Simulation of a two-dimensional binary gas mixture outflow into vacuum through a thin slit on the basis of direct solution of the Boltzmann kinetic equation

Two-dimensional binary gas mixture outflow from a vessel into vacuum through a thin slit is studied on the basis of direct solution of the Boltzmann kinetic equation. For evaluation of collision integrals in the Boltzmann equation a conservative projection method is used. Numerical simulation of a two-dimensional argon-neon gas mixture outflow from a vessel into vacuum was performed. Graphs of mixture components flow rate dependence on time during the flow formation, as well as fields of molecular density and temperature for steady-state regime, were obtained.

Analytical solution to the problem of diffusion of the light component of the binary gas mixture in a plane channel

Within the framework of the kinetic approach, an analytical solution to the problem of diffusion of the light component of a binary mixture in a flat channel with infinite parallel walls is constructed. It is assumed that the mass of light component molecules and their concentration is much less than the mass of molecules and the concentration of heavy components. The flow rate of the heavy component is assumed to be zero. The change in the state of a light gas component is described on the basis of the BGK (Bhatnagar, Gross, Kruk) model of the Boltzmann kinetic equation. The diffuse reflection model is used as a boundary condition on the channel walls. The mass velocity profile of the light gas component is constructed. The flow rate of the light gas component per unit channel width is calculated. A comparison with similar results presented in open sources was done.

Tracing X-ray-induced formation of warm dense gold with Boltzmann kinetic equations

In this paper, we report on the Boltzmann kinetic equation approach adapted for simulations of warm dense matter created by irradiation of bulk gold with intense ultrashort X-ray pulses. X-rays can excite inner-shell electrons, which triggers creation of deep-lying core holes. Their relaxation, especially in heavier elements such as gold (atomic number $$Z= 79$$ Z = 79 ) takes complicated pathways, involving collisional processes, and leading through a large number of active configurations. This number can be so high that solving a set of evolution equations for each configuration becomes computationally inefficient, and another modeling approach should be used instead. Here, we use the earlier introduced ’predominant excitation and relaxation path’ approach. It still uses true atomic configurations but limits their number by restricting material relaxation to a selected set of predominant pathways for material excitation and relaxation. With that, we obtain time-resolved predictions for excitation and relaxation in X-ray irradiated bulk of gold, including the respective change of gold optical properties. We compare the predictions with the available data from high-energy-density experiments. Their good agreement indicates ability of the Boltzmann kinetic equation approach to describe warm dense matter created from high-Z materials after their irradiation with X rays, which can be validated in future experiments. Graphic Abstract

Modeling the dynamic properties of iii-nitrides in strong electric fields

This paper proposes a method of modeling the dynamic properties of multi-valley semiconductors. The model is applied to the relevant materials GaN, AlN, and InN, which are now known by the general name of III-nitrides. The method is distinguished by economical use of computational resources without significant loss of accuracy and the possibility of application for both dynamic time-dependent tasks and the fields variable in space. The proposed approach is based on solving a system of differential equations, which are known as relaxation ones, and derived from the Boltzmann kinetic equation in the approximation of relaxation time by the function of distribution over k-space. Unlike the conventional system of equations for the concentration of carriers, their pulse and energy, we have used, instead of the energy relaxation equation, an equation of electronic temperature as a measure of the energy of the chaotic motion only. Relaxation times are defined not as integral values from the static characteristics of the material but the averaging of quantum-mechanic speeds for certain types of scattering is used. Averaging was carried out according to the Maxwellian distribution function in the approximation of electronic temperature, as a result of which various mechanisms of dispersion of carriers are taken into consideration through specific relaxation times. The system of equations includes equations in partial derivatives from time and coordinates, which makes it possible to investigate the pulse properties of the examined materials. In particular, the dynamic effect of the "overshoot" in drift velocity and a spatial "ballistic transport" of carriers. The use of Fourier transforms of pulse dependence of the drift carrier velocity to calculate maximum conductivity frequencies is considered. It has been shown that the limit frequencies are hundreds of gigahertz and, for aluminum nitride, exceed a thousand gigahertz

On Analytical Solution of a Plasma Flow over a Moving Plate under the Effect of an Applied Magnetic Field

Our objective of this investigation is to mainly focus on the behavior of a plasma gas that is bounded by a moving rigid flat plate; its motion is damping with time. The effects of an external magnetic field on the electrons collected with each other, with positive ions, and with neutral atoms in the plasma fluid are studied. The BGK type of the Boltzmann kinetic equation is used to study the gas dynamics various regimes with Maxwellian velocity distribution functions. An analytical solution of the model equations for the unsteady flow was given using the moment and the traveling wave methods. The manner of the mean velocity of plasmas is illustrated, which is compatible with the variation of the shear stress, viscosity coefficient, and the initial and boundary conditions. Besides, the thermodynamic prediction is investigated by applying irreversible thermodynamic principles and extended Gibbs formula. Finally, qualitative agreements with previous related papers were demonstrated using 3-dimensional graphics for calculating the variables. The significance of this study is due to its vast applications in numerous fields such as in physics, engineering, commercial, and industrial applications.

