The Electron Relaxation to Stationary States in Collision Dominated Plasmas in Molecular Gases

The temporal collision dominated relaxation of electrons to new stationary states, starting from initial stationary states and due to jump-like changes of the electric field, was studied in the plasmas of the molecular gases N₂ and CO. Numerical solving of the time dependent Boltzmann equation for the electrons yields the temporal evolution of their energy distribution function and of resulting macroscopic quantities. The varying relaxation due to different values of the field strength in the final stationary state has been investigated considering the molecules of the plasma only as vibrationally non-excited and, in another case, including the additional impact of collisions with vibrationally excited molecules. The results obtained are discussed and, in particular, the relaxation times found for the transitions to the new stationary states are analysed on the basis of the energy transfer effectiveness by the collision processes. An approximative microphysical basis for the understanding of the main features of the relaxation in such complex molecular gas plasmas could be obtained.     

Multi electron capture processes in slow collisions between X<Superscript>7+</Superscript> (X = N,O and Ne) ions with C<Subscript>60</Subscript>

Electron capture processes in collision between slow X⁷⁺ (X = N, O and Ne) ions and C₆₀ fullerene have been investigated using coincident measurements of the number n of ejected electrons, the mass and charge of the multicharged C₆₀ ^r+ recoil ions and their fragments C_m ⁱ⁺ and the final charge state of the outgoing projectiles X^(q-s)+ ( ). The collision velocity is about 0.4 a.u. The partial cross-sections σ_r ^s , corresponding to r electrons transferred to the projectile with only s electrons stabilized, have been measured. Cross-sections for collisions “inside” and those “outside” the C₆₀ cage have been separated by analyzing the kinetic energy of the outgoing projectile. The mean final charge state for frontal collisions has been measured to 3.1, 2.6 and 2.5 for N⁷⁺, O⁷⁺ and Ne⁷⁺ respectively. These results show the importance of the core effect on the stabilisation processes of captured electrons.     

Effect of electron-neutral collisions on the satellites of the Thomson scattering spectrum in arc plasmas

The effect of electron-neutral collisions on the high frequency spectrum of laser radiation scattered by the free electrons of a plasma is investigated for a partially ionized H₂ are plasma at atmospheric pressure. The calculations are carried out along Gorog's theory solving the linearized Boltzmann equation for electrons with a collision term. The collision integral is approximated by a Krook relaxation model with the collision frequency determined from experimental electron-atom scattering data. The collisions influence size, half width, and position of the high frequency satellites. In a H₂ arc plasma, the change of the satellites' position is negligible as well as the change in half width within experimentally attainable error limits. The change of size is of minor importance, since the general evaluation procedure uses only normalized scattering intensities. Thus, for laser scattering experiments in are plasmas the collision-free theory can be applied.     

Ultrasonic attenuation in the Gd-doped superconductor LaAl2

The ultrasonic attenuation (10–250MHz) in (LaGd)Al₂ with 0.23at% Gd has been measured between 293 K and 0.5 K. Below 10K the absorption is caused by superposition of phonon/electron absorption of Pippard type and a mechanical relaxation process which is attributed to a lattice defect of either vacancy, dislocation or impurity type. The relaxation takes place by interaction of the defect with both conduction electrons and lattice phonons with a mixed relaxation time. Superconductivity offers the unique chance to separate both relaxation mechanisms since during superconducting transition relaxation into the electronic system vanishes and leaves the phonon process alone to determine the defect dynamics. The temperature dependence of the individual relaxation times has been derived.     

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.     

Properties of the Collision Operators of the Electron Boltzmann Equation for a Weakly Ionized Plasma. II. Compactness Proof and Statements on the Spectrum

The compactness has been proved of the inscattering operator covering elastic, exciting and deexciting processes between electrons and heavy neutral particles. Starting point is the proof of the boundedness of the different inscattering operators for the individual collision processes using certain assumptions on the structure of the corresponding differential cross sections. Then, under somewhat more confined conditions the proff of compactness could be performed with the aid of the square integrability of an eightfold iterated kernel. On the basis of this property it was possible to draw conclusions with regard to the spectrum of the total collision operator. They are related to the continuous as well as the discrete part of the spectrum and are discussed in detail. For elastic collisions additional statements can be deduced from our investigation.     

