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The effect of a pulsed (with a duration on the order of 1 ms) and of a constant external electric field on plasma-chemical processes in the lower ionosphere at altitudes of 70–100 km above the Earth’s surface is considered. Interest in these externally stimulated physical settings is associated with traditional radiophysical research and problems of radio-chemical atmospheric physics, which has been actively in recent years due to its various scientific and technical applications. A new page in this field of science (unlike the use of spurious radio signals) opens up the possibility of the purposeful field impact on a GPS receiver on the improvement of work and the further development of satellite navigation systems, which, undoubtedly, has not been discussed previously in the literature. In this work, on the basis of the numerical simulation, the concentrations of the main charged particles and the electron temperature in the presence of a strong external electric field have been calculated at an altitude of 100 km.

For stationary diffusion-type equations, we study the convergence of grid inhomogeneous boundary-value problems of a version of the mimetic finite difference (MFD) technique in which grid scalars are defined inside grid cells and grid vectors are specified by their local normal coordinates on the plane faces of grid cells. Grid equations and boundary conditions are formulated in operator form using consistent grid analogs of invariant first-order differential operators and of boundary operators. Convergence is studied on the basis of the theory of operator difference schemes; i.e., a priori estimates for the norm of the solution error in terms of the norm of the approximation error are obtained that guarantee convergence of the first order under inhomogeneous boundary conditions of the first, second, and third kind in a domain with a curvilinear boundary. Grid analogs of embedding inequalities and approximation relations obtained earlier are used.

The effects of thunderstorm activity on the plasma-chemical processes in the air at an altitude of 95–100 km are studied. Based on numerical simulation, the concentrations of the main charged particles and the temperatures of electrons under conditions of highly charged clouds are determined. Under the same conditions, the plasma composition of air at these altitudes is analyzed. It is shown that the electric fields of clouds that are charged unipolarly after streak lightning discharges increase the concentration of electrons at these altitudes, which should lead, in turn, to a marked increase in the positioning errors of global satellite systems.

Plasma-chemical processes in air are studied. Based on numerical simulations, the background concentrations of the main charged species are determined under normal conditions and at increased rates of formation of fast particle due to seismic activity. An analysis of the composition of air plasma is carried out at various humidities.

Using grids (meshes) formed from polyhedra (polygons in the two-dimensional case), we consider differential and boundary grid operators that are consistent in the sense of satisfying the grid analog of the integral identity – a corollary of the formula for the divergence of the product or a scalar by a vector. These operators are constructed and applied in the Mimetic Finite Difference (MFD) method, in which grid scalars are defined inside the grid cells and grid vectors are defined by their local normal coordinates on the planar faces of the grid cells. We show that the basic grid summation identity is a limit of an integral identity written for piecewise-smooth approximations of the grid functions. We also show that the MFD formula for the reconstruction of a grid vector field is obtained by approximation analysis of the summation identity. Grid embedding theorems are proved, analogous to well-known finite-difference embedding theorems that are used in finite-difference scheme theory to derive prior bounds for convergence analysis of the solutions of finite-difference nonhomogeneous boundary-value problems.

Results of theoretical research on ionization of dry air at different low and moderate values of constant electric field are described. Ionization processes at subthreshold, near-threshold, and suprathreshold values of electric field have been considered. Special attention to the processes of electron attachment to oxygen molecules and electron detachment from negative ions has been paid. New data on the detachment of electrons from oxygen molecular negative ions are taken into account. Plasma ionization during thermal instability has been considered.

The application of the Lagrangian completely conservative implicit operator-difference scheme for the simulation of magnetorotational (MR) processes in astrophysics is described. Results of 2D simulations of MR core-collapsed supernova explosion are represented.

Properties of a version of MFD method are studied for a grid problem on a polyhedral grid in which the grid scalars are defined on grid cells and the grid flows are specified by their local normal coordinates on the plane faces of cells. In a domain with curvilinear boundary, a grid inhomogeneous boundary value problem for stationary diffusion-type equations is considered. An operator statement of the grid problem is given, and a local approximation of the equations and boundary conditions is studied.

