Electron distribution function in a weakly ionized He-Hg mixture

The electron energy distribution functions for He-Hg mixture in a uniform electric field are calculated for differentE/N and relative mercury concentration? from fundamental cross-section data. The Boltzmann equation is applied considering the elastic and inelastic collisions of electrons with neutrals of the both components. From these distributions and elastic collision cross-section (for He and Hg) drift velocity, diffusion coefficient and mean electron energy are computed. The electron energy losses in elastic and inelastic collisions over the considered region of the parameters are discussed.     

The kinetic description of the accelerated-electron flux in solar flares

We propose an accurate quantitative model describing the propagation of flare-accelerated electrons in the solar atmosphere. This model is based on a kinetic equation considering Coulomb collisions of accelerated electrons with thermal electrons and protons in the plasma of the solar corona and chromosphere. Using a self-consistent approach, we find the distribution function of accelerated electrons and the electric field of the reverse current balancing the electric current carried by the accelerated-electron flux. We compare our two-dimensional (in the velocity space) model with the widely used classical one-dimensional model that overlooks the reverse-current effect.     

强激光与高密度气体相互作用中电子和离子加速的数值模拟

在现有的一维粒子模拟程序的基础上发展了带光电离和碰撞电离及蒙特卡罗两体碰撞的模拟程序(1D PIC-MCC). 用此程序模拟研究了短脉冲激光与He气靶相互作用时电子和离子的加速过程. 研究表明当强激光与过临界密度的微米厚度的平面靶相互作用时，靶前表面物质将被激光脉冲前沿迅速离化；新生的电子被激光场有质动力加速成为高能电子，这些电子穿入到靶内，通过电子碰撞电离离化靶内物质；一部分高能电子穿透靶后，会在靶的后表面形成强的电荷分离场，该场迅速离化靶后表面物质，同时使得后表面离子得到加速. 部分穿透靶的超热电子将被电荷分离场重新拉回靶内，在靶的前后表面振荡. 一些振荡电子在此过程中得到电荷分离场加速，离开前表面，在前表面也形成电荷分离场，使前表面离子得到加速. 关键词： 激光等离子体 光电离和碰撞电离 电子加速 离子加速     

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.     

Distribution function of electrons and kinetic coefficients in cesium-argon mixture discharge

The distribution function of electrons in a cesium-argon mixture discharge is found in the present paper by solving Boltzmann's equation. The elastic and inelastic electron-atom collisions and electron-electron collisions are taken into consideration.The influence of the addition of cesium vapours to argon on the quantities characterizing the discharge plasma is explained. From the electron distribution function are calculated: the drift velocity, the mean energy, the ratio of the diffusion and mobility coefficients and the electron energy losses for individual elementary processes as functions of the electric field and the concentration of the neutral gas components.     

Runaway-Ströme hoher Intensität in einer toroidalen Entladung

Intensive currents of runaway electrons with energies of 50 keV or more have been observed at high pressures in a plasma betatron in addition to betatron accelerated electrons at lower pressures. The measurements agree with the assumption that these electrons are accelerated in the external field while they are guided by the self magnetic field of the plasma current. Macroscopic instabilities and plasma waves can be excluded as accelerating mechanisms. The strong dependence of the runaway flux upon the gas pressure and the electric field can be explained by collisions between electrons and the other plasma particles. Furthermore the influence of the external magnetic field on the movement of the plasma current to the torus wall was investigated. A maximum circulating runaway current of more than 2000 A (Xenon) appeared when the plasma current was kept approximately in balance by the external magnetic field.     

On bremsstrahlung radiation of accelerated electrons in solar flares

We have calculated the spectrum and polarization of the bremsstrahlung hard X-ray radiation produced by nonrelativistic electrons that are accelerated during a solar flare. The distribution function of accelerated electrons is taken from the self-consistent solution of the kinetic equation allowing for Coulomb collisions and an electric field of reverse current in plasma. The computed polarization of the hard X-ray polarization is shown to be appreciably lower than the value given by simplified thick-target models without considering the reverse current.     

Glow discharge in rare-gas and metal vapour mixture

Applying the Boltzmann equation to a He-Cd mixture discharge the electron energy distribution functions, kinetic coefficients and collision frequencies are numerically calculated. Calculations are made for a homogeneous and stationary discharge plasma subjected to an externally applied electric field. The collision processes which have been taken into account are elastic and inelastic collisions of electrons with He and Cd atoms as well as mutual encounters of electrons. In this case the electron energy distribution and all the quantities calculated from it are dependent on the reduced electric field, the ionization degree and the relative cadmium concentration.     

On the Kinetics of the Active Zone of the Stationary SF6 Beam Discharge Plasma

The paper deals with the impact of intensive electron attachment on the kinetics of the electrons in the active zone of the stationary band-like beam discharge plasma in SF₆ which is an alternative useful plasma medium for “dry etching”. The energy distribution of the electrons in this plasma was obtained by numerically solving the Boltzmann equation which includes apart from elastic collisions, different exciting collision processes, attachment in electron collisions, direct ionization, the ambipolar loss of electrons, Coulomb interaction between electrons and of electrons with ions and the power input to the electrons by the turbulent electric field. In particular, due to the needed fulfilment of the consistent electron particle balance, for an extended region of the turbulence energy density in this plasma a large impact on the electron kinetics of the intensive electron attachment, which is the prevailing electron loss process, was found enforcing independent of the turbulence energy density always a large power input to the electrons, smooth and only slowly decreasing energy distributions even in the energy region of direct ionization.     

Calculation of characterisctics of electron drift in neon under a DC electric field

The features of the energy distribution function of electrons drifting in a monatomic gas are analyzed. The case of electron drift in neon under typical experimental conditions for dust structures in plasma is considered. The results of calculation of the energy balance of electrons and drift characteristics in an electric field at strengths of 0.1 < E/N < 1000 Td taking into account inelastic collisions are presented.     

