Motion of a two-temperature plasma in the channel of a disc-type magnetohydrodynamic generator

A study was made of the fully developed homogeneous flow of a two-temperature partially ionized plasma in the channel of a disc-type Hall generator. Experiments with a disc-type generator are described in [1, 2]. In a simplified statement, the problem is analogous to that considered in [3]. The present article takes the chemical reactions of ionization and recombination into account. The energy equation for an electron gas is brought down to a differential form which permits clarification of the question of the applicability of the Kerrebrock [4] formula for the difference in the temperatures of the electrons and the heavy particles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 18–25, November–December, 1970.In conclusion, the author thanks V. V. Gogosov for his interest in the work and for his valuable observations.     

Kinetics of electron recombination in a molecular gas expanding into a cavity

The kinetics of recombination in a diatomic or polyatomic gas dispersing into a cavity is investigated in a model gas with one ionization potential and one electron affinity. In addition to the recombination reaction in triple collisions, which play the most important role in the case of a monatomic gas [1], dissociative recombination, ion-atom charge transfer, and reactions involving negative ions are considered. The qualitative differences in the kinetics of recombination of a molecular gas (in comparison with a monatomic gas) are due to the smallness of the relative electron concentrations at the instant of disturbance of ionization equilibrium and to the important contribution of dissociative recombination reactions and the kinetics of formation and recombination of negative ions.In addition, owing to the greater specific heat of a polyatomic gas and the corresponding lower rate of cooling on dispersion, recombination due to collision of three charged particles is not, as distinct from the case of a monatomic gas, decisive for the asymptotic values of the adiabatic exponent and residual ionization. For this reason the values of the adiabatic exponent can be assigned irrespective of a in the solution of the equations of the kinetics of recombination of diatomic and polyatomic gases. Expressions for the instant of failure of the equilibrium relationship between electrons and, respectively, positive and negative ions are obtained.The relationship between the charged-particle concentration in a gas in ionization nonequilibrium and the time for known values of the reaction rate constants is expressed by quadratures. The values of the rate constants of some ionization processes are known only in order of magnitude. However, available data on rate constants indicate that for practically any initial data for dispersion of the products of explosion or combustion of chemical compounds ionization equilibrium is upset at a time when there is still an equilibrium ratio of concentrations of electrons and negative ions.     

Contraction of a highly nonequilibrium current-bearing plasma

Contracted is the term applied to that inhomogeneous state of a plasma in which it withdraws from the enclosing walls and concentrates in a more or less thin layer through which a current passes. Contraction is the result of instability developed in the original homogeneous state and may be related to the existence of a volt-ampere characteristic segment with negative differential conductivity. This phenomenon is known in semiconductor physics, and various instability mechanisms leading to contraction have been studied [1], Well known in a low-temperature plasma is thermal contraction connected with superheating instability of the electron gas [2–4]. In the present study we will consider a highly nonequilibrium plasma in which contraction may develop as a result of disproportion in the number of electrons, i.e., contraction of a recombination-ionization character. We consider below the homogeneous state of a nonequilibrium weakly ionized plasma with charged-particle concentration n_e- 10¹¹-10¹³ cm^–3 (electron temperature T of the order of thousands of degrees, with gas cold). Disequilibrium is produced by the departure of radiation beyond the limits of the plasma volume. Such a state will be considered with respect to the instability noted, but not studied, in [5]. As a consequence of this instability the plasma may transform to an inhomogeneous (contracted) state, which is considered under conditions such that Joulean electron heating is compensated by losses due to elastic collisions with atoms of the gas. Charge diffusion plays the basic role in establishing the boundaries dividing the currentbearing region from that without current. More complex is the situation where radiation losses of energy are also significant and superheating, as well as ionization instability, is possible. This case is evaluated briefly at the close of the study.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 45–54, January–February, 1975.     

