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.     

Optimum conditions for pumping laser transitions of cadmium ions by various processes in a hollow-cathode discharge

The interaction of electrons of various energies with helium and cadmium atoms in a hollow-cathode discharge is analyzed. On the basis of the results of this analysis the conclusion is made that helium is ionized predominantly by electrons moving from the cathode wall to the cavity axis and having energies 70<ε<300 eV, whereas helium and cadmium are ionized predominantly by electrons with energies 9<ε<70 eV which move chaotically. For each of these energy ranges, the kinetic equation is solved and the electron energy distribution function (EDF) is determined, which is used for calculating pumping rates for laser transitions of cadmium ions. The conclusion is made that the rate of population of laser transitions through charge transfer is determined by electrons having a predominant direction of motion and an anisotropic EDF. The population rate associated with electron impact and the Penning ionization is determined by electrons moving chaotically and having an isotropic EDF. The analysis of the EDF made it possible to explain differences in discharge conditions (helium and cadmium pressures) providing optimum lasing for lines pumped by different processes. Radial profiles of pump rates obtained from the analysis made it possible to calculate and explain the dependence of the laser output power on the cathode diameter.     

Dissipation of strong Langmuir turbulence in nonisothermal non-Maxwellian plasma

The regime of strong Langmuir turbulence characterized by the plasma nonisothermality and by the presence of an appreciable non-Maxwellian hot-electron component was experimentally studied. Turbulence was excited in the preliminary produced plasma by the relativistic electron beam. Thomson scattering of laser IR radiation served as the main diagnostic method. The spatial spectra of the Langmuir turbulence and of the attendant ion-sound turbulence were studied using Thomson collective scattering. Thomson incoherent scattering was used for studying the plasma electron distribution function and searching for the local dips of plasma density. Stark spectroscopy of turbulent microfields and the method of observation of plasma radiation at the double plasma frequency were also used. Based on the experimental data, the mechanism of Langmuir oscillation damping by plasma electrons was analyzed. The Langmuir wave conversion induced by the ion-sound turbulence is the most probable channel for energy transfer from the turbulence to plasma electrons, the low-frequency fluctuations being the direct consequence of the strong Langmuir turbulence.     

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.     

Formation of narrow-focused electron beams generated by a source with a plasma cathode in the forevacuum pressure range

Results are presented from experimental studies of the formation of focused electron beams produced by extracting electrons from the plasma of a steady-state discharge with a hollow cathode in the forevacuum pressure range. Based on the measurements of the energy spectrum and diameter of the electron beam, as well as of the emission parameters of the plasma produced in the course of beam-gas interaction, a conclusion is drawn about the excitation of a beam-plasma discharge that deteriorates the beam focusing conditions. The threshold beam current density for the excitation of a beam-plasma discharge is found to increase with accelerating voltage and gas pressure.     

同轴空心阴极氦等离子体的电子激发温度研究

利用同轴空心阴极放电装置,产生氦低温等离子体。通过对等离子体的发射光谱进行测量和计算,研究放电功率以及氦气压强对等离子体的电子激发温度的影响。结果表明:氦低温等离子体的发射光谱主要由连续谱和原子谱线构成,放电功率和压强对谱线的强度具有明显影响。压强的变化不仅影响电子从电场中获得的能量,还会影响电子与原子的碰撞频率,从而导致电子激发温度随着氦气压强的增大,出现先上升后下降的变化趋势。     

Parametric amplification of laser-driven electron acceleration in underdense plasma

A new mechanism is reported that increases electron energy gain from a laser beam of ultrarelativistic intensity in underdense plasma. The increase occurs when the laser produces an ion channel that confines accelerated electrons. The frequency of electron oscillations across the channel is strongly modulated by the laser beam, which causes parametric amplification of the oscillations and enhances the electron energy gain. This mechanism has a threshold determined by a product of beam intensity and ion density.     

Relaxation of the electron temperature in an inert-gas afterglow plasma at elevated pressures

The relaxation of the electron temperature T _e in helium and neon afterglow at elevated pressures is studied theoretically and experimentally. It is shown that the processes in which fast electrons are produced are accompanied by the heating of thermal electrons. The high-energy part of the electron energy distribution function is studied in the intermediate regime (between the local and nonlocal regimes) of its formation. It is shown that, in this case, the calculated effective energy transferred from the fast electrons to the thermal electrons depends substantially on the wall potential of the discharge tube. Comparison of these calculations with experiments testifies to the reliability of the probe technique for measuring T _e in an afterglow at elevated pressures.     

