Electron distribution function relaxation in monatomic gases

The authors discuss an analytic solution of the Boltzmann equation which describes the relaxation in time of the electron distribution function for electrons in a plasma derived from the monatomic gases He, Ne, Ar, and Xe. It is assumed that there are no perturbing forces on the electrons and that at t=0 they have a Maxwellian distribution function corresponding to an average energy of 2 eV. The electrons then lose energy through elastic collisions with neutrals and eventually energy-equilibrate with the neutrals, which are assumed to be cold. The evolution of the electron distribution function in time and velocity space is calculated for each gas. This model is approximately correct for the afterglow period of an electrical discharge in a monatomic gas. It is possible to calculate a time which is a measure of the decay time of the electron energy in an afterglow plasma     

Relaxation of Plasma Electrons towards Stationary States as Related to Different Initial Energy Distributions and for a Wide Range of the Final Electric Field Strength

Starting from former investigations concerning the collision dominated relaxation of the electron component in weakly ionized inert gas plasma we generalize the results obtained. Also in the present paper we use the same adaquate kinetic equation for the electron energy distribution function. On one side the influence of non-stationary, analytically given initial energy distributions on the relaxation behaviour and on the resulting adjustment time of stationary states was investigated. On the other side the calculation, especially of the adjustment time, was extended to a whole variety of final stationary states ranging from those determined only by energy loss due to elastic collisions to those determined only by exciting collisions. The adjustment time obtained varies by about four orders of magnitude within this wide range of final stationary states.     

Die Berücksichtigung der Ionisation durch Elektronenstoß in der Elektronenkinetik des schwachionisierten anisothermen Plasmas III. Das instationäre Verhalten bei großer impulsförmiger Feldstörung

The Influence of Ionization by Electron Collisions on the Electron Kinetics of the Low Ionized Anisothermal Plasmas The time behaviour of the electron component was calculated during the additional application of a single pulse to the electric field in the plasma. The investigations were performed for the weakly ionized Ne-plasma as a typical example taking into account supplementarily the direct ionization due to electron collisions and an electron loss term with a constant life time besides elastic and exciting collisions. Using the instationary Boltzmann equation we determined the time behaviour of the essential macroscopic quantities. Besides the caluclation of the marked temporal development of such quantities as the electron concentration, the electron collision frequencies for excitation and ionization and the different energy transfer rates especially the relaxation of the electron component was analysed after switch on and switch off the additional rectangular pulse.     

Deceleration and acceleration of fast electrons in a dense gas in an electric field

The propagation of electrons in a gas at energies higher than the excitation energy of the K shell of the gas atoms is simulated numerically. Calculations show that, without a field, the penetration depth of the electrons into a gas heavier than nitrogen is limited primarily by their elastic collisions with atomic nuclei. For electrons moving in an electric field, the effect of elastic collisions is that there is no definite electric field strength above which an electron with a given energy will be continuously accelerated. Even in an electric field much stronger than the critical one, only a fraction of electrons are accelerated. The remaining electrons turn back due to elastic collisions and lose their energy in deceleration by the field. In this case, the propagation velocity of the centroid of the electrons tends to a constant value.     

Striations als Eigenlösungen der Elektronenbewegung im elektrischen Feld

A simple model for the motion of electrons in an inhomogeneous electric field is derived. With this model the striations in a weakly ionized low pressure discharge can be explained as a phenomenon of the energy relaxation. In a periodical electric field resonances occur, for which the voltage across one striation equals the average energy gain of an electron between two inelastic collisions, divided by an integer. These resonances are recognized as eigensolutions in the homogeneous field. The influence of the elastic and ineiastic collisions on the damping of the striations is discussed. In a first approximation the energy loss at the elastic collisions can be taken into account by a frictional contribution to the voltage across one striation. This voltage and the energy distribution function in moving striations are calculated and compared with measurements of other authors.     