The boundary layers of a fully ionized two-temperature plasma with given component temperatures at an electrode

The flow of a plasma with different component temperatures in the boundary layers at the electrodes of an MHD channel is investigated without any assumptions as to self-similarity. For the calculation of the electron temperature, the full energy equation for an electron gas [1] is solved with allowance for the estimates given in [2]. In contrast to [3, 4], the calculation includes the change in temperature of electrons and ions along the channel caused by the collective transport of energy, the work done by the partial pressure forces, and the Joule heating and the energy exchange between the components. The problem of the boundary layers in the flow of a two-temperature, partially ionized plasma past an electrode is solved in simplified form by the local similarity method in [5–7]. In these papers, either the Kerrebrock equation is used [5, 6] or the collective terms are omitted from the electron energy equation [7].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 3–10, September–October, 1972.The author thanks V. V. Gogosov and A. E. Yakubenko for interest in this work.     

Applicability of a model of the formation of a molecular beam under conditions of translational disequilibrium

In the model of the formation of a molecular beam proposed in [1], Kantrowitz and Grey assumed ideal conditions, namely, the gas stream expands in accordance with an isentropic law, the introduction of the skimmer into the gas stream does not disturb the flow upstream, and the entrance section of the skimmer is the surface of the last collisions. In reality, these assumptions are not always satisfied. In the case of rapid expansion of a supersonic stream of rarefied gas there is a departure from isentropic behavior because of the freezing of the relaxation processes, and the formation of a molecular beam by means of a skimmer changes the gas-dynamic parameters [2, 3]. The aim of the present work was to make a direct experimental verification of the applicability of the model of molecular beam formation from a supersonic stream of rarefied gas under conditions of translational disequilibrium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 170–173, May–June, 1980.     

The flow of a nonequilibrium ionized radiating gas around a body with consideration of temperature difference between electrons and ions

The flow around a blunt body at hypersonic speed by a current of nonequilibrium ionized monatomic nonviscous radiating gas is studied, with consideration of temperature difference between the electron gas and the ion-atom gas. Atomic excitation due to collisions with electrons and subsequent ionization, as well as photoionization, are taken into consideration. Since the value of the shock wave separation is small in comparison with the characteristic dimension of the body, the radiation transfer equation is written in the local onedimensional planar layer approximation. The influence of incident flow parameters upon the flow field across the shock wave and the distribution of radiation thermal flux are studied.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 9–14, January-February, 1972.     

Decay of a plasma produced by a pulsed beam of accelerated electrons in an He-Ne mixture at high pressure

Increased interest has recently been shown in the low-temperature plasma produced by the action of electron beams on dense gases. This interest is due to the possibility of investigating plasma-chemical reactions in highly nonequilibrium conditions [1] and also to the prospect of introducing new methods of pumping gas lasers: by recombination [12], charge transfer [3], the formation of complex compounds [4, 5], etc. The plasma in question is characterized by high rates of reactions involving charged and neutral particles, which largely accounts for the difficulty of investigating such a plasma experimentally. For instance, problems of determining the kind of ions predominating in the plasma, the mechanism of recombination decay, the nature of the luminescence on individual spectral transitions, etc., become nontrivial. In this paper we investigate the decay of a plasma in neon and in an He-Ne mixture at high gas pressure.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 16–22, January–February, 1978.We thank G. A, Mesyats for assistance in this work and Yu. I. Bychkov and V. V. Ryzhov for discussion of the results.     

Some methods of calculating the steady motion of a rarefied gas

Vacuum molecular pumps have been long known and have several advantages [1–3].Several studies have been devoted to the design of vacuum molecular pumps [7–10]. The methods developed in these studies have been based either on the formulas for gas diffusion in long pipes or on the integral equations of material balance. However, these theories do not permit obtaining design data for real designs of molecular pumps which are close to the experimental data, and, moreover, do not permit solving the practically important problem of optimizing the parameters and geometry of the molecular and turbomolecular pumps with respect to output and compression ratio. The calculations made in [8–10] are valid only for rotor speeds which are much less than the average velocities of the gas molecules. However, the studies in the second direction cannot be continued to a final result in view of the extreme complexity of the solution of the resulting system of integral equations.In the following we describe the calculation of vacuum molecular pumps, based on the Monte-Carlo method (the Monte-Carlo method has been used to calculate the conductance of the elements of vacuum lines in the free molecular regime in [4, 5, 6] and to calculate using the method of sequential approximations the flow of a rarefied gas with account for the collisions between molecules in [11]).We shall apply this method not only to systems with a high vacuum, when the collisions between molecules may be neglected, but also to systems in which in addition to the molecule collisions with the wall it is necessary to consider the possibility of a small number of mutual collisions.     

