in ballistic transport in the range of tens of mT of the external field and are attributed to switching between Zeeman and Stern-Gerlach modes--the former dominating at low electron densities.     

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.     

A Monte Carlo scheme for tracking filling fronts

A Monte Carlo (MC) scheme for tracking filling fronts is developed. The test problem of tracking fluid injected into a thin mold is considered. The MC scheme iteratively redistributes the volume entering the mold among the cells of a spatial discretization. The transition probabilities used in the MC scheme, which determine how the fluid volume is redistributed, are derived from a discrete representation of the governing steady-state pressure equation. Analysis shows that the MC steps are equivalent to an iterative solution of the discrete equations. Further, it is shown that the MC scheme can be reconfigured into the form of a standard Lattice Boltzmann Method (LBM). Results show that the proposed MC scheme is accurate, does not require an explicit field calculation of the fluid pressure field, and, when compared with existing numerical filling algorithms, exhibits computation times over 1000 times faster.     

Scaling,propagation, and kinetic roughening of flame fronts in random media

We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density below which the front associated with the temperature field stops propagating. The critical exponents associated with this transition are shown to be consistent with meanfield theory of percolation. Second, we study the kinetic roughening associated with a moving planar flame front above the critical density. By numerically calculating the time-dependent width and equal-time height correlation function of the front, we demonstrate that the roughening process belongs to the universality class of the Kardar-Parisi-Zhang interface equation. Finally, we show how this interface equation can be analytically derived from our model in the limit of almost uniform background density.     

Excitation of an upper hybrid wave by two intense laser beams and particle acceleration

This Letter presents an investigation of the excitation of an upper hybrid wave (UHW) by cross focusing of two intense laser beams in a collisionless hot magnetoplasma, when relativistic and ponderomotive nonlinearities are operative. The electric vectors of the two beams are polarized along uniform static magnetic field and the beams propagate perpendicular to the static magnetic field. Analytical expressions for the beam width of the laser beams, electric vector and power of the excited UHW and energy gain have been obtained. The UHW generation at the difference frequency and particle acceleration has also been studied. The nonlinear coupling between intense laser beams and UHW is so strong that UHW gets excited and a large fraction of the laser beam energy gets transferred to UHW and this UHW accelerates electrons. It has been shown that the presence of a magnetic field affects significantly the power of the UHW and energy gain by the electron in the presence of the UHW.     

One-Dimensional Fluid Model for Dust Particles in Dual-Frequency Capacitively Coupled Silane Discharges

A self-consistent fluid model, which incorporates density and flux balances of electrons, ions, neutrals and nanoparticles, electron energy balance, and Poisson＇s equation, is employed to investigate the capacitively coupled silane discharge modulated by dual-frequency electric sources. In this discharge process, nanoparticles are formed by a successive chemical reactions of anion with silane. The density distributions of the precursors in the dust particle formation are put forward, and the charging, transport and growth of nanoparticles are simulated. In this work, we focus our main attention on the influences of the high-frequency and low-frequency voltage on nanoparticle densities, nanoparticle charge distributions in both the bulk plasma and sheath region.     

Control of the Interface Between Electron‐Hole and Electron‐Ion Plasmas: Hybrid Semiconductor‐Gas Phase Devices as a Gateway for Plasma Science

