Heating mechanism in one-dimensional bounded magnetized inductively coupled plasma

A self-consistent nonlocal kinetic model has been established to investigate the electron heating mechanism in an one-dimensional bounded magnetized inductively coupled plasma (MICP) under low pressures. The interaction function of electrons with rf electric field and electron energy distribution function (EEDF) are determined by solving the linearized Boltzmann equation incorporating with the Maxwell equations. The numerical results show that the presence of the direct-current (dc) magnetic field plays an important role in the EEDF and high-energy electrons are efficiently heated by the Azbel–Kaner resonances under the anomalous skin-effect conditions.     

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)     

Multiquantum scattering processes and transmission electron energy loss spectra

Microscopic many-body theory for electronic properties of solid states is developed with an emphasis on the role of correlation memory effects. Heisenberg equation of motion, fluctuation-dissipation theorem and operators of commutation have been used to calculate multiplasmon transmission electron energy loss spectra. Multiquantum integral kinetic equation for the longitudinal complex dielectric function is derived. Strong interaction between high-energy probe beam electrons penetrating the solid state and plasma of valence electrons is taken into account. It is shown that average number of high-frequency plasmons generated in every collision process is more than one for typical values of metal parameters. It is obtained that excitation of a good few plasmons is simultaneous event. Calculated multiplasmon structure of electron energy loss spectra coincides with experimental.     

Cascade multiplication of strongly non-equilibrium charge carriers in metals by low energy electron excitation

The steady-state distribution function of the energies of non-equilibrium electrons and holes formed as a result of a cascade of electron-electron collisions in the presence of a primary electron flux is found by solving the linearized transport equation in the isotropic scattering approximation. The distributions obtained in this way include dependences on the energy of primary electrons and on the characteristics of the medium. Near the Fermi level they have a singularity and are close to a power law far from this level. A study is made of the possibility of deriving distributions for crystals with a complex energy band structure (in particular, of tungsten).     

ELECTRON TRANSPORT BEHAVIOURS IN THE NITROGEN DIRECT CURRENT GLOW DISCHARGE

A Monte Carlo simulation is presented to describe the electron transport behaviours in the nitrogen direct current glow discharge. The energy and angular distributions of the electrons at different positions of the cathode dark space are calculated; their energy and density distribution features throughout the entire discharge are discussed. The influence of molecular vibrational excitation, typical for electron－molecule collisions, has been studied and the elementary process of active species generation has been illustrated. The simulated results reveal that, in the cathode dark space, the high-energy electrons are mainly forward scattering and behave as a high-energy ‘electron beam'. The sharp increase of the number of secondary electrons plays an important role in producing active species at the interface between the cathode dark space and the negative glow region. The vibrational excitation enhances the energy loss of electrons in the negative glow region.     

Eikonal expansion in electron scattering: I. Elastic scattering

A systematic eikonal expansion for the scattering of high-energy electrons from nuclei is derived which starts from the iterated Dirac equation. The resulting scattering amplitude is written in an impact parameter representation depending on eikonal phases which are proportional to inverse powers of the energy. The first two correction terms to the leading Glauber-Baker amplitude are calculated. For a Coulomb potential they agree with a sinθ-expansion of the relativistic Coulomb scattering amplitude. In the case of scattering from an extended charge distribution at sufficiently high energies numerical partial wave calculations are accurately reproduced.     

Kinetic theory of ionization and electron capture by a charged impurity in a semiconductor

Inelastic electron-phonon scattering in which the electron is captured or escapes from the Coulomb field of an impurity is taken into account in the kinetic equation for conduction electrons. This scattering is shown to become strong in a certain energy range. In this range, the distribution functions of free and bound electrons are correlated in such a way that there is a balance between the trapping and ionization processes. The existence of a region of strong scattering is the decisive factor in calculating the experimentally measurable trapping and ionization coefficients, which enter into the electron balance equation.     

Influence of substance characteristics on the interaction parameters of high-energy photons with free electrons

Various types of interaction of high-energy photons with free electrons in substances have been studied. It is shown that photon absorption by electrons, coherent photon scattering, noncoherent photon scattering, and electron-stopping after interaction with photons can be observed in substances. The dependence of the photon-wavelength variation after interaction with electrons on substance parameters and electron propagation velocity is obtained.     

Algorithms for statistical modeling of radiation diffusion in a medium with a reflecting surface

An algorithm has been developed for calculating the transient propagation of a narrow collimated light beam in a scattering medium near a reflecting surface. The solution is applicable to a medium with an arbitrary scattering indicatrix and particle-size distribution. The angular reflection function and the albedo of the reflector are also arbitrary. Tabulated transmission functions are supplied, which allows the algorithm to be extended to the infrared region.We are indebted to G. V. Rozenberg and V. E. Zvev for proposing the topic.     

Peculiarities of elastic scattering of intermediate-energy electrons related to their capture at quasi-stationary levels of an atom in a continuous spectrum

A theoretical model of electron scattering on an atom is constructed to study elastic atomic scattering of intermediate-energy electrons. The proposed model is based upon the combined Mensing potential with two spheres of atomic electrons, which admits analytical solutions of the radial Schröbinger equation. A procedure for matching the parameters of this scatterer to an approximate electrostatic potential of an atom in the form of a screened Coulomb potential has been determined. The screening radius of the latter potential has been calculated proceeding from the properties corresponding to the Thomas-Fermi method. A model of a scatterer determined according to the aforementioned procedure can be used to calculate the energy dependence of the cross section of elastic electron scattering on some atoms with s, p, and d shells representing elements neighboring zirconium. The main result is the establishment of factors responsible for the appearance of maxima on the energy dependences of the cross section of elastic electron scattering. These maxima are related to the resonant trapping of impinging electrons by quasi-stationary levels in a continuous spectrum.     

