Free‐Electron Gas Spectrum Uniqueness in the Mixture of Noble Gases

Gas mixtures can reach the Maxwell's specter shape in case of low‐ionized mono‐atomic mixtures in the weak electric field. The parameters pertaining to the Maxwell spectrum of free electrons' gas straightforwardly settle on the insulating characteristics of the examined gas mixture at the fundamental level. In this paper, a condition for breakdown has been accomplished taking as a starting point the ionization coefficients derived accordingly, as well as the conditions for breakdown in keeping with the Townsend mechanism. The dc breakdown voltage value of noble gases mixture has been measured in the experimental part of the paper. The hypothesis that the free‐electron gas spectrum is unique in the noble gas mixture and is of Maxwell's type has been verified. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Singular Energy Distributions in Driven and Undriven Granular Media

We study the kinetic theory of driven and undriven granular gases, taking into account both translational and rotational degrees of freedom. We obtain the high-energy tail of the stationary bivariate energy distribution, depending on the total energy E and the ratio of rotational energy E _w to total energy. Extremely energetic particles have a unique and well-defined distribution f(x) which has several remarkable features: x is not uniformly distributed as in molecular gases; f(x) is not smooth but has multiple singularities. The latter behavior is sensitive to material properties such as the collision parameters, the moment of inertia and the collision rate. Interestingly, there are preferred ratios of rotational-to-total energy. In general, f(x) is strongly correlated with energy and the deviations from a uniform distribution grow with energy. We also solve for the energy distribution of freely cooling Maxwell Molecules and find qualitatively similar behavior.     

Field Free Relaxation of the Electron Component in the Temporally Decaying Molecular Gas Plasmas Hydrogen and Nitrogen

This paper deals with the temporal relaxation of the electron component of weakly ionized, anisothermal and collision dominated plasma in the molecular gases hydrogen and nitrogen after jump-like switching off of the electric field starting from stationary states. The investigation is based upon a solution of the non-stationary Boltzmann equation using a finite difference approach of the resulting partial differential equation. Besides the temporal development of the energy distribution and of some macroscopic quantities of the electrons especially the characteristic relaxation times and their physical nature are discussed and compared with former results on the relaxation in an inert gas plasma.     

弱电离大气等离子体电子能量分布函数的理论研究

使用球谐展开的方法求解玻尔兹曼方程,得到了弱电离大气等离子体(79％氮气和21％的氧气)的电子能量分布函数(EEDF).发现当约化电场较小时(E/N＜100 Td),EEDF在2-3 eV急剧下降,在此情况下,高能尾部比麦氏分布要小;当约化电场增加,E/N＞ 400 Td,分布函数趋近于麦氏分布;当约化电场进一步增加,E/N＞ 2000 Td,EEDF的高能尾部(超过200 eV)相对于麦氏分布增加,在高频场作用下,EEDF更倾向于麦氏分布.当ω》vm时,有效电子温度只依赖于E/ω,而与碰撞频率无关;当ω《vm时,有效电子温度只依赖于E/N,与微波频率无关.与一些单原子分子等离子体中电子-电子碰撞在电离度大于10-6时就会影响EEDF不同,空气等离子体中,只有当电离度大于0.1％时,电子-电子碰撞才会对EEDF有明显影响.     

A two-electron group model theory for radio-frequency ionization ofnoble gases with turbulent flow

Equations are derived for predicting the current-voltage characteristic curves of axial RF discharges in noble gases, with turbulent flow. The electrons are considered to be made up of two Maxwellian groups: bulk and tail electrons. The bulk electrons are described by a temperature T_b, and have kinetic energies (1/2 mv²=eV) from 0 to eV _l (eV_l=the threshold energy of the first dominant inelastic collision process). The electrons of the depressed tail of the distribution function are described by another temperature, T_t<T_b, and have (eV>eV_l). The terms in these equations correspond to the prevailing processes occurring inside the noble gas discharge. The rate coefficients given are derived, based on the two-electron group model. The effect of the high velocity flow is accounted for by the terms giving the divergence of the flux of particles in the redirection of flow in each of the continuity equations for the primary species and by adding a diffusion coefficient due to turbulence to the static discharge diffusion coefficients of the ions and metastables     

Zur allgemeinen kinetischen Theorie von partiell ionisierten Plasmen in zeitabhängigen Magnetfeldern und elektromagnetischen Zusatzfeldern

A general method is given for the calculation of the electron distribution function of a weakly ionized plasma in external time-dependent magnetic fields and additional electromagnetic fields. The Boltzmann equation of kinetic theory is solved taking into account elastic collisions between electrons and neutrals. The isotropic part f⁰ of the distribution function follows from a general linear integro-differential equation and contains all known standard distributions (Druyvesteyn, Davydov, Margenau and others) as special cases. The direction-dependent part f¹ gives the transport tensors.     

