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.     

High field transport properties in a GaN/AlGaN heterostructure

The drift velocity, electron temperature, electron energy and momentum loss rates of a two-dimensional electron gas are calculated in a GaN/AlGaN heterojunction (HJ) at high electric fields employing the energy and momentum balance technique, assuming the drifted Fermi–Dirac (F–D) distribution function for electrons. Besides the conventional scattering mechanisms, roughness induced new scattering mechanisms such as misfit piezoelectric and misfit deformation potential scatterings are considered in momentum relaxation. Energy loss rates due to acoustic phonons and polar optical phonon scattering with hot phonon effect are considered. The calculated drift velocity, electron temperature and energy loss rate are compared with the experimental data and a good agreement is obtained. The hot phonon effect is found to reduce the drift velocity, energy and momentum loss rates, whereas it enhances the electron temperature. Also the effect of using drifted F–D distribution, due to high carrier density in GaN/AlGaN HJs, contrary to the drifted Maxwellian distribution function used in the earlier calculations, is brought out.     

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)     

Conductivity in a system of ferromagnetic nanoclusters: the influence of a magnetic field

A theory of the conductivity of insulator + metal nanoclusters composites was developed. The rate constant for tunnel electron transfer between nanoclusters was obtained. Three current passage regimes are possible, regimes of weak, strong, and superstrong electric fields. At weak fields, the distribution of electrons produced in the ionization of neutral clusters is almost equilibrium. Conductivity under these conditions was calculated. A strong magnetic field dependence of the resistance of ferromagnetic clusters is possible. An exact equation for the magnetic field and temperature dependences of resistance was obtained.     

强磁场等离子体中电子的弛豫时间

用考虑磁场对碰撞影响所得的几率分布动力学方程,研究了磁场高达10~8T,密度10~(26)—10~(27)cm~(-3),温度10keV情况下的电子弛豫过程,计算了弛豫时间,并与不考虑磁场对碰撞影响时的结果进行了比较。     

Cherenkov instability of a magnetized beam-plasma system with allowance for a momentum spread of beam electrons

Cherenkov instability is considered in a completely magnetized homogeneous beam-plasma system featuring a thermal momentum spread of beam electrons. The thermal spread in the beam is described in the scope of both the hydrodynamic approach and the kinetic equation method by giving the electron momentum distribution function in the form of theMaxwellian and semi-Maxwellian distributions. It is shown that two beam-plasma instability regimes, the single-particle and collective Cherenkov effects (Compton and Raman regimes) differing by the physical mechanism and the increments, are possible in a system (waveguide) with homogeneous transverse beam and plasma density profiles. Solutions to dispersion equations for these and a more general regime are obtained and analyzed.     

Quasi-linear stage of synchrotron instability I. The limit of low initial radiation energy density

We consider the initial problem of quasi-linear relaxation of synchrotron instability in a spatially homogeneous system of relativistic electrons embedded in a cold plasma. We analyze evolution of the energy spectrum of electrons and the frequency spectrum of radiation at the limit of low initial radiation energy density. At this limit, the problem is reduced to the solution of a diffusion equation with a stationary diffusion coefficient for the electron distribution over momentum which does not depend on the initial radiation energy density. The radiation frequency spectrum is approximated by the Gaussian profile, and its parameters are expressed via the electron energy density at the given and initial instants of time. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 11, pp. 964–976, November 2006.     

Modeling of plasma-etch processes using well stirred reactorapproximations and including complex gas-phase and surfacereactions

A 0-D or well stirred reactor model determines spatially and time-averaged species composition in plasma-etch reactors, through solution of species, mass, and electron-energy balance equations. The use of well stirred reactor approximations reduces the computational expense of detailed kinetics calculations and allows investigation of the dependence of plasma chemistry on etch-process parameters. The reactor is characterized by a chamber volume, surface area, net mass flow or residence time, pressure, energy loss to surroundings, power deposition, and inlet-gas composition. The electron-energy equation includes a detailed power balance with losses to ions and electrons through the sheath, as well as inelastic and elastic collision losses. The model employs reaction-rate coefficients for electron-impact reactions, which require an assumption of the electron energy distribution function (EEDF). We compare model results using Maxwellian EEDF's, as well as reaction-rate coefficients determined as a function of average electron energy through solution of the Boltzmann equation, for chlorine chemistry. The Boltzmann rates are determined by time-lagging the equilibration of electrons with applied electric fields. The Maxwellian reaction rates give higher ionization fractions than the Boltzmann rates, affecting the predicted electronegativity and positive ion composition for chlorine plasmas. The model also shows a strong sensitivity of the plasma composition to the assumed surface-recombination probability of atomic chlorine     

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.     

