Townsend coefficient,escape curve,and efficiency of runaway-electron beam formation in argon

The ionization and drift characteristics of electrons in argon are simulated by the method of multi-particle dynamics. It is shown that, in argon (as well as in other gases studied earlier), the Townsend regime of ionization sets in even in strong fields if the electrode distance is much larger than the reciprocal Townsend coefficient. The dependences of the basic ionization and drift characteristics on the reduced field intensity are obtained, and an escape curve is constructed separating the region of effective electron multiplication from the region where the electrons leave the discharge gap having no time to multiply. The formation efficiency of a runaway-electron beam is calculated. It is shown that the dependence of the electrode voltage generating a given fraction of runaway electrons on the product of the pressure by the electrode distance has a form that qualitatively agrees with the runaway curve. When the efficiency is not too high (≤20%), the runaway curves virtually coincide with isoefficiency curves.     

Townsend coefficient and runaway of electrons at relativistic velocities

An electron-multiplication regime at large field strengths, in which case an electron can acquire a relativistic kinetic energy over the multiplication length, is considered. It is shown that, even in such superstrong fields, the Townsend electron-multiplication mechanism is valid if the distance between the electrodes is rather large. The Townsend coefficient and the drift velocity in helium are obtained in such fields. The electron-escape curve, which separates the region of efficient electron multiplication from the region where electrons escape from the gap without undergoing multiplication, is obtained.     

Townsend coefficient and efficiency of the formation of runaway electrons in neon

Basic ionization and drift properties are simulated for neon by the method of multiparticle dynamics. This calculation revealed that, in neon—in just the same way as in other gases that were studied previously—the Townsend ionization regime is realized even in strong fields if the distance between electrodes is rather large. The dependences of basic ionization and drift properties on the reduced electric-field strength are obtained. The results agree with available experimental data. The escape curve separating the region of efficient electron multiplication from the region in which electrons leave the discharge gap without undergoing multiplication is found for neon. The efficiency of the formation of a runaway-electron beam in helium and neon is simulated.     

The townsend coefficient and runaway of electrons in electronegative gas

We have studied the character of variation of the number of electrons formed in an electronegative gas (SF₆) under the action of an external electric field. At any value of the electric field strength E, the number of generated electrons exponentially increases with the distance from the cathode, while the average velocity and energy of electrons attain constant values. At small values of the reduced field strength, E/p<94 V/(cm Torr) (p is the gas pressure), the regime of electron attachment prevails that is characterized by negative values of the exponent (negative Townsend coefficients). For E/p>94 V/(cm Torr), the electron multiplication proceeds in the usual Townsend regime with positive exponents. In the intermediate region of E/p=40–160 V/(cm Torr), the electron multiplication coefficient exhibits a linear dependence on E/p. Numerical calculations based on a simple model show that the Townsend multiplication regime takes place even in very strong fields where the drag caused by ionization can be ignored. A universal function describing the electron runaway in SF₆ is obtained.     

Electron swarm coefficients in 1,1,1,2 tetrafluoroethane (R134a) and its mixtures with Ar

Using a pulsed Townsend technique, we have measured the drift velocity, the longitudinal diffusion coefficient and the effective ionisation coefficient of electrons in R134a and R134a-Ar over a wide range of the density-reduced electric field intensity, E/N. Regarding the measurement of the electron drift velocities and of the effective ionization coefficients, we have covered a wider range than that hitherto achieved for pure R134a. Both the electron drift velocity and the effective ionisation coefficient have been found in very good agreement with those published in the literature, covering a shorter range of E/N. On the other hand, the swarm coefficients on R134a-Ar are, to the best of our knowledge, the first to be published. It is hoped that these data will be of interest for the test/derivation of electron collision cross sections for this important hydrofluorocarbon gas, which is nowadays of great use in gaseous detectors.     

Die Elektronenbewegung im Neutralgas bei hohen elektrischen Feldern

In strong electric fields the acceleration of the electrons by the field exceeds the deceleration by collisions with neutral molecules. Thus run-away or beam electrons are produced. This paper investigates the motion of the beam electrons in a neutral gas considering ionization processes by electron-molecule-impacts. We start with a time independent current of primary electrons (case a) and a space independant density of primary electrons (case b). The further development of the velocity distribution is calculated. For a molecular hydrogen gas the amplification of the initial electrons, the average ionization, and the velocity distribution of the electrons as a function of space or time respectively is given. The average ionization has an asymptotic solution, which becomes valid, when one primary electron has produced by ionization an avalanche of approximately 100 electrons. The Townsend coefficient α for high values of the field strength is independant of space only in the region of this asymptotic solution.     