Population processes in high-pressure inert-gas-mixture lasers

Working-level-population processes are analyzed on the basis of detailed investigations of the amplitude-time structure of the laser and spontaneous emission following a pulsed electric discharge in the mixtures He + R (R = Ar, Kr, Xe), Ar + Xe. Account is taken in the analysis of excitation by electrons (direct and stepwise) and of population as a result of relaxation processes (collisions of second kind with electrons; radiative cascades, recombination processes; collisions with the atoms of the working and buffer gases; excitation transfer from helium molecules). It is concluded that under optimum efficiency conditions inversion is produced in the lasers considered as a result of direct electron collision with the working atoms (Ar, Kr, Xe), which are in the ground state.Translated from Lazernye Sistemy, pp. 15–34, 1982.     

Der Einfluß der Stoßkenndaten auf die Elektronenkinetik in schwachionisierten Mischplasmen

The Influence of the Characteristic Quantities of the Collision Processes on the Electron Kinetics in the Low Ionized Mixture Plasm Starting from former investigations concerning the electron kinetics in the pure molecular plasma of N₂ and H₂ and in the mixtures of N₂/Ne and N₂/H₂ the influence of the important characteristic quantities of the collision processes on the isotropic distribution function and the energy balance of the electrons was studied for binary mixtures. The conclusions obtained were verified by results calculated numerically for the energy balance in the three mixtures He/Ne, N₂/H₂ and N₂/Ne which were investigated in the relevant range of the normalized electric field strength E/p₀ as a function of the mixture ratio. This analysis demonstrates the sensitive dependence of the macroscopic properties of the binary mixtures on the characteristic quantities of the collision processes of the electrons with the two components of the binary mixture.     

Spin-dependent recombination in GaAsN solid solutions

Room-temperature spin-dependent recombination in a series of GaAs_1?xN_x solid solutions (x = 2.1, 2.7, 3.4%) has been observed as manifested by a more than threefold decrease in intensity of the edge photoluminescence upon switching from circular to linear polarization of the exciting light or upon the application of a transverse magnetic field (～300 G). The interband absorption of the circularly polarized light is accompanied by the spin polarization of conduction electrons, which reaches 35% with an increase in the pumping level. The observed effects are explained in terms of the dynamic polarization of deep paramagnetic centers and the spin-dependent trapping of conduction electrons on these centers. The electron spin relaxation time, as estimated from the dependence of the edge photoluminescence depolarization in the transverse magnetic field (the Hanle effect) on the pumping intensity, is on the order of 1 ns. According to the adopted theory, the electron spin relaxation time in the presence of spin-dependent recombination is determined by a slow spin relaxation of localized electrons. The sign (positive) of the g factor of localized electrons has been experimentally determined from the direction of the magnetic-field-induced rotation of their average spin observed in the three GaAsN crystals studied.     

Mikrophysikalische Bestimmung elektronenkinetischer Kenngrößen im binären Molekül-Mischplasma von Stickstoff und Wasserstoff I. Geschwindigkeitsverteilungsfunktion,Transportgrößen und Stoß-frequenzen für Dissoziation und Direktionisation im Mischplasma

For the low ionized anisothermal plasma in a mixture of moleculare nitrogen and molecular hydrogen the isotropic part of the velocity distribution function of the electrons is calculated and compared with the experimentally determined velocity distribution. the calculation of this distribution is performed by the help of the homogeneous and stationary electron Boltzmann-equation and takes into consideration all essential collision processes between the electrons and the N₂ and H₂ molecules. Furthermore, the calculated results of the mean energy, of the transport coefficients, of the collision frequencies for dissociation and direct ionization of the molecules, of the first Townsend coefficient of the molecules and of the collision rates for the direct ionization of the N- and H-atoms in the mixture are represented for the range 6–100 V/(cm Torr) of the reduced electric field strength and for any composition of the N₂-H₂ mixture.     