Monte Carlo方法模拟低能电子在Al中的散射

基于文献[1]的工作,电子在固体中的弹性散射用Mott微分截面计算;非弹性散射分为单电子激发和等离子激发并由Streitwolf、Gryzinski及Quinn的截面描述.模拟了低能电子在Al块样及薄膜中的散射过程,对不同能量低能电子作用下Al的背散射系统、能谱又透射系数作了计算,结果与实验符合较好.也对背散射电子、低能损背散射电子表面分布作了计算,结果表明低能损背散射电子具有较好的空间分辨率.     

四光束对高能电子的捕获特性研究

依据非线性强场效应的基本原理,提出了一种四光束捕获电子的方案,旨在通过延长电子和强场相互作用时间来提高非线性过程发生的总概率,实现观测信号的增强。其基本原理是基于电子在强激光光束上的非弹性散射。数值模拟结果表明,捕获后的电子和中心光场的相互作用时间得到延长。     

Calculation of coherent backscattering on the basis of Milne solution

In generalizing the Milne equation using the Wiener-Hopf method, the solution of the problem of multiple scattering by a medium with an isotropic single-scattering indicatrix for an arbitrary angle of incidence is found. The resulting solution is used as an initial approximation for calculating the intensity of coherent backscattering for an anisotropic indicatrix.     

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.     

Elastic and inelastic contributions to the auger electron appearance potential spectrum of titanium

The energy distribution of electrons contributing to the L-shell Auger electron appearance potential spectrum of a polycrystalline titanium surface has been measured. The Auger electron appearance potential spectrum is obtained by differentiating the total secondary electron yield of an electron bombarded sample as a function of incident electron energy. At the threshold for scattering from a core level the secondary yield increases. Most of the electrons contributing to this increase have energies below 30 eV, and result from secondary processes following Auger recombination of the core hole. The elastic yield decreases at the threshold, however, due to opening a new channel for inelastic scattering. A comparison of the elastic yield spectrum (DAPS), the total yield spectrum (AEAPS) and the soft X-ray yield spectrum (SXAPS), shows very similar line shapes, but differences in the relative strengths of the lines.     

Untersuchung der Prozesse in der aktiven Zone der Hohlkatodenbogenentladung I. Die Energieverteilungsfunktion der Elektronen,die Anregungs- und Ionisationsgeschwindigkeit

In this paper the processes of excitation and ionization inside the cathode of a hollow cathode are discharge will be studied. The electron energy distribution function is calculated from the kinetic equation. For this we take into account the following processes: elastic and inelastic collisions of electrons with atoms, Coulomb interaction between emitted fast electrons and electrons of the plasma.     

Separation of angular and energy relaxations of nonequilibrium electrons in a solid

We demonstrate that the collision integral of the kinetic equation for the interaction of hot electrons with phonons can be split into substantially different parts that correspond to elastic and inelastic collisions. In particular, this applies to electrons with energies of about 1 eV that propagate in semiconductors. The difference in the characteristic energy and momentum relaxation times makes it possible to separate the angular and energy relaxation processes. If the differential cross section of elastic scattering depends, not on the scattering angle, but on the directions of incident and scattered electrons (which is observed, e.g., for the interaction of an electron with piezoelectric lattice vibrations in A^IIIB^V compounds), the Laplacian in the equation that describes the spatial and energy distributions of electrons can be replaced by an elliptical operator; i.e., the electron diffusion turns out to be anisotropic.     

光子与相对论麦克斯韦分布电子散射的能谱角度谱研究

光子与相对论麦克斯韦分布电子散射的描述及能谱角度谱计算非常复杂且费时.本文提出了一种光子与相对论麦克斯韦速度分布电子散射的蒙特卡罗(MC)模拟方法,该方法能够细致模拟高温等离子体中任意能量光子与任意温度电子的Compton和逆Compton散射问题.对于散射后光子的能谱和角度谱参数,可以根据电子温度抽样若干不同状态的电子,分别模拟其与光子发生散射,可以得到各次散射后的光子能量和偏转角度,取统计平均后的结果即可获得该光子与该温度电子散射的能谱和角度谱分布.根据该方法编写了光子与相对论电子散射MC模拟程序,开展了高温全电离等离子体中光子与相对论电子散射的能谱角度谱计算和分析,分析结果显示:热运动电子将展宽出射光子能谱,且低能光子与高温电子散射后的蓝移现象明显;出射光子的角度谱很复杂,其决定于入射光子能量、出射光子能量及电子温度.基于该方法计算并以数表形式给出的光子-相对论电子散射能谱角度谱数据,可以供辐射输运数值模拟程序使用.     

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.     

Abnormal heating of low-energy electrons in low-pressure capacitively coupled discharges

In low-pressure capacitively coupled plasmas, high-energy electrons are collisionlessly heated by large rf fields in the sheaths while low-energy electrons are confined in the bulk plasma by the ambipolar potential. Low-energy electrons are typically inefficiently heated due to their low collisionality and the weak rf electric field present in the bulk. It is shown, however, that as a result of the nonlinear interaction between the electron motion and the weak rf field present in the bulk, low-energy electrons can be efficiently heated. Electrons in the bulk that bounce inside the electrostatic potential well with a frequency equal to the rf excitation frequency are efficiently heated by the coherent interaction with the rf field. This resonant collisionless heating can be very efficient and manifest itself as a plateau in the electron energy probability function.