Limitations of the strong field approximation in ionization of the hydrogen atom by ultrashort pulses

We present a theoretical study of the ionization of hydrogen atoms as a result of the interaction with an ultrashort external electric field. Doubly-differential momentum distributions and angular momentum distributions of ejected electrons calculated in the framework of the Coulomb-Volkov and strong field approximations, as well as classical calculations are compared with the exact solution of the time dependent Schr ödinger equation. We show that in the impulsive limit, the Coulomb-Volkov distorted wave theory reproduces the exact solution. The validity of the strong field approximation is probed both classically and quantum mechanically. We found that classical mechanics describes the proper quantum momentum distributions of the ejected electrons right after a sudden momentum transfer, however pronounced the differences at latter stages that arise during the subsequent electron-nucleus interaction. Although the classical calculations reproduce the quantum momentum distributions, it fails to describe properly the angular momentum distributions, even in the limit of strong fields. The origin of this failure can be attributed to the difference between quantum and classical initial spatial distributions.     

Fluid Model of a Sheath Formed in Front of an Electron Emitting Electrode Immersed in a Plasma with Two Electron Temperatures

The formation of a sheath in front of a negatively biased electrode (collector) that emits electrons is studied by a one‐dimensional fluid model. Electron and ion emission coefficients are introduced in the model. It is assumed that the electrode is immersed in a plasma that contains energetic electrons. The electron velocity distribution function is assumed to be a sum of two Maxwellian distributions with two different temperatures, while the ions and the emitted electrons are assumed to be monoenergetic. The condition for zero electric field at the collector is derived. Using this equation the dependence of electron and ion critical emission coefficients on various parameters ‐ like the ratio between the hot and cool electron density, the ratio between hot and cool electron temperature and the initial velocity of secondary electrons ‐ is calculated for a floating collector. A modification of the Bohm criterion due to the presence of hot and emitted electrons is also given. The transition between space charge limited and temperature limited electron emission for a current‐carrying collector is also analyzed. The critical potential, where this transition occurs, is calculated as a function of several parameters like the Richardson emission current, the ratio between the hot and cool electron density, the ratio between hot and cool electron temperature and the initial velocity of secondary electrons. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonexponential temperature dependence of the rate of threshold inelastic processes in dense media

The influence of the density of the medium on the temperature dependence of the rate constants of inelastic processes is investigated. It is shown that besides the effects like lowering of the ionization potential, which accelerate excitation and ionization processes in a nonideal plasma, there is a stronger mechanism for such acceleration, which is associated with the high frequency of collisions between particles and leads to destruction of the one-to-one relation between the energy and momentum of the particles in a dense medium. It is manifested by the presence of power-law tails in the equilibrium momentum distribution of the particles, which leads to a nonexponential temperature dependence of the rates of inelastic reactions in dense gases and nonideal plasmas. A kinetic equation for the generalized energy and momentum distribution function of electrons in an external electric field, which permits investigation of the effect under consideration under nonequilibrium conditions, is presented. Zh. éksp. Teor. Fiz. 113, 1661–1674 (May 1998)     

Monte-carlo calculation of electron transport in polar semiconductors

The momentum distribution of electrons in a polar semiconductor under the influence of an electric field is calculated using a Monte-Carlo method. The scattering is assumed to be exclusively by polar optical phonons. From the distribution function, average momentum and electron temperature are calculated, and compared with similar calculations based on a displaced Maxwellian distribution. Some characteristic features are common for the two models, in particular the phenomenon of electron cooling at low lattice temperatures. However, in contrast to the displaced Maxwellian distribution computations, the Monte-Carlo calculations show that a rapid increase of electron temperature takes place at very low fields, before the onset of cooling. Also the anisotropy of the distribution is entirely different in the two models.A detailed discussion of runaway in connection with Monte-Carlo calculations is given.     

Kinetic description of vacuum particle production in collisions of ultrarelativistic nuclei

The dynamics of partons that emerge as the result of quantum tunneling in a spatially uniform time-dependent field is studied under conditions prevalent in ultrarelativistic heavy-ion collisions. A self-consistent set of coupled equations that consists of the renormalized Maxwell equation and the Vlasov kinetic equation that involves a source and which is derived on a dynamical basis is solved numerically. The time dependence of the distributions of internal fields and currents for bosons and fermions is investigated within this back-reaction mechanism, and their momentum spectra are constructed. Clear evidence that oscillations in the time dependence of parton distributions in phase-space cells are of a stochastic character is obtained, and a significant irregularity in the momentum distribution on large time scales is found. If the influence of the back reaction is disregarded, these effects disappear completely, the oscillations becoming regular. A possible thermalization scenario for such a quasiparticle plasma is considered in the relaxation-time approximation. A locally equilibrium state is described within the two-component thermodynamics of particles and antiparticles. The possibility of introducing temperature under conditions of a strong vacuum polarization is discussed.     