A principle of consistency for grid operators that ensures grid-operator inhomogeneous boundary-value problems are posed well is considered. Grid analogs of first-order differential operators and boundary operators that are consistent in the sense of fulfilling the grid analogs of integral relations are constructed on an irregular triangular grid. These relations are corollaries to the divergence theorem for vector fields that are the product of a scalar by a vector, the vector product of vectors, or the interior product of a vector by a dyadic. In each grid relation, one function is defined at the nodes; the other, in cells. Construction is performed using a grid-operator interpretation of the corollaries to the integral relations, which hold if one of the functions is a piecewise-linear interpolant to the nodal grid function, and the other is the piecewise-constant interpolant of the cell grid function.

Present investigations are devoted to analysis of air ionization at large spatial and timescales which can be realized in plasma devices. A numerical analysis of plasma creation and gas heating has been made for dry and humid air at atmospheric pressure. Sharp explosion-type rise of electron concentrations and gas temperature at long times have been obtained.

This chapter is devoted to the analysis of electron-ionization and -elimination processes at early stages of electric-discharge development in air at altitudes of mainly 0–90 km. In this chapter, ionization processes in an external electric field, as well as background ionization by fast particles and electron attachment and detachment with participation of atomic and molecular oxygen, are considered. Temperature and concentration dependences of rate constants are described. Analysis of ionization models allowing simplified approaches to detailed computation models is undertaken. It is shown that the electric breakdown process in air, under the influence of an external electric field, comprises several stages that are different with respect to different altitudes over the Earth. Numerical modeling on the basis of a detailed plasma chemical model, taking into account the heating of gas by the discharge, has shown that the relaxation processes leading to gas heating also lead to the appearance of a nonlinear stage of electric breakdown. The considered phenomena can be convenient in the consideration of a high-altitude origination of natural discharges in fields of thunderstorm clouds.

Grid analogs of invariant first-order differential operators and boundary operators are constructed on an irregular triangular grid. They are consistent in the sense of satisfying the grid analogs of integral relations that are consequences of the Gauss-Ostrogradskii formula for the divergence of a vector field as the product of a scalar and a vector, the vector product of vectors, or the inner product of a vector and a dyad. Construction is done using a grid-operator interpretation of integral relations written for piecewise linear interpolations of grid functions defined at the grid nodes. It is shown how to use consistent grid operators in constructing correct grid approximations of inhomogeneous boundary value problems at the operator level.

Computer investigations devoted to hot filaments of streamer microwave (MW) discharge features and to shock wave (SW) (M ≈ 1.5) propagation through the MW filaments area have been made. Analysis of SW propagation through the hot filaments showed that there is a strong influence on SW, which leads to SW destruction at some filament forms and displacement. This shows a possibility of MW discharge hot filament applicability for technologies.

This paper is devoted to analysis of humid air plasmas of pulsed discharge application possibilities for heating of thin layers over water surface where the concentration of water molecules in a layer over water surface contains ~0.5%-4% of water molecules in the temperature range 30 °C-110 °C. Main neutral and charged components have been calculated with the help of detailed plasma-chemical code. Considerable generation of ozone has been detected. This can explain the results of successful discharge sterilization experiment.

Studies of a plasma jet formation and its injection into a propane-air mixture's counterflow have been performed regarding enhancing combustion and ignition by plasma jets. A computational model involves a realistic equation of state, plasma radiation associated with plasma formation inside the plasma generator, and coupling between the internal nozzle and external flow fields. A one-step effective propane-oxygen chemical reaction with energy release was used for modeling of ignition and combustion. Our model uses an Implicit Free-Lagrange method for the computations. The results of computations demonstrate the ignition of propane-air mixtures stimulated by plasma jet generators, each with a power of 15 kW. The incident propane-air stoichiometric mixture temperature is 1000 K.