Emission spectra for ArNe binary crystals

Emission spectra for ArNe binary crystals have been measured in the range of 6–18 eV at the Ar concentration of 0.01 – 100 mol%. Luminescence was excited by slow electrons at T = 5°K. The spectrum of excitons bound on the atomic and molecular type centres is observed. The energies of radiative transition in a crystal appear to be very close to those in a gas phase because of the relaxation processes at which the resonance exchange interaction decreases considerably. The bands of atomic centres display a fine structure which reflects the effect of the lattice crystal field of Ne. For the ArNe crystals it has been shown that excitons are not thermalized completely and there is the independent relaxation of the lowest states of various Wanier series to local excitons. A scheme for the relaxation process in argon involving the formation of a molecular centre Ar₂¹ is given.     

Nuclear Quadrupole spin-lattice relaxation in Rhombohedral Arsenic

The temperature dependence of the spin-lattice relaxation time T₁ in rhombohedral arsenic has been measured by nuclear quadrupole resonance. The relaxation time is inversely proportional to the temperature and of a magnitude which indicates that the relaxation results from the Fermi contact interaction of the conduction electrons and holes and the arsenic nuclei. The density of electrons and holes at the site of the nucleus, averaged over the Fermi surface is approximately 2.6 × 10²¹ carriers cm^?3.     

Electron Kinetics with Attachment and Ionization from Higher Order Solutions of Boltzmann's Equation

An appropriate approach is presented for solving the Boltzmann equation for electron swarms and nonstationary weakly ionized plasmas in the hydrodynamic stage, including ionization and attachment processes. Using a Legendre-polynomial expansion of the electron velocity distribution function the resulting eigenvalue problem has been solved at any even truncation-order. The technique has been used to study velocity distribution, mean collision frequencies, energy transfer rates, nonstationary behaviour and power balance in hydrodynamic stage, of electrons in a model plasma and a plasma of pure SF₆. The calculations have been performed for increasing approximation-orders, up to the converged solution of the problem. In particular, the transition from dominant attachment to prevailing ionization when increasing the field strength has been studied. Finally the establishment of the hydrodynamic stage for a selected case in the model plasma has been investigated by solving the nonstationary, spatially homogeneous Boltzmann equation in twoterm approximation.     

Interaction of dielectrics with femtosecond laser pulses: application of kinetic approach and multiple rate equation

We calculate the transient free-electron density in laser-irradiated dielectrics with two different approaches, both considering the energy distribution of excited electrons. The kinetic approach solves a system of complete Boltzmann collision integrals describing different excitation and relaxation processes in detail. The multiple rate equation (MRE) is an approximative way to keep track of the energy distribution of excited electrons with reduced numerical effort. Both methods are applied to trace dielectric breakdown, considering the changing optical parameters during irradiation with a high-intensity laser pulse. In the MRE approach we include also fast recombination, leading to a delay of the increase of the electronic density and to a decrease of the maximum number of free electrons.     

Optical polarization of nuclei and ODNMR in GaAs/AlGaAs quantum wells

Optical orientation of electrons was used to polarize the crystal lattice nuclei in quantum-size heterostructures and to study the effect of the conduction band spin splitting on the spin states of quasi-two-dimensional (2D) electrons drifting in an external electric field. High (～1%) nuclear polarization was registered using polarized luminescence and ODNMR in single GaAs/AlGaAs quantum wells. Measurement was made of the hyperfine interaction fields created by polarized nuclei on electrons and by electrons on nuclei. The spin-lattice relaxation of nuclei on the non-degenerate 2D electron gas was calculated. A comparison of the theoretical and experimental longitudinal relaxation times permitted the conclusion that the localized charge carriers are responsible for nuclear polarization in quantum wells in the temperature range of 2–77 K. A new effect has been studied, i.e. induction of an effective magnetic field acting on 2D electron spins when electrons drift in an external electric field in the quantum well plane. This effective field B_eff is due to the spin splitting of the conduction band of 2D electrons. The paper discusses possible registration of an ODNMR signal when the field B_eff is modulated by an electric current during optical orientation.     

