Cathode spots on electrode slag films in an open-cycle MHD generator

A study has been made of the function of the electrodes (cathodes) in an open-cycle MHD generator for several different reasons [1–3], because the electrode processes have marked effects on the erosion and electrical characteristics of the electrodes. The specific features of the conditions in an MHD generator channel include, particularly, the high-temperature plasma composed of combustion products together with the deposition of potassium salts on the electrodes. These factors have a marked effect on the behavior of the cathode spots. In the case of an MHD generator fueled by coal, the plasma contains the incombustible mineral part of the fuel (ash). Therefore, the electrode surfaces receive not only potash salts, but also slag, which consists of various refractory oxides that differ from the potassium compounds in electrical conductivity, thermal conductivity, and emissivity. These films may substantially affect the parameters of the cathode spots, and hence the erosion, and the values may differ substantially from those given in [3]. We have examined the major features of the cathode spot behavior for an open-cycle MHD generator fueled by coal.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 29–33, July–August, 1976.     

Influence of the hall effect on the characteristics of a MHD generator with two pairs of electrodes

The characteristics of segmented-electrode MHD generators with Hall currents are at present the object of considerable interest. Various types of electrode connections ate being examined: ordinary segmented-electrode generators, Hall generators, mixed-type generators, and Montardy generators. Research is being pushed in several directions. In some cases infinitely fine segmentation is assumed [1--4]. In these studies it is considered that the current density j in the duct is everywhere uniform; the net characteristics or the most favorable electrode connection angle are determined. In another group of studies periodic problems are solved, it being assumed that the processes taking place in a single elementary celi are repeated in the other ceils; fringe effects are not taken into account. In this case it is usually assumed that the lengths of the electrodes and insulators are finite, but small as compared with the duct height [5–7 ]. Finally, in a last group of studies nonperiodic problems are considered. In [3] Vatazhin solves the problem of the current distribution in a duct with a single pair of electrodes between infinitely long insulators. In [8] a general expression is found for the current density function in the case of an arbitrary number of electrode pairs and for any scheme of electrode connection at finite electrode and insulator dimensions. However, numerical calculations are made only for the periodic problem, whose solution is also obtained in [8]; the effect of segment pitch on the characteristics of a Montardy generator is studied.The present author has investigated the influence of the Hall effect on the characteristics of a MHD generator having two pairs of electrodes with symmetrical and crossed electrode connections. Although it is obvious that in practice only multisegment ducts will be employed, the examination of a generator with two pairs of electrodes makes possible the qualitative anatysis of the various effects observed in segmented-electrode ducts in which the electrodes are connected in different ways. Numerical calculations, based on formulas obtained by solving the corresponding problems, have been made on a M-20 computer. Integrated characteristics of the various generator systems have been obtained as a function of electrode and insulator length, external loads, and Hall parameter w.In conclusion, the author thanks A. B. Vatazhin and A. N. Kraiko for their helpful advice.     

An experimental investigation of the effect of oxygen on the erosion of a multichannel tungsten cathode