On Analytical Solution of a Plasma over a Moving Rigid Plate under the Influence of Non-linear Non-uniform Applied External Magnetic Field

In this study, we mainly focus on the behavior of an electron gas produced by argon plasma that is bounded by a moving rigid flat plate. The effects of an external magnetic field on the electrons collected with each other, with positive ions, and with neutral atoms in the plasma fluid are investigated. We used the BGK model of the Boltzmann kinetic equation, which is fundamental in the study of the gas dynamics from the continuum flow to the free-molecular regimes with Maxwellian velocity distribution functions of the various species. An exact analytical solution of the model equations for the unsteady flow is given using the moment and the traveling wave methods. The behavior of the mean velocity of electrons is illustrated, which compatible with the variation of the shear stress, viscosity coefficient, and the initial and boundary conditions. Besides, the thermodynamic prediction is investigated by applying the principles of irreversible thermodynamics and Gibbs formula. It is found that the thermodynamic variables verify the Boltzmann’s H–theorem, the principle of Le Chatelier, and the Thermodynamics Second Law for the non-equilibrium processes of the system. Qualitative agreements with previous related papers are introducing. 3-Dimensional graphics for the calculating variables are offering, and their behavior is deeply discussed.

Characteristics of the Nanosecond Overvoltage Discharge Between CuInSe2 Chalcopyrite Electrodes in Oxygen-Free Gas Media

The characteristics of the nanosecond overvoltage discharge ignited between semiconductor electrodes based on the CuInSe2 chalcopyrite compound in the argon and nitrogen atmospheres at gas pressures of 5.3–101 kPa are reported. Due to the electrode sputtering, chalcopyrite vapor enters the discharge plasma, so that some CuInSe2 molecules become destroyed, whereas the others become partially deposited in the form of thin films on solid dielectric substrates located near the plasma electrode system. The main products of the chalcopyrite molecule decomposition in the nanosecond overvoltage discharge are determined; these are atoms and singly charged ions of copper and indium in the excited and ionized states. Spectral lines emitted by copper and indium atoms and ions are proposed, which can be used to control the deposition of thin chalcopyrite films in the real-time mode. By numerically solving the Boltzmann kinetic equation for the electron energy distribution function, the electron temperature and density in the discharge, the specific losses of a discharge power for the main electronic processes, and the rate constants of electronic processes, as well as their dependences on the parameter E/N, are calculated for the plasma of vapor-gas mixtures on the basis of nitrogen and chalcopyrite. Thin chalcopyrite films that effectively absorb light in a wide spectral interval (200–800 nm) are synthesized on quartz substrates, by using the gas-discharge method, which opens new prospects for their application in photovoltaic devices.

Velocity and Absorption Coefficient of Sound Waves in Classical Gases

The velocity and absorption coefficient of plane sound waves in classical gases are obtained by solving the Boltzmann kinetic equation. This is done within the linear response theory as a reaction of the single-particle distribution function to a periodic external field. The nonperturbative dispersion equation is derived in the relaxation time approximation and solved numerically. The obtained theoretical results demonstrate an universal dependence of the sound velocity and scaled absorption coefficient on the variable wт , where w is the sound frequency, and т−1 is the particle collision frequency. In the region of wт ∼ 1, a transition from the frequent- to rare-collision regime takes place. The sound velocity increases sharply, and the scaled absorption coefficient has a maximum – both theoretical findings are in agreement with the data.

Estimation of the charged defect density from hot-electron transport studies in epitaxial ZnO

High-field electron transport measurements by applying short (few ns) voltage pulses on nominally undoped n-type Zn-polar ZnO epilayers are reported and interpreted in terms of the Boltzmann kinetic equation. The transient measurements do not demonstrate a significant change in the electron density up to 320 kV/cm electric field. This result together with the experimental data on the current allows one to estimate the electron drift velocity from the measured current: the highest value of ~2.9 × 107 cm/s is obtained at the pre-breakdown field of 320 kV/cm for the ZnO layer with the electron density of 1.5 × 1017 cm–3. The densities of double-charged oxygen vacancies (~1.6 × 1017 cm–3) and other charged centres (~1.7 × 1017 cm–3) are assumed for the best fit of the simulated and measured hot-electron effect. A correlation with the epilayer growth conditions is demonstrated: the higher Zn cell temperature favours the formation of a higher density of the oxygen vacancies (1.9 × 1017 cm–3 at 347°C).