Eine Untersuchung der Elektronenkomponente von Elektronenlawinen im homogenen Feld II

Electron avalanches in uniform fields are studied by means of a short duration spark light source. Electron drift velocities ν_? are measured in hydrogen, nitrogen, oxygen, and some vapours. It is shown, that in hydrogen and nitrogen the number of electrons increases exponentially by gas amplification with a time constant 1/αν_?, in accordance with a conventional assumption and with previous measurements in methane, α is the first Townsend coefficient. In oxygen and air it is, however, demonstrated that the number of electrons increases considerably less than exp (αυ_?·t), and the multiplication process takes longer time. This is evidently due to time losses of the electrons on their paths across the gap. Thus the mean time interval for successors, started by photons at the cathode, is increased. — In addition, this paper gives details of some measurements of the first Townsend coefficient α, the electron diffusion coefficient, and ionic drift velocities for certain gases.     

On the electron energy distribution in the gas discharge positive column: Langmuir paradox

The results of calculations of electron drift characteristics in a dc spatially inhomogeneous periodic electric field are presented. It is shown that the effect of field inhomogeneities on the drift velocity and the average electron energy is insignificant under typical conditions of experiments with gas-discharge plasma at low gas pressures. However, the intensity of the processes of excitation, ionization, and plasma spatial distribution are strongly affected by the inhomogeneity (variance) and field variation behavior. It is shown that the electric field inhomogeneity in the gas discharge positive column leads to maxwellization of the electron energy distribution function.     

Processes in condensed inert gases involving excess electrons

Drift of an excess electron in dense and condensed inert gases in external electric field and excitation of atoms by electron impact in these systems are analyzed. The effective potential energy surface for an excess electron at a given electric field strength consists of wells and hills, and the actions of neighboring atoms are therefore separated by saddles of the potential energy. At such atomic densities that the difference of interaction potentials for an excess electron between neighboring wells and hills of the potential energy surface becomes small, the electron mobility is large. This is realized for heavy inert gases (Ar, Kr, Xe) with a negative scattering length of an electron on individual atoms. In these cases, the average potential energy of the electron interaction with atoms corresponds to attraction at low atomic densities and to repulsion at high densities. The transition from attraction to repulsion at moderate atomic densities leads to a maximum of the electron mobility. A gas model for electron drift in condensed inert gases is constructed on the basis of this character of interaction. Due to high electron mobility, condensed inert gases provide high efficiency of transformation of the electric field energy into the energy of emitting photons through drifting electrons. It is shown that, although the role of formation of autodetaching states in the course of electron drift is more important for condensed inert gases than for rare gases, this effect acts weakly on exciton production at optimal atomic densities. The parameters of a self-maintained electric discharge in condensed inert gases as a source of ultraviolet radiation are discussed from the standpoint of electron drift processes.     

霍尔漂移对阳极层霍尔等离子体加速器电离效率的影响

以洛伦兹变换方法为基础,分析了阳极层霍尔等离子体加速器中电子的霍尔漂移,结果表明在交叉场中,霍尔漂移并不总是存在的,E/B的比值大于光速时,霍尔漂移将不存在.进一步的分析表明,霍尔漂移也并不总是回旋形式的,不同的电磁场配置以及不同的电子初始能量将带来不同形式的漂移,包括回旋形式,波浪线形式,甚至直线形式.电磁场的配置也决定着霍尔漂移的速度,在很大程度上影响着电子的能量,这就决定了放电时的电离效率.对不同电磁场配置进行数值模拟发现,合理的电磁场比值能够得到更好的电离效率(对于氩,这个数值大约为4×10⁶).不同的气体,根据其电离碰撞截面与电子能量的关系,都有不同的合理比值.     

Mechanism for the streamer propagation toward the anode and cathode due to background electron multiplication

A simple mechanism for the propagation of an ionization wave in a dense gas due to the multiplication of background electrons in a nonuniform electric field is proposed. The mechanism does not depend on the sign of the field projection onto the streamer propagation direction. The streamer propagation is caused by the enhancement of the electric field at the streamer head. It is shown that, in a prebreakdown field, the intense multiplication of electrons takes place in both electropositive and electronegative gases. The prebreakdown multiplication can provide a fairly high density of background electrons; this allows one to treat the background as a continuous medium when considering streamer propagation as a multiplication wave. The initial ionization is enabled by the natural background of ionizing radiation and cosmic rays. An analytical expression for the velocity of the ionization front is obtained based on a simple equation for the multiplication of background electrons. This expression is in good agreement with numerical simulations performed within both a simple model of background electron multiplication and a more comprehensive drift-diffusion model. In particular, the drift-diffusion model predicts the propagation of the ionization front from a small-radius anode to the cathode due to the multiplication of background electrons. The velocity of the ionization wave front is calculated as a function of the electric field at the streamer head for helium, xenon, nitrogen, and sulfur hexafluoride. It is shown that some features of streamer propagation (e.g., its jerky motion) can be related to the recently found nonmonotonic dependence of ionization frequency on the electric field.     