The problem of the preservation of electrodes and the reduction of their depletion to a minimum has decisive significance among the practical questions of maintaining the efficiency of steady sources and plasma accelerators during an extended period of operation. For this purpose electrodes are made, as a rule, out of the refractory metals in familiar designs. In particular, tungsten, which has the highest phase-transition; temperatures among all the metals, thus permitting an appreciable reduction in the evaporation rate of the material under the thermally stressed operating conditions of these devices, is attractive. However, there exist other factors besides evaporation which affect the integrity of hot tungsten electrodes and their ablation (chemical processes, erosion in microarcs, ion bombardment, and so on). One of these factors requiring special investigation is the chemical interaction of tungsten with the oxygen contained in the working medium as an industrial impurity. Such an impurity can, for example, be present in industrially pure alkali and alkali-earth metals used as the working media. In addition, these metals can be contaminated by the oxygen of the air in the process of different industrial operations, in particular, in connection with the servicing of the supply system. The entrance into the working material of oxygen liberated from the structural elements of the supply route and the operating cavities of the plasma source is not excluded. In practice it is impossible to eliminate oxygen, even when using contemporary methods of deep cleaning of lithium, due to its great affinity for oxygen. The actual role of the oxygen impurity and the necessity for taking it into account in connection with the creation and operation of plasma devices can only be revealed as a result of direct experimental investigation on samples having an electrode. geometry similar to the class of sources or accelerators in question. Results are presented in this article of an experimental investigation of the erosion of a multichannel tungsten electrode [1–4] and a coaxial source of lithium plasma [5]. The use of lithium as the main plasma-forming material ensured the maintainance of a discharge distributed over the electrodes and having a small value of the potential drop next to the cathode, which lies below the threshold of cathode erosion upon bombardment of the surface of polycrystalline tungsten by lithium ions [6]. Thus, the phenomena of cathode destruction associated with microarcs and ion bombardment could be exluded from consideration in practice. Thus evaporation and chemical ablation due to interaction with the oxygen of the working medium remain the principal, competing processes contributing to the erosion of the cathode mass. Therefore, in order to obtain reliable quantitative relationships which characterize differential erosion due to oxidation and evaporation, the oxygen content in the working medium was varied in the experiments described within limits extending beyond the framework of the usual industrial impurity, which does not exceed tenths of a percent. One should note that in the process of investigating the role of an industrial oxygen impurity in causing the erosion of a tungsten cathode in a lithium plasma its direct effect was revealed on the anomalous current of a hollow cathode, which is characterized by the recorded average densities of the discharge current exceeding significantly the values of the emission current given at the same surface temperature by the Richardson-Schottky equation [7–9].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 67–73, May–June, 1979.The authors express their gratitude to S. S. Kellin, N. P. Mezhevov, and V. N. Belinskii for their participation in the preparation and performance of the experiment.     

Boundary layer development in supersonic MHD generators

A numerical model of the turbulent boundary layers in the gas dynamic channel of a supersonic MHD generator is constructed. This model describes the development and structure of the layers in the nozzle, on the electrode and insulating walls of the duct, in the two-dimensional approximation. The characteristics of the boundary layers in various generator operating regimes are investigated numerically. The integral boundary layer thicknesses characterizing the nonuniformity of the gas dynamic and electrodynamic quantities are calculated. The limits of applicability of the integral calculation method are determined for typical MHD generator operating conditions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 35–41, May–June, 1990.The authors wish to thank A. B. Vatazhin, V. A. Bityurin, and V. A. Zhelnin for discussing the formulation of the problem, A. A. Yakushev for participating in the discussion of the results, and Yu. V. Rakseeva and L. V. Yashina for preparing the article.     

Electric field in the transverse cross section of the channel of an MHD generator

During the motion of a partially ionized gas in magnetohydrodynamic channels the distribution of the electrical conductivity is usually inhomogeneous due to the cooling of the plasma near the electrode walls. In Hall-type MHD generators with electrodes short-circuited in the transverse cross section of the channel the development of inhomogeneities results in a decrease of the efficiency of the MHD converter [1]. A two-dimensional electric field develops in the transverse section. Numerical computations of this effect for channels of rectangular cross section have been done in [2, 3], At the same time it is advisable to construct analytic solutions of model problems on the potential distribution in Hall channels, which would permit a qualitative analysis of the effect of the inhomogeneous conductivity on local and integral characteristics of the generators. In the present work an exact solution of the transverse two-dimensional problem is given for the case of a channel with elliptical cross section stretched along the magnetic field. The parametric model of the distribution of the electrical conductivity of boundary layer type has been used for obtaining the solution. The dependences of the electric field and the current and also of the integral electrical characteristics of the generator on the inhomogeneity parameters are analyzed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 3–10, January–February, 1973.     

Solution of a variational problem for the flow in an MHD generator

The most complete study and construction of extremal plasma flow regimes in the channel of an MHD generator may be accomplished using the methods of variational calculus. The variational problem of conducting-gas motion in an MHD channel was first discussed in [1]. The general formulation of the problem for the MHD generator was considered in [2]. Solutions of variational problems for particular cases of extremal flows are given in [2–5].The present study obtains the solution of the variational problem of the flow of a variable conductivity plasma in an MHD generator which has maximal output power for given channel length or volume. An analysis of the solution is made, and a comparison of the extremal flows with optimized flow in a generator with constant values of the electrical efficiency and flow Mach number is carried out.     

Plasma density and electeic field strength distributions at a boundary with an electrode

Close to the cathode in an arc discharge, or to the surface of a probe operating on the ionic branch of its characteristic, conditions are obtained under which the Langmuir layer freely passes ions coming from the plasma, while the reverse ion flow is virtually zero. The plasma density, ion distribution, and electric fieid-strength close to the electrode are found in the present paper. The extrapolated length is evaluated for the plasma density. The absolute value of the electric field strength increases logarithmically at the boundary with the electrode.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No, 2, pp. 4–6, March–April, 1970.     