On the three-term approximation of the solution of the Boltzmann equation for weakly ionized gases

In this paper we discuss an improvement of the current technique of solution of the Boltzmann equation for weakly ionized gases in an electric field. The method is based on the usual expansion of the velocity distribution in spherical harmonics, but three terms of the expansion are retained instead of two. In the light of the results obtained for a particular interaction law between charged and neutral particles, a procedure is established which is consistent in the orders of approximation. This procedure requires an improvement of the degree of accuracy commonly used for the terms deriving from the Boltzmann collision operator. For this reason, the general expression of the isotropic collision operator correct to second order in the ion-neutral mass ratio is calculated. Finally, a new steady-state solution of the Boltzmann equation is obtained which is valid both for electrons and light ions in heavy gases.     

弱电离大气等离子体电子碰撞能量损失的理论研究

在前期计算电子能量分布函数的基础上, 求出弱电离大气等离子体中各碰撞反应过程的电子能量损失. 由于在弹性碰撞中电子-重粒子能量交换很少, 同时氮气、氧气分子又有很多能量阈值较低的转动、振动能级存在, 因此在大气等离子体中弹性碰撞电子能量损失所占份额很小(直流电场下小于6%). 研究发现, 弱电离大气等离子体中在不同能量区间占主导的能量损失过程不同. 随着有效电子温度(或约化场强)增加, 占主导的电子能量损失过程依次为转动激发、振动激发、电子态激发、碰撞电离、加速电离产生的二次电子. 在约化场强E/N=1350 Td (或有效电子温度为14 eV)附近, 平均电离一个电子所需的能量最小, 约为57 eV. 因此可以根据不同的需求调节电场强度, 从而达到较高的能量利用率. 关键词： 弱电离大气等离子体 碰撞反应过程 电子能量损失     

Group equations for moments of the relativistic electron distribution function in a cold gas of neutral atomic particles in an external electric field

A set of multigroup equations is derived for the first three moments of the distribution function for high-energy electrons in a gas of immobile atomic particles. The equations are intended for numerical simulation of processes in a dense weakly ionized plasma with the participation of high-energy electrons, including runaway electrons.     

Fokker-Planck equation and relevant Chapman-Cowling-Davydov expression modified for coulomb scattering

Summary TheP ₁ approximation to the Boltzmann equation in the case of slightly ionized gases leads to the usual Fokker-Planck equation whose solution in steady-state condition is the Chapman-Cowling-Davydov (CCD) expression. We have extended the same procedure to include electron-ion interactions when the corresponding collision frequency is of the same order of, or larger than, the electron-neutral molecule collision frequency. We have considered a case where, after an initial ionization of a column of gas, the majority of the electrons have diffused to, and have been captured by, the walls of the chamber so that we may neglect the electron-electron interactions. We have found a modified CCD expression. However, numerical calculations show that the differences between the modified expressions and the standard ones in which the electron-ion collision frequency for momentum transfer is added to the electron-neutral collision frequency are beyond the present experimental accuracy.     

Runaway of electrons in dense gases and mechanism of generation of high-power subnanosecond beams

New understanding of mechanism of the runaway electrons beam generation in gases is presented. It is shown that the Townsend mechanism of the avalanche electron multiplication is valid even for the strong electric fields when the electron ionization friction on gas may be neglected. A non-local criterion for a runaway electron generation is proposed. This criterion results in the universal two-valued dependence of critical voltage U _cr on pd for a certain gas (p is a pressure, d is an interelectrode distance). This dependence subdivides a plane (U _cr , pd) onto the area of the efficient electron multiplication and the area where the electrons leave the gas gap without multiplication. On the basis of this dependence analogs of Paschen’s curves are constructed, which contain an additional new upper branch. This brunch demarcates the area of discharge and the area of e-beam. The mechanism of the formation of the recently created atomospheric pressure subnanosecond e-beams is discussed. It is shown that the beam of the runaway electrons is formed at an instant when the plasma of the discharge gap approaches to the runaway electrons is formed at an instant when the plasma of the discharge gap approaches to the anode. In this case a basic pulse of the electron beam is formed according to the non-local criterion of the runaway electrons generation. The role of the discharge gap preionization by the fast electrons, emitted from the plasma non-uniformities on the cathode, as well as a propagation of an electron multiplication wave from cathode to anode in a dense gas are considered.     