On stream inhomogeneities in a pulsed electromagnetic accelerator

In a number of papers [1–7] carried out on various pulsed electromagnetic accelerators the appearance of a lamellar structure in the stream of accelerated ionized gas occurs having an oscillation frequency of several megahertz. The majority of authors relate the development of irregularities in the stream with local peculiarities in the flow of electric currents (secondary breakdowns [6], the formation of micropinches [3–5], the motion of a current spiral [2], etc.). Notwithstanding the generality of many properties of the irregularities recorded under various conditions, no unified point of view exists as yet concerning the nature of their development.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 143–149, July–August, 1970.     

Flow of a dual-temperature plasma in the channel of a disk-magnetohydrodynamic generator,taking account of nonequilibrium ionization and recombination reactions

The establishment of a supersonic one-dimensional flow of a dual-temperature, partially ionized plasma is investigated in the channel of a disk-MHD generator, taking account of nonequilibrium ionization and recombination reactions. A detailed formulation of the problem is given in [1]; flows are considered in the absence of ionization and recombination reactions and in the case of equilibrium reactions.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 135–142, November–December, 1972.     

Flow of a relaxed gas in the vicinity of a solid surface

Behavior of a polyatomic relaxed gas in the vicinity of a solid surface was studied. The case in which the size of the relaxation zone exceeds considerably the mean free path between the elastic collisions (suppressed exchange of translational and internal energies) was considered. A smooth validity of the asymptotic expansion for the distribution function with defined assumptions was indicated. A solution for the zero-approximation equation and boundary conditions for the surface flow, based on this solution and generalized model for a diffusive gas reflection from the surface were derived. The latter problem was partially studied in [1] by the Grad method and in [2] in terms of an analysis of the temperature jump.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 33–39, July–August, 1973.     

Boundary layer on a flat plate with strong longitudinal magnetic field

The influence of a magnetic field on the boundary layer on a flat plate in a sufficiently strongly ionized gas stream is studied. The magnetic field is parallel to the plate and to the velocity of the free stream, and it is so strong that the transport coefficients become anisotropic (the cyclotron rotation frequency of the charged particles is greater than or equal to the order of the frequency of the particle collisions). Using the results of [1–3] it is shown that the effect of the strong longitudinal magnetic field with a sufficiently high degree of gas ionization leads to a reduction in the thermal flux to the plate. For low degrees of ionization this effect is very small, since the viscosity and heat conduction in this case are determined by the neutral component of the gas.Results are presented of numerical calculations of the considered problem with account for the dependence of the transport coefficients on the thermodynamic parameters. It is assumed throughout that the magnetic Reynolds number is small (R_m1).     

Concentration jump on the plane surface in a binary gas mixture

From the solution of linearized Boltzmann equations with the collision operators in the Gross and Krook form the authors have obtained an expression for the concentration jump of a vapor evaporating from a plane liquid surface into a stationary gas, for which the liquid surface is impermeable. Langmuir [1] was the first to point out that at the surface of an evaporating liquid the vapor pressure differs from saturated vapor pressure, i.e., a jump occurs in vapor concentration. An expression was obtained by Brock [2] for the concentration jump at the plane surface in the binary gas mixture with identical molecular masses of components by gas kinetic analysis. No solution has yet been obtained to the problem at different molecular masses of components.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 119–122, March–April, 1972.     