离子振荡对低压脉冲负电性放电条件的影响

为了研究该离子振荡及其对低气压负电性放电自持条件的影响，建立了一个整体模型描述低气压正负离子等离子体中离子振荡与少量电子的相互作用. 在模型中引入参数r描述电子流体与电极碰撞后的动量保存(或损失)的程度. 发现体系存在一个临界值r=r_c,它导致了两种不同性质的电子损失机理. 另一临界值r=4r_c决定了两种不同的电子密度随时间增长的阈值. 这使得该阈值随r非单调变化, 进而导致RF负电性脉冲放电主动放电阶段初期的自持放电条件参数空间中可以存在间隙. PIC-MCC 关键词： 负电性放电 脉冲放电 离子振荡     

Temporal relaxation of plasma electrons acted upon by directcurrent electric and magnetic fields

On the basis of the time-dependent electron Boltzmann equation the temporal relaxation of the electrons in the presence of electric and magnetic fields in weakly ionized, collision dominated plasmas has been studied. The relaxation process is treated by using a strict time-dependent two-term approximation of the velocity distribution function expansion in spherical harmonics. A new technique for solving the time-dependent electron kinetic equation in this two-term approximation for arbitrary angles between the electric and magnetic fields has been developed and the main aspects of the efficient solution method are presented. Using this new approach and starting from steady-state plasmas under the action of time-independent electric fields only, the impact of superimposed DC magnetic fields on the electron relaxation is analyzed with regard to the control of a neon plasma. The investigations reveal an important effect of the magnetic field on the temporal relaxation process. In particular, it has been found that the relaxation time of the electron component with respect to the establishment of steady-state can be enlarged by some orders of magnitude when increasing the magnetic field strength     

Collision processes of Hydride species in Hydrogen plasmas: III. The Silane family

Cross sections are provided for most important collision processes of the Silicon‐Hydrides from the “Silanefamily”: SiH_y (y = 1 ? 4) molecules and their ions SiH⁺_y, with (plasma) electrons and protons. The processes include: electron impact ionization and dissociation of SiH_y, dissociative excitation, ionization and recombination of SiH⁺_y ions with electrons, and charge ‐ and atom ‐ exchange in proton collisions with SiH_y. All important channels of dissociative processes are considered. Information is also provided on the energetics (reactants/products energy loss / gain) of each individual reaction channel. Total and partial cross sections are presented in compact analytic forms. The critical assessment of data, derivation of new data and presentation of results follow closely the concepts of the recently published related databases for Carbon‐Hydrides, namely for the Methane family [1, 2], and for the Ethane‐ and the Propane families [3], respectively. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Energy distribution of electrons emitted from Al-Al2O3-Al system

On sandwich cathodes of the Al-Al₂O₃-Al structure were measured both the VA characteristics of leakage and emission currents and the distribution of emitted electrons according to a normal energy componentN(W _x ) for various voltages thicknesses of dielectric and upper metal films, and various voltages superimposed on cathode (leakage voltage). On the basis of experimental dependences obtained, the influence of single parts of the system on the transported electrons has been discussed. Three groups of distribution ofN(W _x ) were found differing in their form on the one hand and in their position in the energy band diagram of the studied system, on the other one. The dependence of the distribution width and the position of its maximum on the thickness of the dielectric layer and electric field intensity was followed. To describe the processes in a dielectric layer a model assuming the random collision processes has been applied. All three groups of measured distributions may be expressed by a single equation of the typeN(W _x )=N ₀(W _x ). P(z). D(W), except a small number of cases where the influence of the upper electrode barrier due to higher voltages on cathode is not taken into account and thus theD(W) term need not be considered.