Die Methode der Normallösungen für die Vlasov-BGK-Gleichung

The linearized Vlasov equation with collision damping is solved by the method of normal modes of Van Kampen and Case. The system considered is an infinitely extended nonrelativistic nondegenerate electron gas with neutralizing ion background and neutral particles. There is no magnetic field. Collision damping is taken into account by complete Bhatnagar-Gross-Krook collision integrals for electron-electron collisions and electronion collisions; in the case of a partially ionized gas elastic collisions between electrons and neutrals can be included likewise. The Vlasov-BGK operator is transformed into an integral operator yielding complex singular normal modes even if the equilibrium distribution is a Maxwellian. The adjoint integral equation belongs to a more complicated type than that of a collision-free system. Its solutions must be orthogonalized. The set of all normal modes is complete rendering the exact solution of the initial value problem possible. The completeness is shown by transformations and regularization of the singular integral equation of the initial value problem, the techniques of Case not being applicable because of the complicated type of this equation.     

Excitation of helium atoms in collisions with plasma electrons in an electric field

The rate constants are evaluated for excitation of helium atoms in metastable states by electron impact if ionized helium is located in an external electric field and is supported by it, such that a typical electron energy is small compared to the atomic excitation energy. Under these conditions, atomic excitation is determined both by the electron traveling in the space of electron energies toward the excitation threshold and by the subsequent atomic excitation, which is a self-consistent process because it leads to a sharp decrease in the energy distribution function of electrons, which in turn determines the excitation rate. The excitation rate constant is calculated for the regimes of low and high electron densities, and in the last case, it is small compared to the equilibrium rate constant where the Maxwell distribution function is realized including its tail. Quenching of metastable atomic states by electron impact results in excitation of higher excited states, rather than transition to the ground electron state for the electric field strengths under consideration. Therefore, at restricted electron number densities, the rate of emission of resonant photons of the wavelength 58 nm, which results from the transition from the 2¹ P state of the helium atom to the ground state, is close to the excitation rate of metastable atomic states. The efficiency of atomic excitation in ionized helium, i.e., the part of energy of an electric field injected in ionized helium that is spent on atomic excitation, is evaluated. The results exhibit the importance of electron kinetics for an ionized gas located in an electric field.     

Stationary states and energy cascades in inelastic gases

We find a general class of nontrivial stationary states in inelastic gases where, due to dissipation, energy is transferred from large velocity scales to small velocity scales. These steady states exist for arbitrary collision rules and arbitrary dimension. Their signature is a stationary velocity distribution f(v) with an algebraic high-energy tail, f(v) approximately v(-sigma). The exponent sigma is obtained analytically and it varies continuously with the spatial dimension, the homogeneity index characterizing the collision rate, and the restitution coefficient. We observe these stationary states in numerical simulations in which energy is injected into the system by infrequently boosting particles to high velocities. We propose that these states may be realized experimentally in driven granular systems.     

The collision frequency of electron-neutral-particle in the weakly ionized plasma with the power-law velocity distribution

We study the collision frequency of electron-neutral-particle in the weakly ionized plasma with the power-law velocity q-distribution and derive the formulation of the average collision frequency. We find that the average collision frequency in the q-distributed plasma also depends strongly on the q-parameter and thus is generally different from that in the Maxwell-distributed plasma, which therefore modifies the transport coefficients in the previous studies of the weakly ionized plasmas with the power-law velocity distributions.     

Qualitative difference between the angular anisotropy parameters in fast electron scattering and photoionization

It is demonstrated for the first time that in spite of well known big similarities between atomic ionization by photons and fast electrons, a qualitative difference exists in angular anisotropy parameters of electrons knocked out in these processes. The difference is disclosed here and attributed to distinction between normal (transverse) and virtual (longitudinal) photons. Formulas are derived for dipole and non-dipole angular anisotropy parameters in fast electron-atom scattering. The ratio of quadrupole-to-dipole matrix elements is determined by the parameter ωR/v < 1, where ω is the transferred in collision energy, R is the ionized shell radius, and v is the speed of projectile. This factor can be much larger than that in the case of photoionization, where one has the speed of light c that is much higher than v. We illustrate general formulas by concrete results for outer s subshells of noble gas atoms Ar and Xe. Even for very low momentum transfer q, in the so-called optical limit, the deviation from photoionization case is prominent and instructive.     

