Stoßbestimmte Relaxation des Elektronenensembles im Plasma bei zusätzlicher Aufheizung durch ein elektrisches Feld. III. Das periodische Verhalten der Elektronenkomponente im elektrischen Feld großen Modulationsgrades

Collision Dominated Relaxation of the Electron Ensemble in a Plasma with Additional Heating by an Electric Field. III. The Periodic Behaviour of the Electron Component in an Electric Field with a Large Modulation Amplitude With the aid of the non-stationary Boltzmann-equation the periodic behaviour of the isotropic part of the velocity distribution of electrons and thereby determined macroscopic quantities is calculated for periodic electric fields with large modulation amplitude. The investigations concern a weakly ionized column plasma in neon under typical low and medium pressure conditions. Based on the numerical results for typical ranges of field strength and cycle times of the electric field a qualitative physical interpretation for the periodic behaviour of the electron component is obtained. The introduction of special field-dependent adjustment times allows the formalution of conditions which characterize the case of quasi-stationary behaviour and also the case of small amplitudes of modulation in the macroscopic quantities determined by the isotropic distribution function. The periodic states between these two limiting cases can be interpreted as due to two competing processes. The first one is the energy input controlled by the electric field and the second one is the energy loss in binary collisions of the electrons with the atoms.     

Die Berücksichtigung der Ionisation durch Elektronenstoß in der Elektronenkinetik des schwachionisierten anisothermen Plasmas. I. Analyse des Ionisierungsstoßintegrals und Ableitung von geeigneten Darstellungen für eine numerische Behandlung

The influence of the Ionization by Electron Collisions on the Electron Kinetics of the Low Ionized Anisothermal Plasma. I. Analysis of the Ionization-Collision-Integral and the Derivation of Representations Appropriate ot Numerical Calculations Starting form the balance of the electrons in the velocity space we determined the contribution of the ionization by electron collisions to the Boltzmann equation for the electrons. After integrating stepwise the derived collision-integral for ionization we obtained the development of the ionization-collision-integral in spherical harmonics, using the impulse and energy balance. From the latter the contributions to the concentration and the energy balance of the electrons were determined. Using special asumptions concerning the differential scattering cross section for the ionization we derived representations of the collision-integral suitable for numerical calculations. Especially the important contribution of this collision-integral to the equation of isotropic distribution function depends on the total cross section for ionization only.     

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.     

Die Relaxation der Geschwindigkeitsverteilungsfunktion der Elektronen im homogenen elektrischen Feld mit elastischen und anregenden Stößen. II. Das Verhalten des Elektronenensembles bei aperiodischer Feldänderung zwischen zwei stationären Zuständen

Recently the relaxation of the electron component was investigated under field-free conditions after sudden switch-off the electric field and otherwise after sudden changing the electric field to a new value of field strength. To continue these papers we consider now the relaxation process of the electron ensemble in the presence of a monotonous time variable electric field. The investigations are based on a computation of time change in the isotropic part of the velocity distribution function of the electrons and of the macroscopic parameters determined by the distribution function. The start-ing-point is the non-stationary Boltzmann equation with stationary initial states taking into consideration elastic and exciting collisions. Besides the representation of the received numerical results a physical interpretation is obtained for the duration of the whole relaxation process, for its initial stage as well as for the momentary stage of the relaxation by introduction of normalized characteristic time quantities. Further characterizing conditions are found related to the relaxation after quasi-jumplike change of the electric field and in the case of quasistationary field alteration respectively. With the introduced characteristic time quantities statements about the degree of realization of one of this limiting cases are possible for any given monotonous field. The investigations are per-formed in a low ionized non-thermal neon plasma.     

Long‐Time Evolution of a Low Pressure Laboratory Plasma after Application of Transient high Voltage Positive Pulses

The long‐time evolution of weakly‐collisional plasma with application of high voltage positive pulses to an electrode immersed in plasma, with pulse widths less than as well as more than ion plasma periods, is studied. The plasma is produced by electron impact ionization of argon or helium gas, where electrons are coming out from dc biased hot thoriated tungsten filaments. It is observed that during the temporal evolution of argon plasma, a beam component exists along with temporal bulk electrons giving rise to a double hump profile of transient Electron Distribution Function (EDF). However, in the case of temporal evolution of helium plasma, only a bulk electron population is present. The obtained results are explained by understanding the role played by thermionically emitted electrons during the plasma evolution, the role of the difference of ionization rates of helium and argon, and the higher temporal plasma potential. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electron Energy Distribution Functions in RF Molecular Plasmas: The Role of Second Kind Collisions

Electron energy distribution functions in rf molecular plasmas have been calculated by solving the time dependent Boltzmann equation in the presence as well as the absence of vibrationally and electronically excited molecules and thus of first kind and second kind (superelastic) collisions with them. The results, which refer to a model plasma composed by three components (the ground state, a lumped vibrational state and a lumped electronic state), show that these collisions with vibrationally and electronically excited molecules strongly affect the modulation of the electron energy distribution function and related quantities.     