Non-Maxwellian electron distributions in time-dependent simulations of low-Z materials illuminated by a high-intensity X-ray laser

The interaction of high intensity X-ray lasers with matter is modeled. A collisional-radiative time-dependent module is implemented to study radiation transport in matter from ultrashort and ultraintense X-ray bursts. Inverse bremsstrahlung absorption by free electrons, electron conduction or hydrodynamic effects are not considered. The collisional-radiative system is coupled with the electron distribution evolution treated with a Fokker-Planck approach with additional inelastic terms. The model includes spontaneous emission, resonant photoabsorption, collisional excitation and de-excitation, radiative recombination, photoionization, collisional ionization, three-body recombination, autoionization and dielectronic capture. It is found that for high densities, but still below solid, collisions play an important role and thermalization times are not short enough to ensure a thermal electron distribution. At these densities Maxwellian and non-Maxwellian electron distribution models yield substantial differences in collisional rates, modifying the atomic population dynamics.     

Investigation of the wake of a hypersonic sphere in air by means of an open microwave resonator

The use of an open microwave resonator with plane-parallel mirrors for plasma diagnostics was first proposed in [1]. A resonator with spherical mirrors, which provides better spatial resolution in addition to high sensitivity, was used later [2, 3] to investigate the wake flow of models moving through air at hypersonic velocities. The presence of free electrons in the flow field is caused by ionization processes behind the bow shock and in the model boundary layer in this case. However, only the results of measurements of the density of electrons are presented in [2, 3], and no information is given on another important plasma parameter: the effective collision frequency of electrons with heavy particles. In the present study we use a microwave (8-mm range) resonator for an experimental study of the flow of gas in the wake of a polymer (Kaprolon) sphere traveling through air at hypersonic velocity. The flow is visualized by the schlieren technique. The electron densities and effective collision frequency of electrons with heavy particles are determined as a function of the distance behind the sphere.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 156–160, July–August, 1978.     

The effects of ionization on the compression of a gas by a converging shell

One of the effective methods of obtaining a dense high-temperature plasma is compression of the gas by converging shells, which can be accelerated to high velocities by the products of an explosion either as a result of ablation caused by laser radiation, or by an electron beam [1–3]. In order to interpret the results of such experiments, it is very important to construct satisfactory physical models which enable us to obtain plausible estimates for the parameters of the plasma which are realized as a result of the compression. In a number of cases the process of compression may be described with sufficient accuracy by a system of simple hydro-dynamic equations which have particular analytical solutions (see, for example, [4–7]); however, as a rule, for more realistic estimates it is necessary to take into account the complex of physical phenomena accompanying the process, and in such cases the most effective method is numerical simulation of the process, which enables a fuller study to be made of the effect of various factors [7–9]. Compression regimes corresponding to velocities of projection of the shells of some tens of kilometers a second (attainable in experiments with laser compression of shells of a width of some microns) have at present been considered in detail in studies devoted to a pulse thermonuclear synthesis (for example, [8–10]), from which it follows that the process corresponds with sufficient accuracy to the compression of a gas which is completely ionized at the initial moment. In experiments with more massive shells (of the order of 100 m and more), the velocities attained in practice do not exceed 5–20 km/sec [1]. At such velocities, the energy densities contained in the shock wave detaching from the shell may turn out to be insufficient for complete ionization of the gas which has been compressed, and this must have an effect on its further compression and heating. The present study considers precisely these regimes of compression of gas-filled targets. The studies were carried out by the numerical method. For comparison, the studies were made in a number of cases both with allowance for ionization of the gas which was being compressed, and also on the assumption that the gas was already completely ionized at the initial moment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 155–160, January–February, 1935.In conclusion the author expresses his appreciation to S. I. Anisimov for his constant attention to this study, and to M. F. Ivanov for his help in carrying out the calculations.     

Electrical conductivity of a partially ionized gas mixture in a magnetic field

A considerable number of papers [1–5] has been devoted to determining the electrical conductivity of a partially ionized gas on the basis of kinetic theory. In so doing, a three-component plasma model (electrons, ions, neutrals) is generally employed. The general expressions for the electrical conductivity of a many-component system are fairly complicated [1], and the calculation of their determinants is most laborious.The case of a N-component gas mixture in which one of the components is partially ionized (N+2-component plasma) is considered below. A series of simplifications in the solution of the initial system of equations allows one to represent the expressions for the electrical conductivity of such a mixture in the same form as for the three-component plasma case, but with certain effective parameter values. The results obtained correspond to the second approximation of Cowling [1.6].     