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.     

Integral characteristics of MHD channel with nonconducting baffles

The electromagnetic characteristics of an MHD channel with insulated walls, two quite long electrodes, and nonconducting baffles are obtained for arbitrary magnetic field distribution law along the channel. Some specific cases of magnetic field and baffle location specification are examined in detail.Translated from Zhurnal Prikladnoi Mekhaniki Tekhnicheskoi Fiziki, Vol. 10, No. 6, pp. 30–39, November–December, 1969.     

Calculation of the thermally nonequilibrium near-electrode region in an alkali-metal-seeded plasma

Distribution of parameters in the region of disturbance of a plasma near the surface of an electrode is considered based on diffusion equations. Thermoelectronic and thermionic emission from the electrode surface, the Schottky effect, and volume ionization and recombination are borne in mind. Two regions are assumed in the solution, namely, the region of ambipolar diffusion and the region of the space charge. A comparatively simple geometry for the discharge gap, given in the form of two infinite plane-parallel electrodes, is considered. A comparison is carried out with calculations for a thermally balanced region of a plasma disturbance.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 13–17, January–February, 1976.     

Some electrodynamic effects in a MHD generator duct

Theoretical and experimental studies made in recent years show that the plasma flow in the duct of a real MHD generator differs significantly from the quasi-uniform model of the flow in an idealized MHD duct. This difference appears primarily in the analysis of the electrodynamics of the MHD generator. Usually the actual electrical characteristics of the generator are poorer than expected, which may be caused, in particular, by flow nonuniformities and electrical leaks in the duct. The influence of these factors shows up particularly strongly in the presence of the Hall effect.Some qualitative and quantitative estimates of these phenomena have already been made in the literature. The necessity for taking into account the influence of the cold boundary layer on the effective conductance of the plasma in the duct was shown in [1]; in [2] it was shown that this influence increases markedly in the presence of the Hall effect. The influence of shunting of the plasma by the electrically conductive walls of the duct was considered in [3–5].The present paper describes an analysis of the combined influence of the effects associated with flow nonuniformities and electrical leaks for the case of anisotropy of the plasma conductivity, and an example is presented of the calculation of flow in a MHD generator with finite variation of the parameters.     

Dynamics of a nonuniformly conducting gas flow in a magnetic field

The dynamics of a nonuniformly conducting gas flow in the channel of a MHD generator are investigated on the basis of numerical modeling. The initial shape of the plasmoids periodically entering the MHD channel qualitatively correspond to that noted in [6, 7]. The alkali metal seed is uniformly distributed over the entire flow. The mechanism of dynamic interaction of the plasmoids and the low-conductivity gas flowing over them, the variation of the shape of the plasmoids and the evolution of the gas dynamic structure of the flow are studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 135–145, September–October, 1989.     

Transmission coefficient of a grid electrode

The behavior of conducting emulsion drops (carrying a constant charge) in the region between electrodes connected to dc sources is studied. Assuming that the concentration of the dispersed phase is reasonably low, the problem may be reduced to one of determining the motion of an isolated drop close to the electrode. The trajectories of the drops in a flow passing around the electrode are then calculated, allowing for charge exchange between the drops and the electrode, and the electrode transmission coefficient is determined in relation to the parameters of the problem. An analogous situation was envisaged in earlier papers [1, 2] for a single cylindrical electrode but without allowing for the recharging of the particles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 157–158, May–June, 1974.     

Motion of a conductive piston in a channel with variable inductance

The motion of a conductive piston in the channel of a magnetohydrodynamic (MHD) generator of the conduction type with compound electrodes is considered. Formulas are obtained for calculation of the energy characteristics of the pulse MHD generator for various operational regimes. It is shown that in an MHD generator at magnetic Reynolds number values Re_m = ₀u₀ 1 (where ₀ is the permeability of a vacuum, is the electrical conductivity of the piston, u₀ is the initial velocity, and is the characteristic dimension), the energy transferred to an ohmic load may significantly exceed the values obtained in [1, 2]. Conditions for high-efficiency transformation of piston kinetic energy to electrical energy are considered for limiting values of the ratio of the latter to initial magnetic field energy in the generator channel.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 41–46, November–December, 1973.The authors thank V. I. Yakovlev for his helpful evaluation.     