确定SF6-CO2预放电参数的激光脉冲方法

在均匀电场中,用高能激光脉冲释放初始电子以研究负电性气体的电子崩的发展,决定预放电过程的基本参数(游离系数α,吸附系数η和漂移速度v等)是一个有用的方法,本文对此方法做了详细的分析。采用这种方法对SF₆-CO₂混合气体做了研究,获得了10⁸个以上的初始电子及其分布,并给出了α/P,η/P和ν与E/P(E=电场强度,P=气体压力)的关系。本文还对所用的测量系统做了讨论,提出了改进办法。 关键词：     

Theory of a normal high-pressure glow discharge

In the present work, a theoretical model considering the processes of generation and losses of charged particles in the cathode region of a glow discharge in the drift approximation for ion and electron motion is developed. Exact analytical solutions, which can be used to calculate the current-voltage characteristics of the glow discharge in an arbitrary gas with the known Townsend ionization coefficient, are derived. The calculated parameters of the normal glow discharge (the current density, discharge burning voltage, and width of the space charge region) for different gases are in good agreement with the available experimental data. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 71–77, February, 2006.     

Stoletov constant and effective ionization potential of a diatomic gas molecule

Applying the dimension theory methods to the experimental data on static electric gas breakdown, we established the dependence of the empirical Stoletov constant on gas characteristics. This constant was shown to be 2.72 times larger than the energy expended by electrons to ionization of one gas particle (atom and molecule). Based on the analysis of elementary processes with participation of metastable levels of molecules and atoms under the optimum electron multiplication condition in a diatomic gas we concluded that the mean energy expended by the electrons to ionization of one molecule is the effective ionization potential of a gas molecule.     

Electron Kinetics in the Cathode Region of a Glow Discharge and in Hollow Cathodes

On the basis of an improved cascade model a multi-group theory for studying the electron kinetics in the cathode region of a glow discharge and in hollow cathodes is developed. The secondary electrons newly created by ionization are taken into account. The electrons are divided in groups with respect to the interval where they were created or where they made an inelastic collision. The inelastic collisions and the forward scattering are assumed to dominate. The mean energies of two neighbouring groups are taken to be different by the ionization energy or by parts of it. For the flux densities of the various electron groups a set of ordinary first order differential equations and corresponding boundary conditions are obtained and solved for He. These formulae are valid for any electric potentials. The results relatively well agree with those of Monte Carlo simulations. The first Townsend ionization coefficient differs substantially from that resulting from the Townsend formula. The velocity distribution function spatially varies and contains several groups of fast electrons. Using the detour factor the angular scattering can be included in the calculations.     

Compilation of Cross Section Data of Elementary Processes of HCI Applicable for Plasma Modeling

In this current work an cross section data for HCI elementary processes were calculated on the base of calculated and experimental data comparison on electrons drift rate and Townsend coefficients of dissociative attachment. Cross sections data of HCI electronic excitation are obtained for the first time.     

The electrical breakdown of gases in the presence of crossed electric and magnetic fields

The breakdown characteristics of a gas in the presence of crossed electric and magnetic fields are discussed in terms of the Townsend ionization coefficients. The “equivalent pressure” concept is used to assess the effect of a transverse magnetic field on the first Townsend coefficient and the objections which have been raised to the application of this approach to breakdown potentials are shown to be removed by a consideration of the dependence of the second Townsend coefficient upon electric and magnetic field strengths.     

Electron energy distribution function and dense-gas ionization in the presence of a strong field

The mechanism for dense-gas ionization is analyzed in the case when the deceleration of electrons by gas can be neglected in the equation of motion of a single electron. An expression for the electron energy distribution function in the presence of a strong field is derived. The characteristic width of the distribution corresponds to the energy acquired by the electron at a length determined by the inverse Townsend coefficient. The electron energy distributions are calculated for various distances form the cathode. It is demonstrated that the distribution becomes independent of the coordinate at a distance from the cathode that is significantly greater than the inverse Townsend coefficient. In this case, the distribution coincides with the distribution obtained with analytical calculations. The absence of the coordinate dependence is realized even in the presence of an extremely strong field when, in accordance with the commonly accepted point of view, the majority of electrons are runaway electrons.     

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.     

Electron temperature in a decaying krypton plasma in the presence of a low electric field

The influence of low electric fields on the average electron energy in an afterglow krypton plasma is studied by means of probe diagnostics and theoretical analysis. It is shown that, when the average electron energy is lower than the energy corresponding to the minimum scattering transport cross section, the degree of plasma ionization substantially affects the shape of the electron energy distribution function (EEDF). The nonequlibrium character of the EEDF results in the density dependence of the coefficient of ambipolar diffusion, which leads to a change in the radial profile of the charged particle density, an increase in the drop in the ambipolar potential across the plasma, and an increase in the rate of diffusive plasma decay. These effects substantially enhance the diffusive cooling of electrons, which is probably a decisive factor influencing the electron energy balance in high-Z noble gases.