Plasma jet ignition and combustion of stoichiometric propane-air mixture are considered at application of a flat plasma jet in the crossflow. Computationally, it is demonstrated that a flat plasma jet from a slot creates a combustion wave in the fuel that realizes the combustion.

Investigations on creation of a non-selfmaintained discharge based on electron beam from the electron accelerator EOL-400M for impact on propane-air mixture have been made. Experiments on detection of some plasma and gas parameters have been realized. Works on modeling of electron-molecule processes in propane-air mixture in external electric field and E-beam at different values of stoichiometricity have been realized.

Theoretical modeling of electron-molecule processes in propane-air mixture in external electric field and electron beam have been made. Evolution of main charged and neutral particles in time has been obtained. Gas temperature evolution has allowed to make conclusions on the ignition of propane-air mixture at different concentrations of propane in humid propane-air mixture. The delay time of ignition decreases in lean mixtures.

A plasma-aerodynamic model of the interaction of airflow and E-beam (EB) plasma has been developed. The results of the 2-D numerical simulation of the process of plasma jet generation under EB impact in air are presented. The complicated structure of plasma flow is caused by the nonuniformity of EB power put into the gas. The generation of active particles NO+ and NO takes place during the EB-flow interaction.

We present the results of two-dimensional calculations of a magneto-rotational (MR) supernova explosion with a collapsing core for various core masses, rotational angular momenta, and magnetic-field configurations. It is shown that the MR mechanism produces an explosion energy that corresponds to observed values. The form of the explosion depends substantially on the initial configuration of the magnetic field. MR instability develops during the evolution of the magnetic field in an MR supernova explosion, resulting in an exponential increase of all components of the magnetic field, thereby substantially decreasing the time scale of the MR explosion. The energy of the supernova increases with the core’s mass and initial rotational energy.

The projection approach is applied to construct and investigate an operator-difference scheme for fluid dynamics in Lagrangean variables which has first-order local approximation in the axisymmetric case near the symmetry axis. The scheme also has operator properties that make it suitable for rederiving and substantiating previous results, methods, and algorithms.

The projection approach is applied to construct and investigate a grid fluid-dynamic problem in moving coordinates, which is operator in space and differential in time. The grid problem has a first-order local approximation near the symmetry axis in the axisymmetric case and is well-posed (i.e., uniquely solvable and stable) in the linear approximation.

A new case of probe diagnostics of plasma density under the condition typical for plasma aerodynamic applications (high voltage and electric e eld, high nonequilibrium between components, high gas pressures, and a considerable compression effect ) has been examined. The experiments have been carried out in dc and pulsed periodic discharges in supersonic aire ows with Mach number M = 2 at the static ambient pressure range 10 ‐200 torr. A personal-computer controlled double probe with an optogalvanic isolation based on an optocoupler and a e ber optical waveguide have been developed and tested in the gas discharges. A new theory of probe diagnostics of plasmas with a very high electric e eld in a supersonic aire ow is developed based on a computer simulation of the interaction of the probe and the plasma e ow. A combined effect of the e ow compression and the electric e eld perturbation on the plasma density near the probe is revealed. This effect can limit the area of applicability of the probe diagnostics. Measures to prevent this negative effect are suggested. The results of probe diagnostics of the plasma density are in good agreement with those obtained using the microwave interferometer and the spectral method.

Studies of a plasma jet interaction with cross flows has been made for a development of a concept of plasma jets flow control application. A magneto plasma compressor is considered as a promising plasma jet, which parameters and characteristics are given. A computer simulation of a cross flow nitrogen plasma nitrogen jet from the divergent plasma generator has been carried out. This model involves a realistic equation of state, plasma radiation associated with plasma formation inside the plasma jet as well as coupling between the internal nozzle with external flow fields. Our model facilitates the application of the implicit free-Lagrange method for carrying out of computations, which have been carried out for jet injection angles 135° into the cross flow. These show the complex and non-homogeneous structure of the flow. They represent the necessary step in understanding of applicability of the plasma jets for a flow control.