The collision frequency of electron-neutral-particle in weakly ionized plasmas with non-Maxwellian velocity distributions

The collision frequencies of electron-neutral-particle in weakly ionized complex plasmas with the non-Maxwellian velocity distributions are studied. The average collision frequencies of electron-neutral-particle in plasmas are accurately derived. We find that these collision frequencies are significantly dependent on the power-law spectral indices of non-Maxwellian distribution functions and so they are generally different from the collision frequencies in plasmas with a Maxwellian velocity distribution, which will affect the transport properties of the charged particles in plasmas. Numerically analyses are made to show the roles of the spectral indices in the average collision frequencies respectively.     

具有非广延分布电子的碰撞等离子体磁鞘的结构

很多关于等离子体鞘层的研究工作都是基于电子满足经典的麦克斯韦速度分布函数,而等离子体中的粒子具有长程电磁相互作用,使用Tsallis提出的非广延分布来描述电子更为恰当.本文建立一个具有非广延分布电子的碰撞等离子体磁鞘模型,理论推导出受非广延参数q影响的玻姆判据,离子马赫数的下限数值会随着参数q的增大而减小.经过数值模拟,发现与具有麦克斯韦分布(q=1)电子的碰撞等离子体磁鞘对比,具有超广延分布(q<1)和亚广延分布(q>1)电子的碰撞等离子体磁鞘的结构各有不同,包括空间电势分布、离子电子密度分布、空间电荷密度分布.模拟结果显示非广延分布的参数q对碰撞等离子体磁鞘的结构具有不可忽略的影响.希望这些结论对相关的天体物理、等离子体边界问题的研究有参考价值.     

Long-term deconditioning of gas-filled surge arresters

The aim of this paper is to identify parameters that influence the long-term deconditioning effect of gas-filled surge arrester (GFSA) and to provide practical recommendations for mitigating this effect. Namely, after some period of time, on order of hours or days, during which there is no activation due to overvoltage, the deconditioning of GFSA occurs. This effect was observed experimentally within the paper. The observed parameters that could influence the long-term deconditioning effect were the following: shape of voltage load, gas type, gas pressure, interelectrode distance, electrode material, electrode surface topography as well as GFSA design such as two- or three-electrode configuration. According to the results obtained, it has been shown that the occurrence of long-term deconditioning in an insulating system, insulated by a noble gas at a subpressure and with small interelectrode distances, is a phenomenon that always occurs when the insulating system is at rest for about an hour. It has been found that the type of noble gas does not influence the long-term deconditioning. Analysis of such insulating systems' parameters, with a prospect of being used as GFSAs, has demonstrated that this phenomenon is less pronounced at higher pressures (for the same value of the pressure (p) and interelectrode distance (d) product) and for electrodes with microscopically embossed surfaces. According to the results that were obtained by noble gases and their mixtures, as well as the results that were obtained by mixtures of SF6 gas with noble gasses, it can be claimed with confidence that the effect of the long-term deconditioning is an electrode effect. It has also been established that the deconditioning effect does not depend on the electrode material except in the case of electrodes made out of noble metals, which reduce the effect. Based on these results, it can be recommended that the working point of GFSAs be set (according to the DC breakdown voltage value) at a pressure that is as high as possible (with pd?=?const), and that the electrode active surface should have a marked microscopic topography. In addition to this, an essential conclusion for GFSA manufacturers is that long-term system deconditioning is caused by impurities and adsorbed gases that appear at electrode during the state of rest. Out of these two causes, the influence of impurities is probably the dominant one, which is proved by considerably reduced long-term deconditioning in the case of noble metal electrodes, not susceptible to corrosion. This has also been confirmed by a less distinct effect of long-term deconditioning in the case of sandblasted electrodes that have a stronger tendency towards gas adsorption and a weaker tendency towards corrosion. However, it has been shown that adding of the third electrode (that is concentric to the main electrode system) on a free floating potential along with usage of sandblasted electrodes and with smaller interelectrode distance significantly reduces the effects of the long-term deconditioning.