Breakdown of the near-electrode layer in a flow of ionized gas

An electric discharge in a flow of ionized gas is widely used in many physics and engineering problems. Among them are problems associated with current flow in various magnetohydrodynamic devices (generators, accelerators), arc shunting in a plasmatron, physical experiments in shock tubes, etc. It is known that with cold electrodes providing the contact between the plasma and the external circuit and relatively high pressures, two modes of current flow occur: at low current, the discharge is of a distributed nature; as the applied voltage increases, the discharge abruptly shifts into a discharge with a clearly developed cathode spot at some critical current density (we call this form of discharge an arc discharge). Existing experimental data [1–20] refers to varying experimental conditions. Furthermore, the critical voltage (or current) at which the transition of the discharge from a distributed discharge to an arc discharge occurs varies within very broad limits. From an analysis of the experimental data, a condition is formulated which the discharge parameters satisfy at the time of transition from a distributed discharge to an arc discharge.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 16–23, May–June, 1973.The author thanks Yu. A. Nikuev for invaluable help in the analysis of experimental data.     

Multirail electromagnetic launcher powered from a pulsed magnetohydrodynamic generator

The operation of an electromagnetic multirail launcher of solids powered from a pulsed magnetohydrodynamic (MHD) generator is studied. The plasma flow in the channel of the pulsed MHD generator and the possibility of launching solids in a rapid-fire mode of launcher operation are considered. It is shown that this mode of launcher operation can be implemented by matching the plasma flow dynamics in the channel of the pulsed MHD generator and the launching conditions. It is also shown that powerful pulsed MHD generators can be used as a source of electrical energy for rapid-fire electromagnetic rail launchers operating in a burst mode.     

Conditions near the electrode in a plasma with an alkali admixture

An analysis is made of the effects of certain processes in the interior of the gas and at the electrode surface on the potential drop near the electrode in a discharge in a dense, slightly ionized gas. Thermionic emission from the electrode, the Schottky effect, diffusion, and volume and surface ionization and recombination are taken into account. The analysis is carried out for a simple discharge-gap geometry: two infinite, plane-parallel electrodes. Relations are found for the potential drop near the electrode in a two-temperature plasma as a function of the discharge parameters and emission characteristics of the material. The calculated results are compared with experiment.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 3–12, July–August, 1971.The authors thank G. A. Lyubimov for interest in the study and for discussion of the results, and B. V. Parfenov for graciously furnishing the necessary experimental data from [13].     

Ion distribution function at the boundary with an electrode

The ion distribution function is found in the case in which the Langmuir layer freely passes the ions incident from the plasma while the reverse ion flux is zero. These conditions are realized near the cathode in an arc discharge and at the surface of a probe operating on the ion branch of the characteristic. The electric field outside the Langmuir layer is assumed small. We obtain the connection between ion current and plasma density at the boundary with the electrode, the expressions for the ion mean kinetic energy and for the mean energy removed from the plasma by the ion, which differ markedly from the corresponding expressions in the Maxwellian distribution case.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 3, pp. 47–54, May–June, 1969.     

Experimental investigation of cathode spots on metallic electrodes protruding in plasma flow

The behavior of cathode spots on metallic electrodes is investigated. The dependence of the basic characteristics of the spots (current per spot, life time, rate of displacement, average area and so forth) on the nature of the flow of the plasma past the surface of the electrode, the surface temperature of the electrode, the total current in the electrode, and the magnetic field is obtained. The investigations were done in connection with the study of the operation of electrodes of open cycle magnetohydrodynamic generators. The experiments were conducted with copper electrodes introduced in the plasma formed by the combustion products of natural gas with potassium added to it.     

Instability and flow of a weakly conducting fluid in the presence of oxidation-reduction reactions at electrodes and recombination

Experiments show that a weakly conducting fluid in a plane-parallel system of electrodes is set into motion if the field intensity is sufficiently great [1–5]. The loss of stability is due to the formation of charges near the electrodes and the influence of the Coulomb forces on these charges. The formation of the space charges is usually attributed to oxidation-reduction electrode reactions and bulk recombination of the ions formed at the electrodes [1–4]. In the present paper, the stability of a weakly conducting fluid in a plane-parallel system of electrodes with symmetric distribution of the space charge is studied. The methods of the theory of solution bifurcation are used to construct the stationary flow which arises after the loss of stability and to investigate the stability of this flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 20–26, July–August, 1981.