On the feasibility of the coulomb explosion of a metal

The mechanism of the Coulomb explosion of a metal in an external pulsed electric field is discussed. In the case of a low-frequency field, when its frequency is lower than the frequency of electron collisions, it is impossible to reach the conditions of the Coulomb explosion of a metal if the field pulse duration is shorter than the time of electron energy relaxation upon elastic collisions, and the electron temperature is well above the Fermi energy and the work function. In the case of a high-frequency field, e.g., in a powerful pulse of ultraviolet laser radiation, the Coulomb explosion can occur if the field strength is well above the intraatomic field strength (i.e., when the laser power density is ≥10¹⁹ W/cm²).     

Dynamics of electron beams in plasmas

The characteristic features of the relaxation of the energy and momentum distribution functions of the electrons in a plasma produced by a low-voltage beam discharge in helium are investigated. It is established that, contrary to widely held opinion, the energy of an intense electron beam may relax due to the wave excitation. The critical currents corresponding to a jumplike transition from one relaxation mechanism to another are measured. The density of metastable helium atoms is determined from the comparative analysis of theoretical and experimental results on the structure of the energy spectrum of the electrons of an intense beam. An intense electron beam is found to become more isotropic in the course of its interaction with Langmuir waves in a collisionless plasma. The cross section for quasi-elastic collisions between the electrons and Langmuir plasmons is estimated. The wave nature of the beam-plasma mechanism for the relaxation of the anisotropic electron energy distribution function is demonstrated, and the mechanism itself is shown to come into play when the discharge current exceeds a certain critical level. The experimental threshold criterion for the energy relaxation of an intense monoenergetic beam is obtained for the first time. It is shown that the relaxation occurs in two stages: the isotropization stage, in which the beam energy decreases insignificantly, is followed by the stage in which the beam relaxes to a state with a plateau-like energy distribution function. The threshold criterion for the relaxation of the anisotropic electron energy distribution function is universal in character regardless of the cause of anisotropy.     

Die Relaxation der Isotropverteilung und makroskopischer Kenngrößen der Elektronen im abklingenden feldfreien Neon-Plasma

Relaxation of Distribution Function and Macroscopic Parameters of Electrons in Temporal Decaying Neon Plasma without Field Heating We investigate the field-free collision-dominated relaxation in the afterglow of a weak ionized plasma in the first period of temporal decay which is determined especially by the quick alterations in the electron component because of the small inertia of electrons. Therefore the evolution in time of the electron distribution and hence the macroscopic coefficients determined thereby are calculated in dependence on the action of elastic and exciting collisions between electrons and neutral atoms. On the basis of these results we have found characteristic times controlling the relaxation process which depend especially on the action of the different kinds of collisions. Thus it is possible to get a good microscopic understanding of the field free collision dominated relaxation of the electron component.     

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     

含振动能激发Boltzmann模型方程气体动理论统一算法验证与分析

为模拟研究高温高马赫数下多原子气体内能激发对跨流域非平衡流动的影响,将转动能、振动能分别作为气体分子速度分布函数的自变量,把转动能和振动能处理为连续分布的能量模式,将Boltzmann方程的碰撞项分解成弹性碰撞项和非弹性碰撞项,同时将非弹性碰撞按一定松弛速率分解为平动-转动能松弛过程和平动-转动-振动能松弛过程,构造了一类考虑振动能激发的Boltzmann模型方程,并证明了其守恒性和H定理.基于内部能量变量对分布函数无穷积分,引入三个约化速度分布函数,得到一组考虑振动能激发的约化速度分布函数控制方程组,使用离散速度坐标法,基于LU-SGS隐式格式和有限体积法求解离散速度分布函数,建立含振动能激发的气体动理论统一算法.通过开展高稀薄流到连续流圆柱绕流问题统一算法与直接模拟蒙特卡罗法模拟结果对比分析,特别是过渡流区平动、转动、振动非平衡效应对绕流流场与物面力热特性的影响机制,证实了所建立的含振动能激发的Boltzmann模型方程及气体动理论统一算法的准确可靠性.     