Nonlocal electron kinetics in collisional gas discharge plasmas

Nonlocal phenomena in electron kinetics of collisional gas discharge plasmas, their kinetic treatment by a nonlocal approach, and relevant experimental results are reviewed in this paper. Using the traditional two-term approximation for the electron distribution function, a general method to analyze electron kinetics in nonuniform plasmas in DC and RF fields for atomic gases is presented for the nonlocal case, when the electron energy relaxation length exceeds the characteristic spatial scale of bounded plasmas. The nonlocal method, which is based on the great difference between the electron mean free path for the momentum transfer and the electron energy relaxation length, considerably simplifies the solution of the kinetic equation and, in a number of cases, allows one to obtain analytical and semi-analytical solutions. The main simplification is achieved for trapped electrons by averaging the Boltzmann equation over space and fast electron motion. Numerous examples of spatial nonlocality are considered in the positive column and near the electrodes of DC glow discharges, in spatial relaxation of the electron distribution and in striations, and in capacitively and inductively coupled low-pressure RF discharges. The modeling of fast beam-like electrons is based on a continuous-energy-loss approximation with the assumption of forward scattering. Simple analytic expressions for the fast electron spectrum are obtained in cathode regions of DC discharges with planar and hollow cathodes     

Scattering of ultrashort laser pulses on “ion‐sphere” in dense plasmas

Scattering of ultrashort electromagnetic pulses on the dense strongly coupled plasma is under consideration in the frame of hard ion sphere model. The electron distribution inside the ion sphere is obtained from self‐consistent solution of the Shrodinger equation for bound electrons and the Poisson equation for free electrons. The electron density distribution is determined by plasma electron temperatures. The ion density of Al plasmas under consideration is of the order of 10²⁰–10²² cm^?3, the electron temperature changes between 54 and 816 eV. Dynamical polarizability of the hard sphere determining the scattering cross sections is calculated using the modified local plasma frequency approximation. The spectrum of scattering cross section has maxima in the vicinity of the mean plasma frequency. Dependencies of scattering probability on carrier frequency and pulse duration are analysed in detail. The transition of the total scattering probabilities from nonlinear time dependence at small times to standard linear ones with the increase of pulse duration is demonstrated.     

Probability of electron emission in photoemission from doped semiconductor

Electron motion is investigated in a strong-field region —in the region of bending of the band close to the surface of a semiconductor. In this region there is a change in the electron distribution function under the action of the electric field and interaction mechanisms leading to energy loss of the hot electrons. The main characteristics of the external photoeffect are determined by the energy lost by the electron in the region of band bending and the size of the barrier at the semiconductor-vacuum interface. The electron-emission probability from a crystal containing a space-charge region is determined from the solution of the Boltzmann kinetic equation. The energy dependence of the energy scattering length of the hot electrons is taken into account in the calculation. The calculation is made for photoemission from GaAs in conditions when the interaction with polar optical phonons is the most effective energy-scattering mechanism. An expression is obtained for the energy distribution function of the emitted electrons for the case of strong electric fields. The position of the distribution-function maximum depends on the electric field and the effective interaction constant with phonons. The current and quantum yield of the photoeffect are calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 81–87, October, 1978.In conclusion, it remains to extend profound thanks to V. L. Bonch-Bruevich for Ms constant interest in the work.     

Multi-patch model for transport properties of cuprate superconductors

A number of normal state transport properties of cuprate superconductors are analyzed in detail using the Boltzmann equation. The momentum dependence of the electronic structure and the strong momentum anisotropy of the electronic scattering are included in a phenomenological way via a multi-patch model. The Brillouin zone and the Fermi surface are divided in regions where scattering between the electrons is strong and the Fermi velocity is low (hot patches) and in regions where the scattering is weak and the Fermi velocity is large (cold patches). We present several motivations for this phenomenology starting from various microscopic approaches. A solution of the Boltzmann equation in the case of N patches is obtained and an expression for the distribution function away from equilibrium is given. Within this framework, and limiting our analysis to the two patches case, the temperature dependence of resistivity, thermoelectric power, Hall angle, magnetoresistance and thermal Hall conductivity are studied in a systematic way analyzing the role of the patch geometry and the temperature dependence of the scattering rates. In the case of Bi-based cuprates, using ARPES data for the electronic structure, and assuming an inter-patch scattering between hot and cold states with a linear temperature dependence, a reasonable agreement with the available experiments is obtained. Received 3 August 2001 and Received in final form 1st November 2001     

飞秒强激光作用下线性等离子体层中光场和电子密度的自洽分布

自洽求解了圆偏振的飞秒强激光作用下线性等离子体层中光场和电子密度的分布.研究发现在激光有质动力的作用下，电子密度分布严重偏离离子密度分布，甚至出现了一系列的“电子岛”和“电子空腔”.由于电荷分离，等离子体内形成了很强的静电场，一部分激光能量转化为等离子体内的静电能.线性等离子体层储存静电能的大小随着入射激光强度的增加而显著上升. 关键词： 飞秒激光 相对论等离子体 电子密度 有质动力