Modelling of Secondary Electron Impact on the Self-Consistent RF Bulk Plasma Description

The impact of a secondary electron beam, generated at the electrodes and accelerated in the sheaths, on the self-consistent treatment of the electron behaviour in an rf bulk plasma has been investigated by a parametric study. Source of electrons in the plasma are collisional ionization and secondary electron injection. Electrons are lost by ambipolar diffusion to the electrodes of a parallel plate rf discharge configuration. The non-stationary Boltzmann equation is used to determine self-consistently the rf field amplitude necessary for maintaining the steady-state rf bulk plasma as well as the time resolved behaviour of the electron energy distribution function and of all contributions to the electron particle and power balance, at given source rate and energy distribution of secondary electron injection.     

Mechanisms for formation of the electron distribution function in the positive column of discharges under Langmuir-paradox conditions

The form of the electron distribution function in the positive column of low-pressure discharges is examined under conditions such that the electron mean free path exceeds the vessel radius. Its formation is analyzed taking all major factors into account, including elastic and inelastic collisions, radial and axial electric fields, and the loss of fast electrons to the wall. It is shown that the main mechanism controlling the fast part of the distribution function is the loss of electrons to the wall, which is determined by the scattering of electrons into a comparatively small loss cone that depends on the relationship between the axial and radial components of the velocity. Since the elastic collision rate for all elements has a weak dependence on the energy beyond the ionization threshold, ultimately the high-energy part of the electron energy distribution function in the positive column of low-pressure discharges is nearly Maxwellian. The subthreshold portion of the distribution function, in turn, is determined by the energy diffusion, in a comparatively strong field, of Maxwellian electrons which arrive after inelastic collisions. The final electron distribution function is well approximated by an exponential with a single slope over the entire energy range. Only within a narrow range of scattering angles is the electron distribution function strongly depleted by the loss of electrons to the vessel walls. In the end, it is concluded that this phenomenon, like the Langmuir paradox, may be related to aspects of the physics of the formation of the electron distribution function owing to a combination of already known mechanisms, rather than to a hypothetical mechanism for thermalization of the electrons, as assumed up to now in the literature. A comparison of solutions of the model kinetic equation given here with published Monte Carlo calculations and experimental data shows that they are in good agreement. Zh. Tekh. Fiz. 69, 34–41 (November 1999)     

Anode plasma structure in a gas discharge with neutral density depleted by ionization

We consider the anode plasma structure in a gas discharge with density of neutral atoms (neutrals) depleted by strong ionization. We obtain analytical solutions of the quasi-neutrality equation for the potential distribution and a condition for the existence of anode plasma in the one-dimensional case for arbitrary potential dependences of the neutral depletion frequency and the electron density. We consider the special cases of a constant neutral depletion frequency, ionization by Maxwellian electrons, and ionization by an intense electron beam under the conditions of collisionless ion motion and Boltzmann thermal electron distribution. The solutions for the first two cases at zero depletion parameter, i.e., at constant gas density, match those obtained in [1] by a power series expansion. In the case of ionization by Maxwellian electrons, the formation of anode plasma at reasonable working-gas flow rates is shown to be possible only at a fairly high electron temperature (if, e.g., xenon is used as the working gas, then T _e ≥ 5 eV). Steady-state solutions of the quasi-neutrality equation under ionization by an intense electron beam exist only if the ratio of the electron beam density to the maximum thermal electron density does not exceed a certain limiting value.     

入射电子能量对低密度聚乙烯深层充电特性的影响

高能带电粒子与航天器介质材料相互作用引起的深层带电现象, 一直是威胁航天器安全运行的重要因素之一. 考虑入射电子在介质中的电荷沉积、能量沉积分布以及介质中的非线性暗电导和辐射诱导电导, 建立了介质深层充电的单极性电荷输运物理模型. 通过求解电荷连续性方程和泊松方程, 可以得出不同能量 (0.1–0.5 MeV) 电子辐射下, 低密度聚乙烯 (厚度为1 mm) 介质中的电荷输运特性. 计算结果表明, 不同能量的电子辐射下, 介质充电达到平衡时, 最大电场随入射能量的增加而减小; 同一能量辐射下, 最大电场随束流密度的增大而增加. 入射电子能量较低时 (≤ 0.3 MeV) , 最大电场随束流密度的变化趋势基本相同. 具体表现为: 当束流密度大于3× 10^-9 A/m²时, 最大场强超过击穿阈值2×10⁷ V/m, 发生静电放电 (ESD) 的可能性较大. 随着入射电子能量的增加, 发生静电放电 (ESD) 的临界束流密度增大, 在能量为0.4 MeV时, 临界束流密度为6×10^-8 A/m². 当能量大于等于0.5 MeV时, 在束流密度为10^-9–10^-6 A/m²的范围内, 均不会发生静电放电 (ESD) . 该物理模型对于深入研究深层充放电效应、评估航天器在空间环境下 深层带电程度及防护设计具有重要的意义. 关键词： 高能电子辐射 低密度聚乙烯(LDPE) 介质深层充电 电导特性     