Classical Molecular Dynamics Model for Coupled Two‐Component Plasmas – Ionization Balance and Time Considerations

The dynamic properties of ion‐electron two‐component plasmas (TCP) are studied by using classical molecular dynamics (MD) simulations. There is a variety of time dependent and structural results that MD is able to provide in complement to other methods, e.g., useful micro‐field sequences can be generated. The method deals with some specific difficulties: the mass ratio between ions and electrons enforces very small time‐steps appropriate to follow electrons motion while, ions must move significantly in order to build, self consistently, their spatial structure. This results in expensive simulations. Electron trajectories are trapped and de‐trapped with multiple electron collisions around ions resulting in the occurrence of quasi metastable bound electron states. An analysis of micro‐fields at neutral in a hydrogen plasma reveals the need to consider a complete hierarchy of time scales extended typically over 7 order of magnitude, i.e., from a time‐step: ～10^‐19s, to a time required to obtain statistical averages, ～10^‐11s. In order to extend the MD capabilities in representing real coupled plasmas a classical ionization/recombination process has been implemented allowing to follow the evolution of plasmas involving several ion stages and model the ionization balance. Here again TCP simulations deal with extended time‐scale providing information about relaxation of non equilibrium plasma states (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Die Relaxation der Geschwindigkeitsverteilungsfunktion der Elektronen im homogenen Feld mit elastischen und anregenden Stößen. III. Die Einstellung des periodischen Verhaltens der Elektronen-komponente im elektrischen Feld großen Modulationsgrades

To continue the kinetic investigations concerning the periodic behaviour of the electron component of a low ionized Ne-plasma of a glow discharge column in a periodic electric field [4] with high degree of modulation in this paper the adjustment of the isotropic distribution function of the electrons and by the latter determined macroscopic quantities are calculated and discussed. Starting with the non-stationary Boltzmann equation the adjustment process is considered using different direct components of the field but nearly constant degree of modulation. In the whole range from a nearly momentary adjustment to an adjustment in the high frequency limit of only small modulated distribution function we obtained results concerning the adjustment behaviour and its characteristic times by variation of the cycle time of the electric field starting from the different stationary states. At the other hand the influence of the different degrees of modulation on the adjustment process and its characteristic times was investigated and interpreted. For this interpretation the spectrum of adjustment times of stationary states corresponding to all momentary values of the periodic electric field strength in one cycle plays a dominant role. From the investigations follows that the adjustment times of periodic states can alter their values by some orders of magnitudes in dependence on the parameters of the electric field.     

Non-Maxwellian Electron Velocity Distribution Resulting from Electron-SF6 Attachment Collisions

A model reaction system is considered consisting of a heat bath of argon atoms (c) and small concentrations of SF₆-molecules (m) and electrons (e) (number densities: n_e ? n_m ? n_c). Within the model the time behaviour of the electron velocity distribution function is studied under the influence of elastic electron-argon collisions and electron SF₆ attachment collisions. On the basis of the distribution function time-dependent macroscopic quantities (kinetic electron temperature. nonequilibrium rate constant of the attachment reaction) are calculated.     

Electon spectroscopy using exeted atoms and photons of Penning ionization of the rare gases

A study has been made of the Penning ionization electron spectra resulting from collisions between rare gas atoms and helium metastable atoms. The results are compared and contrasted with photoelectron spectra at 584 Å. Additional bands appear in the electron spectra and are explained on the basis of fast neutral-neutral collisions involving curve crossing mechanisms. Electron spectra from mixed rare gas systems at higher pressures are examined.     