Boundary layer on a blunt body in a flow of dusty gas

The problem of interaction of gas-dust flows with solid surfaces arose in connection with the study of the motion of aircraft in a dusty atmosphere [1–2], the motion of a gas suspension in power generators, and in a number of other applications [3]. The presence of a disperse admixture may lead to a significant increase in the heat fluxes [4] and to erosion of the surface [5]. These phenomena are due to the joint influence of several factors — the change in the structure of the carrier-phase boundary layer due to the presence of the particles, collisions of the particles with the surface, roughness of the ablating surface, and so forth. This paper continues an investigation begun earlier [6–7] into the influence of particles on the structure of the dynamical and thermal two-phase boundary layer formed around a blunt body in a flow. The model of the dusty gas [8] has an incompressible carrier phase. The method of matched asymptotic expansions [9] is used to obtain the equations of the two-phase boundary layer. In the frame-work of the refined classification made by Stulov [6], it is shown that the form of the boundary layer equations is different in the presence and absence of inertial precipitation of the particles. The equations are solved numerically in the neighborhood of the stagnation point of the blunt body. The temperature and phase velocity distributions in the boundary layer, and also the friction coefficients and the heat transfer of the carrier phase are found for a wide range of the determining parameters. In the case of an admixture of low-inertia particles that are not precipitated on the body, it is shown that even when the mass concentration of the particles in the undisturbed flow is small their accumulation in the boundary layer can lead to a sharp increase in the thermal fluxes at the stagnation point.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–107, September–October, 1985.I thank V. P. Strulov for a discussion.     

Jumps in the density and temperature of one of the components of a binary gas mixture over the plane surface of a liquid

We consider a problem concerning the vaporization (or condensation) of one of the components of a binary gas mixture situated over the plane surface of a liquid. The kinetic equation in the model form of [1] is used to describe the system. As is well known, this model agrees well with experiment and is simpler than the Boltzmann equation so far as mathematical relations are concerned. This model fails to describe a number of effects because it is assumed that the collision time of the particles is independent of their velocity. This relates primarily to the phenomenon of thermal diffusion of the gases. Thus the formulas given below are applicable to gas mixtures having a small thermal-diffusion coefficient. The model equation is solved by an approximate method developed in [2]. In [3] the temperature jump of a single-component gas at a solid wall is calculated by this method, and the method is also employed in [4] in the calculation of the slipping rate of a binary gas mixture in the field of a temperature gradient. In both cases the results agree with numerical calculations by other authors within an accuracy of 1.5%.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 142–148, September–October, 1973.     

Calculation of unsteady supersonic flow past a two-dimensional cascade of plates ween vorticity inhomogeneities of the flow act on it

In the framework of the linear theory of small perturbations the problem of unsteady subsonic flow past a two-dimensional cascade of plates has been considered in a number of papers. Thus, the unsteady aerodynamic characteristics of a cascade of vibrating plates were calculated in [1] by the method of integral equations, while the same method was used in [2, 3] to calculate the sound fields that are excited when sound waves Coming from outside or vorticity inhomogeneities of the oncoming flow act on the cascade. The problem of a two-dimensional cascade of vibrating plates in a supersonic flow was solved in [4, 5]. In [4] the solution was constructed on the basis of the well-known solution of the problem of vibrations of a single plate, while in [5] a variant of the method of integral equations was used which differed slightly from the usual formulation of this method [1–3]. The approach proposed in [5] is used below to calculate the unsteady flow past a two-dimensional cascade of plates in the case when vorticity inhomogeneities of a supersonic oncoming flow act on it. Equations are obtained for the strength of the unsteady pressure jumps arising in such a flow and the vortex wakes shed from the trailing edges of the plates. Examples of the calculations illustrating the accuracy of the method and its possibilities are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp, 152–160, May–June, 1986.