Electron beam formation in a gas diode at high pressures

Electron beam formation in krypton, neon, helium, and nitrogen at elevated pressures are experimentally investigated. It is shown that, when the krypton, neon, and helium pressures are varied, respectively, from 70 to 760 Torr, from 150 to 760 Torr, and from 300 to 4560 Torr, runaway electrons are beamed at the instant the plasma in the discharge gap approaches the anode and the nonlocal criterion for electron runaway is fulfilled. The fast-electron simulation of discharge gap preionization is performed. The simulation data demonstrate that preionization in the discharge gap is provided if the voltage pulse rise time is shorter than a nanosecond under atmospheric pressure.     

Determination of the densities and temperatures of two low energy electron groups in a hollow cathode discharge

A new method of Langmuir probe analysis for non-Maxwellian plasmas is proposed. The method consists of computer fitting a mathematical function to the normal probe voltage-current characteristic, assuming two groups of electrons, each with a Maxwellian distribution. The advantages of the method are that both the temperatures and the densities of the two groups may be determined and that the electron energy distribution function is a tractable mathematical function. The two groups are proven to be very nearly Maxwellian in the pressure range of 1.8 to 3.8 torr helium and the results are in excellent qualitative agreement with results obtained spectroscopically by other authors.     

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     

On the Question of Increasing Maxwellization of the Electron Energy Distribution Function due to Electron — Electron Interaction with Growing Ionization Degree in the Beam Discharge Plasma

The question of the establishment of an almost complete Maxwellian energy distribution of the electrons in a given discharge plasma is of importance, especially under the aspect of a more convenient determination of transport and rate coefficients. In [5] an energy space averaged criterion for the establishment of such a structure of the electron energy distribution function in the stationary beam discharge plasma of molecular gases was formulated from a heuristic point of view. This paper investigates this question in detail starting from the adequate Boltzmann equation of such plasmas. Energy resolved conditions for the establishment of an almost complete Maxwellian distribution are derived from the kinetic equation. Using one of these conditions, the formal derivation of the mentioned averaged condition is performed and its limitations are shown. The fulfilment of the energy resolved and of the averaged conditions are illustrated and discussed using solutions of the kinetic equation in purely molecular hydrogen for two parameter sets yielding larger and smaller deviations of the real distribution function from the Maxwellian form.     

Applicability of the Hydrodynamic Approach to the Electron Component in Plasmachemical Reactors of a Beam Plasma Type

In the present work the question of the possible use of the hydrodynamic approach for describing a plasma beam discharge is investigated. It is shown that the condition ν_ei > (ν_ei + ν_en) X W/nT is the Maxwelliazation criterion of moderate energy particles in a plasma beam discharge. In this case the value of moderate energy is less than 3÷4 values of plasma electrons thermal ernergy. The influence of the tail of the distribution function on electron heating is considered qualitatively.     

Statistical Theory of Two-Sided Multipactor

We develop a statistical theory of secondary-emission discharge (SED) taking the energy distribution of secondary electrons into account. The theory allows one to describe quantitatively the initial stage of development of a two-sided multipactor. For an arbitrary probability density of normal components of the ejection velocity and an arbitrary distance between the walls enclosing the microwave discharge plasma, we construct an analytical solution for the electron distribution function over transit times. The performed analysis is based on the results of a detailed study of conditions under which an electron reaches the opposite side. With allowance for the spread in thermal velocities, we derive a recurrence relation between the electron distribution functions over emission phases and formulate a general integral equation from which the resulting stationary distribution and the threshold of SED onset are determined.     

Femtosecond laser interactions with dielectric materials: insights of a detailed modeling of electronic excitation and relaxation processes

Electronic excitation–relaxation processes induced by ultra-short laser pulses are studied numerically for dielectric targets. A detailed kinetic approach is used in the calculations accounting for the absence of equilibrium in the electronic subsystem. Such processes as electron–photon–phonon, electron–phonon and electron–electron scatterings are considered in the model. In addition, both laser field ionization ranging from multi-photon to tunneling one, and electron impact (avalanche) ionization processes are included in the model. The calculation results provide electron energy distribution. Based on the time-evolution of the energy distribution function, we estimate the electron thermalization time as a function of laser parameters. The effect of the density of conduction band electrons on this time is examined. By using the average electron energy, a new criterion is proposed based on determined damage threshold in agreement with recent experiments (Sanner et al. in Appl. Phys. Lett. 96:071111, 2010).