Coupling electron‐hole (e^–‐ h⁺) and electron‐ion plasmas across a narrow potential barrier with a strong electric field provides an interface between the two plasma genres and a pathway to electronic and photonic device functionality. The magnitude of the electric field present in the sheath of a low temperature, nonequilibrium microplasma is sufficient to influence the band structure of a semiconductor region in immediate proximity to the solid‐gas phase interface. Optoelectronic devices demonstrated by leveraging this interaction are described here. A hybrid microplasma/semiconductor photodetector, having a Si cathode in the form of an inverted square pyramid encompassing a neon microplasma, exhibits a photosensitivity in the ～420–1100 nm region as high as 3.5 A/W. Direct tunneling of electrons into the collector and the Auger neutralization of ions arriving at the Si surface appear to be facilitated by an n ‐type inversion layer at the cathode surface resulting from bandbending by the microplasma sheath electric field. Recently, an npn plasma bipolar junction transistor (PBJT), in which a low temperature plasma serves as the collector in an otherwise Si device, has also been demonstrated. Having a measured small signal current gain h_fe as large as 10, this phototransistor is capable of modulat‐ing and extinguishing the collector plasma with emitter‐base bias voltages <1 V. Electrons injected into the base when the emitter‐base junction is forward‐biased serve primarily to replace conduction band electrons lost to the collector plasma by secondary emission and ion‐enhanced field emission in which ions arriving at the base‐collector junction deform the electrostatic potential near the base surface, narrowing the potential barrier and thereby facilitating the tunneling of electrons into the collector. Of greatest significance, therefore, are the implications of active, plasma/solid state interfaces as a new frontier for plasma science. Specifically, the PBJT provides the first opportunity to control the electronic properties of a material at the boundary of, and interacting with, a plasma. By specifying the relative number densities of free (conduction band) and bound (valence band) electrons at the base‐collector interface, the PBJT's emitter‐base junction is able to dictate the rates of secondary electron emission (including Auger neutralization) at the semiconductor‐plasma interface, thereby offering the ability to vary at will the effective secondary electron emission coefficient for the base surface (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Floating Potential of an Electron Emitting Collector that Terminates a Bounded Plasma System

Potential formation in one‐dimensional bounded plasma system terminated by a floating, electron emitting collector is studied by a fully kinetic one‐dimensional model and particle‐in‐cell (PIC) computer simulation. As the electron emission from the collector is gradually increased, the floating potential of the collector and the electric field at the collector both increase quite strongly. When the critical emission is reached, the electric field becomes zero. If the emission is increased further, the electric field changes sign and becomes positive and a virtual cathode is formed in front of the collector. The floating potential of the collector also increases, but much more slowly, than below the critical emission level. If the ratio between the temperatures of the emitted and of the bulk electrons is high enough, the floating potential of the collector may even exceed the zero potential of the source, but in this case the simulation becomes unstable, when the positive ions start to flow back from the collector towards the source. Simulation results obtained below the critical emission level are in very good agreement with the model, provided that the particle densities obtained from the simulation are normalized correctly. In this case the potential and electric field profiles found from the PIC simulation match almost perfectly to the profiles obtained from the numerical solution of the Poisson equation (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

长脉冲二极管绝缘子真空表面闪络

 在长脉冲强流无箔二极管实验过程中观察到绝缘子沿面闪络现象。分析实验现象认为是屏蔽环与绝缘子距离过近造成了屏蔽环边缘高场强,从而产生场致发射电子。电子在强电磁场作用下撞击绝缘子表面引起了二次电子雪崩从而导致真空表面闪络。运用静电场模拟和粒子束模拟,改进屏蔽环结构。改进后的二极管工作电压500 kV,电流12 kA,在1 T引导磁场下稳定运行,没有再发生真空表面闪络。     

Particle in cell simulation of relativistic Buneman instability in a current-carrying plasma

Abstract

Non-linear evolution of the relativistic Buneman instability in a current-carrying plasma is investigated by a particle in cell simulation. These simulations show that as the time progresses, some electrons are trapped in phase space holes and thus counter-streaming and plateau can be formed. Moreover, the electron and ion density profiles indicate a periodic pattern of the density steepening. This density distribution is similar to the generation of the grating-like patterns which strongly depends on the initial electron velocity and saturation time. It is also shown that the electric field profile has the sawtooth form; charged particles can be accelerated by this field. Finally, it is found that increasing the electron velocity increases the saturation time and consequently the growth rate decreases which is in good agreement with the result obtained by the fluid model.     

A numerical model of streamlines in coplanar electrodes induced by non-uniform electric field

A new model for investigating the non-uniform electric field and potential distribution of fluid flow and streamlines induced by non-uniform electric field with the induced charge in the electrical double layer on the electrode surfaces is presented. Accurate computation of the non-uniform electric field is a pre-requisite for observing fluid flow and streamlines. The electric field distribution is obtained from Laplace's and Neumann's equations. Finite Element Methods is adopted for this work. The simulation results has been compared with available experimental observations of the fluid flow profile obtained by superimposing images of particle movement in a plane normal to the electrode surface. A good agreement is found between the numerical and experimental streamlines.