Surface heating of deuterium clusters by the field of a superintense ultrashort laser pulse for implementing the nuclear reaction d+d → 3He+n

A new mechanism for heating the electron component of plasmas formed upon the application of a superintense ultrashort laser pulse to atomic clusters is proposed. Clusters considered here consist of deuterium atoms. Upon the emission of a large number of electrons, an irradiated cluster, which acquires a positive charge, explodes (Coulomb explosion). Deuterons that are ejected as the result of this possess high kinetic energies, so that collisions between them can result in ³He formation accompanied by neutron emission. The new mechanism of the heating of the electron plasma from clusters is based on the conjecture that, when an ionization electron is reflected from the inner surface of the cluster ion in the presence of a laser field, it predominantly absorbs (rather than emits) laser photons.     

Monte Carlo study of impact ionization in n-type InAs induced by intense ultrashort terahertz pulses

Electron impact ionization induced in n-type InAs by single-cycle pulses of picosecond and subpicosecond duration has been investigated by Monte Carlo method. It is established that the rate of generation of electron–hole pairs decreases with the decrease of the pulse duration. The impact ionization threshold field is found to depend linearly on frequency for the fields oscillating at frequencies much higher than reciprocal momentum relaxation time. Good agreement between calculations and available experimental data has been obtained.     

Predicting secondary ion formation in molecular dynamics simulations of sputtering

We present a model to incorporate the excitation and ionization of sputtered particles into molecular dynamics simulations of ion bombardment-induced collision cascades in metals. The kinetic excitation of the solid is described by electronic friction experienced by all moving particles and electron promotion in close atomic collisions. Transport of the resulting excitation energy is treated by a nonlinear diffusion equation. The resulting space- and time-dependent electron temperature is then introduced into a rate equation model describing the ionization of ejected particles. This way, secondary ion formation is described by assigning an individual ionization probability to every sputtered atom. Averaging over the entire flux, this allows the prediction of measurable quantities like integral or spectral ionization probabilities as well as velocity spectra of secondary ions.     

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.     

激光触发SF6-N2混合气体开关的数值模拟

 在气体放电物理的基础上，对SF₆和N₂采用双光子电离模型，对碳氢化合物的光电离采用3能级模型，并考虑了混合气体的热电离和激光对气体的欧姆加热作用，建立了激光触发SF₆-N₂混合气体开关的数值模型，模拟了激光触发SF6-N2混合气体多级间隙开关实验。激光触发延迟时间的计算值与实验结果符合较好。理论计算表明：激光触发SF₆-N₂混合气体间隙开关的延迟时间随SF₆含量的增加呈上升趋势，而随激光脉冲能量、充气压力等的上升呈下降趋势。     

Distribution and evolution of electrons in a cluster plasma created by a laser pulse

We analyze the properties and the character of the evolution of an electron subsystem of a large cluster (with a number of atoms n～10⁴?10⁶) interacting with a short laser pulse of high intensity (10¹⁷?10¹⁹ W/cm²). As a result of ionization in a strong laser field, cluster atoms are converted into multicharged ions, part of the electrons being formed leaves the cluster, and the other electrons move in a self-consistent field of the charged cluster and the laser wave. It is shown that electron-electron collisions are inessential both during the cluster irradiation by the laser pulse and in the course of cluster expansion; the electron distribution in the cluster therefore does not transform into the Maxwell distribution even during cluster expansion. During cluster expansion, the Coulomb field of a cluster charge acts on cluster ions more strongly than the pressure resulting from electron-ion collisions. In addition, bound electrons remain inside the cluster in the course of its expansion, and cluster expansion therefore does not lead to additional cluster ionization.     

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.     

The Impact of Direct Ionization by Beam Electrons on the Electron Kinetics of the Beam Discharge Plasma in Molecular Hydrogen

In a recent paper the stationary beam plasma discharge in partially dissociated hydrogen was investigated where the electron component was described by the Boltzmann equation for a mixture of atomic and molecular hydrogen and the main heavy charged and neutral particles by balance equations. It was assumed that, via the quasilinear beam plasma interaction, the electron beam produces only the turbulent electric field whilst an additional production of plasma electrons due to direct ionization by the beam and thus a direct influence on the balances of charge carriers were neglected. Now the additional production of plasma electrons due to direct ionization by the beam is studied on the basis of a generalized Boltzmann equation but for the simpler model of a purely molecular hydrogen plasma. For experimentally obtainable values of the turbulence energy density, beam energy, beam ionization degree and electron life time the calculation of the electron energy distribution function and of the direct beam contribution to the electron particle balance shows a marked influence of the direct beam ionization with increasing degree of beam ionization.