Energy relaxation and thermalization of hot electrons in quantum wires

We develop a theory of energy relaxation and thermalization of hot carriers in clean quantum wires. Our theory is based on a controlled perturbative approach for large excitation energies and emphasizes the important roles of the electron spin and finite temperature. Unlike in higher dimensions, relaxation in one-dimensional electron liquids requires three-body collisions and is much faster for particles than holes which relax at nonzero temperatures only. Moreover, comoving carriers thermalize more rapidly than counterpropagating carriers. Our results are quantitatively consistent with a recent experiment.     

Ultrafast dynamics of electron thermalization in gold

Time-resolved surface second-harmonic generation (SHG) is used to probe electron relaxation processes in gold following intense laser excitation at 1.55 eV. For the first time, an electron temperature ( T(e)) dependent enhancement in the SHG signal is clearly observed at T(e) above 0.7 eV, which is shown to relate to the thermalization of nonequilibrium hot electrons. Therefore, the relaxation dynamics of the transient nonequilibrium electrons in the high T(e) regime is directly resolved by monitoring the time evolution of the SHG signal.     

Kinetic theory of monochromatic waves bunching in a low-voltage beam discharge in rare gases

The kinetic theory of phase focusing, that is bunching in a low-voltage beam discharge in rare gases (LVBD) during the propagation of longitudinal electrostatic oscillations at the Knudsen numbers of the order of unity have developed. The anomalous relaxation of the almost monoenergetic electron beam in momentum and energy is described for the case when this process cannot be explained by electron–atom collisions. The paper has shown the important role of electrons that have the beam energy and isotropic directional distribution, which is formed as a result of elastic collisions between the beam electrons and atoms. The dependence of the anomalous relaxation length on parameters of the LVBD in rare gases is studied.The developed theory makes it possible to quantitatively interpret experimental data on the LVBD under conditions when the electron mean free path is of the order of the interelectrode gap. According to these data, regardless of the density of the charged particles in the LVBD plasma in rare gases, five Langmuir plasma wavelengths fit along the length of the anomalous relaxation of the electron beam. The study of the electron beam dynamics laws in a plasma is important for the development of plasma-electrical devices, where the beam discharge is applied, namely: widely used all-movable stabilizers, sources of intense electromagnetic radiation, controlled elements of electronic circuits, plasma chemical reactors, etc.     

CO_2与高振动激发K_2碰撞中的全分辨转动态分布

在K_2+CO_2中,受激发射泵浦得到K_2(E=3 500和4 000cm~(-1))高位振动态,研究了高振动激发K_2与CO_2碰撞产生的CO_2全分辨转动态分布。利用高分辨瞬时激光诱导荧光(LIF)测量了CO_2(0000)J=2~74的转动和平移能量轮廓,利用双高斯函数拟合,分别确定各转动态的产生和倒空线宽,从而得到碰撞产生的Doppler展宽、平移温度和平移能。对于K_2不同的激发能E,能量转移的机制是相似的,为振动-转动/平移弛豫机制。但碰撞出现部分的平移温度均超出池温,而碰撞倒空部分的平移温度均略低于池温,平移能随E的增加而增大,E增加14%,平移能增加40%。CO_2(0000)转动态分布的半对数描绘给出了双指数分布,对于K_2E=3 500cm~(-1),低J态分布T_a=(523±60)K,高J态分布T_b=(1 890±210)K。Ta接近池温,说明低J态为近弹性碰撞,属单量子弛豫过程,而高J态为非弹性碰撞,属多量子驰豫过程。对于K_2E=4 000cm~(-1)同样有双指数行为,低J分布T_a=(620±65)K,高J分布T_b=(2 240±250)K。高振动态K_2(E)与CO_2碰撞,E=4 000cm~(-1)比E=3 500cm~(-1)的Ta和Tb均约高19%,说明转动分布对于K_2不同能量是敏感的,但弹性和非弹性分支比是基本相同的,弱碰撞约占82%,强碰撞约占18%。     