Present investigations have been devoted to analysis of electron ionization and elimination processes at early stages of electric discharge development at altitudes 0$100 km. In the report we consider processes of ionization in the external field and due to background ionization, as well as of attachment, detachment of electrons in collisions with atomic and molecular oxygen, charge$exchange and conversion of negative ions. Pr essure dependences of rate constants have been taken into consideration. It is shown that a significant decrease of the breakdown electric field takes place at altitudes 30$100 km due to dec rease of molecular oxygen with which a velocity of negative ions conversion process decreases.

Works on non-selfmaintained discharge system with a help electron beam installation for impact on propane-air mixture have been considered. New type of compact sealed off electron beam installation has been discussed. Works on modeling of electron-molecule processes in lean propane-air mixture in external electric field under impact of the E-beam and external electric field have been made. I. Introduction his paper is devoted to continuation of investigations [1-3] on application of the nonselfmaintained discharge with the application of the electron beam (Eb) accelerator for irradiation of the propane-air mixture. In [1-3] we have created the experimental chamber, controlling devices and the diagnostic complex for Eb experiments. First experiments on inflammation of the flammable mixture in the chamber at the application of the ignition system, of the external electric field and of the ignition system and a combination of the Eb and the electric field in air and flammable mixture have been fulfilled. In the experiments we used the industrial electron accelerator EOL -400M have. The combination of the external electric field and the electron-beam plasma create a non-selfmaintained discharge. The Plasma of the non-selfmaintained discharge has been realized in the conditions without the ignition of the propane-air flow and with it. Experiments on the inflammation of the flammable mixture [1-2] in the chamber and at the injection of the beam into air and flammable mixture have been fulfilled. Experiments have shown sharp increase in the temperature at application of

NOx in exhaust gases of the airplane engine is considered. As a fuel were considered hydrogen and ethylene. Air arriving in the engine had static pressure and temperature corresponding to height of 20 km. Also considered questions of NO formation at electric fields origination near an aircraft.

Works on creation of ignition system of non-selfmaintained discharge based on electron beam from the electron accelerator EOL -400 M for impact on propane-air mixture have been continued. Experiments on development of the ignition system have been realized. Works on modeling of electron-molecule processes in propane-air mixture in external electric field under impact of the ignition system and E-beam have been made.

Н3О + , Н3О + (Н2О), Н3О + (ОН), Н3О + (Н2О)2, Н + (Н2О)2, Н + (Н2О)3, Н + (Н2О)4 negative ions О - , О2 - , О3 - , Н - , ОH - , atoms О and Н, molecules Н2, О2, Н2О, О3, free radicals ОН, НО2, Н2О2, excited states

We consider a number of computational features of two-dimensional Lagrangian schemes on triangular grids: loss of approximation near the axis (cylindrical symmetry) and measures to counteract this effect; approximation and operator interpretation at corner points where the type of the boundary conditions changes; loss of stability with free approximation of type II boundary conditions; distortion of the Lagrangian grid associated with first-order accuracy on the boundary of an irregular grid.

Fundamental theoretical and computer investigations devoted to analysis of hot filaments of streamer MW discharge features and to shock wave propagation through the disturbed by MW filaments area has been made. This analysis includes: a) modeling of the hot fila- ment heating in dead air; b) modeling of SW (M=2) propagation through the hot filament; c) consideration of different filament forms and temperatures. Analysis has shown that rise of the filament temperature up to 2500-3000 K and producing of high concentrations of O and NO components can decrease ignition time of hydrocarbon fuel by hot MW filaments. Analysis of shock wave (SW) propagation through the hot filaments showed that there is strong influence on SW, which leads to SW destruction if long filaments directed in the same way as the SW. This shows the possibility of MW hot filament applicability for flow control.