Multiple acceleration of ionospheric electrons in the approximation of continuous energy losses due to collisions

The multiple acceleration of electrons during active experiments in the ionosphere is related to their returning to a thin layer of the turbulent plasma, created by the powerful radio wave, due to elastic collisions with neutral particles. This effect depends on the magnitude and type of collisional energy losses by the electrons. In this paper, we formulate a system of equations that allows one to describe the process of multiple electron acceleration taking into account collisions of the accelerated particles with thermal electrons and assuming that collisional energy losses are continuous. The above-mentioned collisions become important at small energies where the primary electron acceleration takes place. We obtain asymptotic solutions of the formulated equations using the model power-law dependence of the collision frequency on electron energy. These solutions show that the effect of multiple acceleration of electrons in the ionospheric F-layer can lead to the formation of a slowly-varying high-energy “tail” in the distribution of the accelerated particles at energies of about tens of electron-volts. Institute for Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation of the Russian Academy of Sciences, Troitsk, Moscow Region, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 1, pp. 3–16, January 2000.     

Response of the Electron Kinetics on Spatial Disturbances of the Electric Field in Nonisothermal Plasmas

An efficient method for solving the inhomogeneous electron Boltzmann equation for a weakly ionized collision dominated plasma is represented. As a first application this method is used to investigate in a helium plasma the response of the electron velocity distribution function and of the relevant macroscopic quantities to the impact of spatially limited disturbances in the electric field. In addition to the field action elastic and (conservative) inelastic collisions of electrons with gas atoms are taken into account in the kinetic treatment. In this way the spatial relaxation behaviour of the electrons and their establishment into homogeneous plasma states could be studied on a strict kinetic basis. Unexpectedly large relaxation lengths in electron acceleration direction have been found at medium electric fields.     

Average Energy Variations and Trapping of Electrons in the Resonances of Rare Gases

The effect of resonant elastic collisions of electrons in He on their “exact” mean energy variation for free path in the presence of a d.c. electric field is analysed. Different values of E/N and both isotropic and anisotropic initial velocity distributions, just after collision, are considered. It is shown that for sufficiently elevated values of E/N a necessary condition for electron (resonance) trapping becomes satisfied. This result is discussed in the light of an interpretative model advanced to explain some electroluminescence phenomena in rare 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     

Field properties and vacuum electron acceleration in a laser beam of high-order Laguerre–Gaussian mode

The electric field intensity distribution and the phase velocity distribution of high-order Laguerre–Gaussian (LGρ?) mode laser beams are analyzed. Using three-dimensional test particle simulation, the numerical results of electrons accelerated by LG00, LG40 and LG41 mode laser beams are presented. Compared with the LG00 mode (the fundamental mode) laser beam, low-energy injection electrons can be more favorably accelerated in a high-order LG mode laser beam. Contrary to anticipation, a high-order LG mode laser beam with intense axial electric field distribution is inferior to the LG00 mode in capture acceleration for electrons with high injection energy.     

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)     

Beschleunigung von Elektronen in einem Plasmabetatron

A plasma was produced by a high frequency electric quadrupole field (v=200 Megacycles) at gas pressures of 10^?4 to 5·10^?3 mm Hg in a quarz glass torus. The torus was placed between the poles of an air-core betatron with the following properties: radius of equilibrium orbit 20 cm, maximum accelerating field strength 80 V/cm, end energy 1.5 MeV. Associated with conduction currents of some 100 A, energetic Bremsstrahlung was observed and attributed to 1,2 MeV electrons. The number of accelerated electrons was of the order of 10¹¹ per pulse. The intensity and energy of the radiation, together with the time dependence of the plasma current, were observed as function of different parameters, such as the gas pressure, high frequency amplitude, induced acceleration field strength, for different gases. The energetic radiation disappears when, because of the self-induced magnetic field, the stability condition for the betatron equilibrium is no longer fulfilled.     

Characteristics of electron drift in the low-pressure gas discharge

The features of the energy distribution function of electrons during their drift in neon are analyzed for typical conditions of experiments with dust structures in plasma. The energy balance of electrons and drift characteristics in an electric field at strengths 13 < E/N < 42 Td were calculated taking into account inelastic collisions and the effect of electron loss on gas-discharge tube walls.     

Free electron gas spectrum parameters of noble gases in dc electric field

Free electron gas is present in every gas, whether it is of atomic or molecular structure. Since the Maxwell spectrum type is the consequence of only thermal motion of constitutive gas particles; therefore, the presence of electric field leads to change the spectrum of charged particles due to their directed motion. However, it has been shown that in the case of occurrence only of elastic interactions between electrons and neutral gas particles (a condition that has been met in the case of weakly ionized noble gases of a relatively huge volume) the deviation of the gas spectrum of free electrons in the electric field from the Maxwell type is negligible. In such a case, the gas spectrum of free electrons is either of Maxwell type (if the frequency collision value is energy-independent) or of Druyvesteyn type (if the mean free electron path value is energy-independent). The Maxwell and Druyvesteyn distribution types are very similar. The only noticeable difference is that the tail of the Maxwell distribution decreases with the energy exponent to the first degree of energy, and the tail of Druyvesteyn distribution with the energy exponent to the second degree of energy. The aim of this paper is to determine whether the gas spectrum of free electrons in weakly ionized noble gases at small values of the product pd (pressure and inter-electrode distance) follows either the Maxwell's or Druyvesteyn's type, as well as to determine the dependence of spectrum parameters on the product pd. It has been established that better results are obtained on the assumption that the mean value of collision frequency is energy-independent.