He-O_2转动激发截面的理论计算

用公认精确的密耦 (Close Coupling)方法、采用两种不同的相互作用势计算了He -O2 碰撞的态 态转动激发截面 (E =2 6.8meV) ,通过系统研究和计算发现 :低能散射时 ,He -O2 碰撞的弹性散射主要发生在小角部分 ,而非弹性转动激发主要发生在大角部分。研究表明 :转动激发截面对势能表面的方向性和散射角都非常敏感。     

Regular threshold-energy increase with charge for neutral-particle emission in collisions of electrons with oligonucleotide anions

Electron-DNA anion collisions were studied using an electrostatic storage ring with a merging electron-beam technique. The rate of neutral particles emitted in collisions started to increase from definite threshold energies, which increased regularly with ion charges in steps of about 10 eV. These threshold energies were almost independent of the length and sequence of DNA, but depended strongly on the ion charges. Neutral particles came from breaks of DNAs, rather than electron detachment. The step of the threshold energy increase approximately agreed with the plasmon excitation energy. It is deduced that plasmon excitation is closely related to the reaction mechanism.     

Low-pressure RF discharge in the free-flight regime

The self-consistent equations system for low-pressure RF discharge in the free-flight regime is formulated. The expressions for the electron energy diffusion coefficient due to electron-neutral collisions and to the electron collisions with the plasma-space charge moving boundary (stochastic heating) are derived. If the electron-neutral elastic collisions frequency exceeds the inelastic one, the conventional two-term approximation for the electron distribution function (EDF) can be generalized, and the space-time-averaged electron kinetic equation can be reduced to the one-dimensional energy diffusion one. The fast electrons attached to the electrode surface can also be accounted for in this equation. It is shown that in the cases of (a) spatially uniform ion profile, (b) for frequencies that are small compared with the electron bounce frequency, and (c) for frequencies exceeding the electron plasma one in the sheath, the stochastic heating vanishes     

Numerical approach to non-equilibrium carrier relaxation in picosecond and subpicosecond physics

We present a numerical resolution of the time-dependent Boltzmann equation which describes the electron relaxation kinetics in direct gap semiconductors under subpicosecond optical excitation. The calculation is specialized to GaAs. We investigate, around the Mott density, the conditions of internal thermalization and energy relaxation of electrons, which depend strongly on the plasma concentration.     

Monte Carlo determination of the field dependence of the first Townsend ionization coefficient for atomic hydrogen

The Monte Carlo method has been used to find the /p₀ = f(E/p₀) dependence for atomic hydrogen from E/p₀ = 10 to 100 V/cm-torr· For the calculation it was assumed that elastic collisions and ionization could be accompanied by an atomic excitation corresponding to the transition of a ls electron to a 2s or 2p level.Translated from Izvestiya VUZ. Fizika, No. 8, pp. 70–76, August, 1970.In conclusion the authors thank R. K. Peterkop for moral support of the fundamental idea of this paper.     

颗粒介质弹性的弛豫

颗粒介质是复杂的多体相互作用体系, 其弹性源自内部的力链结构, 弹性能量处在亚稳态, 具有复杂的弛豫行为. 在常规作用下, 颗粒介质往往呈现明显的弹性弛豫. 应力松弛是应变恒定时应力的衰减现象, 弹性弛豫是应力松弛的主要原因. 在前期工作基础上, 从弹性势能面和双颗粒温度热力学角度分析了弹性弛豫的机理, 量化了弹性应力演化不可逆过程; 基于双颗粒温度热力学计算得到了弹性能、颗粒温度和应力的演化, 其中应力松弛的计算结果与实验结果基本一致, 讨论了颗粒温度初值和输运系数的影响. 指出, 开展力链结构及其动力学研究是揭示宏观弹性弛豫机理的关键.