Studies of plasma jet injection into a propane-air mixture counterflow have been performed regarding enhancing combustion and ignition by plasma jets. A computational model that we have used is discussed that involves a realistic equation of state, plasma radiation associated with plasma formation inside the plasma jet as well as coupling between the internal nozzle and external flow fields. A one-step effective propane-oxygen chemical reaction model with energy release was used for simulating ignition and combustion. Our model uses an implicit free- Lagrange method for the computations. Results of computations demonstrated ignition of propane-air mixtures stimulated by plasma jet generators each with a power of 15 kW. The incident propane-air stoichiometric mixture temperature was 1000 К. This concept can be applied for creation of quasi-planar jets in a real scramjet using a row of such plasma generators For analysis of ignition and combustion properties of the hydrocarbons in air it is necessary choose the key chemical reactions leading to them. The literature on propane combustion is rather vast and includes different approaches to combustion modeling 7-13

An application of electrical probes for measurements of electric discharge plasma density in supersonic air and air-propane mixture flows and corresponding flame plasmas have been investigated. The electric discharges igniting supersonic air-propane flow have been DC and pulsed ones, and pulsed plasma jets injected into a supersonic flow. Both designs of probe measurement circuits and methods of probe characteristics processing in case of single and double probe have been developed.

Studies of plasma jet injection into quiescent nitrogen and air as well freestream crossflows have been performed regarding enhancing combustion and ignition by plasma jets. A computer simulation of nitrogen plasma jet with divergent conical nozzle in a motionless nitrogen and nitrogen incident flow has been carried out. This model involves a realistic equation of state, plasma radiation associated with plasma formation inside the plasma jet as well as coupling between the internal nozzle and external flow fields. Our model uses an implicit free-Lagrange method for the computations, which have been performed for jet injection angles and conditions close to known experiments. These show the complex and non-homogeneous structure of the flow. Equilibrium densities of atoms and ions in plasma were computed. The atom concentrations are shown to be of the same order of magnitude as the neutral molecule density. Initial experiments with plasma jets have started. Two embodiments of stationary plasma generator with vortex flow stabilization and a diverging plasma nozzle have been constructed. The first plasma generator is a large device for application to complex chemically aggressive media. The second plasma generator is a compact apparatus. It can be applied for creation of a quasi-plane jet in a real scramjet using a row of such plasma generators. Analysis of radiation spectra of the first generator plasma jet shows that for the range of power (input in the plasma relaxation region just downstream of the nozzle exit) the gas temperature lies in the range Tg = (3500 - 6600°) K. This is sufficient for ignition of hydrocarbon fuels

A scientific session of the Division of General Physics and Astronomy of the Russian Academy of Sciences was held on May 14, 1997 at the P L Kapitza Institute for Physical Problems, RAS. The following reports were presented at the session: (1) Mineev V P, Vavilov M G (Landau Institute of Theoretical Physics, RAS, Chernogolovka, Moscow Region) ''De Haas—van Alphen effect in superconductors''; (2) Volkov V A, Takhtamirov E E (Institute of Radio-Engineering and Electronics, RAS, Moscow) ''Dynamics of an electron with space-dependent mass and the effective-mass method for semiconductor heterostructures''; (3) Sukhorukov A P (M V Lomonosov Moscow State University, Moscow) ''New avenue of investigation in the physics of solitons: parametrically-coupled solitons in a quadratically-nonlinear medium''; (4) Bogatov A P (P N Lebedev Physics Institute, RAS, Moscow) ''Optics of semiconductor lasers''; (5) Korovin S D (Institute of High-Power Electronics, Tomsk) ''Generation of high-power microwave radiation on the base of high-current nanosecond electron beams''; (6) Ardelyan N V, Bisnovatyi-Kogan G S, Moiseenko S G (M V Lomonosov Moscow State University, Moscow; Institute of Space Research, Moscow) ''Explosion mechanisms of supernovae: the magnetorotational model''; (7) Slysh V I (Astrocosmic Centre of the P N Lebedev Physics Institute, RAS, Moscow) ''Stars, planets, and cosmic masers''. Summaries of four (1, 2, 6, 7) of the reports are given below.