Electric field excited in air by a pulse of gamma rays

The characteristics of the electric field produced by air polarization during the passage of nonstationary Compton currents excited by a -ray pulse in low-density air are discussed. The influence of the field on the motion of the Compton electrons is taken into account. The amplitude and relaxation time of the field are evaluated. A polarization electric field is created through the action of a directed current of -rays in air because of the movement of the Compton electrons. This paper discusses the basic characteristics of the resultant field in low-density air. A similar problem was raised in [1], where the electromagnetic field excited by a nonstationary source of -radiation in the upper atmosphere was considered. In that case, the Compton-electron currents were specified and their magnitude was assumed to be proportional to the ratio between the gas kinetic ranges of Compton electron and -ray (this ratio is of the order of 0.01 and is indepenent of height). With an increase in electron range, however, the decelerating action of the resultant electric field on the motion of the Compton electron becomes important (eE/ is a criterion for the effect; E is the field intensity, and and are the range and energy of the Compton electron).Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 3–8, July–August, 1970.In conclusion, the authors thank G. M. Gandel'man for several discussion.     

Estimate of the amplitudes of the fields created by an unsteady gamma source

It is known [1–4] that an unsteady gamma source gives rise to an electromagnetic field in the surrounding space. Most of the studies of the characteristics of such fields have been performed in the approximation which is linear in the field [1–3]. An exception is [4] in which the slowing down of Compton electrons by the electric field is taken into account. It follows from [1, 2] that the characteristic scale of the fields created close to the source is of the order of 3 · 10⁴ V/m. Although this value is appreciably lower than the value of breakdown fields in air, electric discharges are observed [5] in the vicinity of a gamma source, indicating the presence of substantially larger fields. One effect not taken into account in the latter approximation which could lead to an increase in the field is the increase in electron termperature due to the electric field [6]. On the one hand, this decreases the electron mobility and consequently also the conductivity of the system, On the other hand, it is known that the electron attachment coefficient for electronegative molecules strongly affects the characteristics of electric fields and depends on the electron energy. Therefore, the electron balance equation must take account of the dependence of on the electric field through the electron energy, and this leads to a further change in conductivity. We take account of these effects on the shaping of electric fields in air in the vicinity of the source. It is assumed that electron lifetimes are determined solely by their attachment to molecules. This is a good approximation for air pressures near normal [1–3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 163–170, July–August, 1976.     

Influence of hall currents on the acceleration of a conducting gas in its own magnetic field

In [1] the author gave a solution of the problem of how the Hall currents influence the flow pattern of a conducting gas which is accelerated in a channel to high velocities in external electric and magnetic fields. The present article considers the influence of Hall currents on the acceleration of a plasma in its own magnetic field, i.e., the magnetic field induced by the currents flowing in the plasma.     

Effect of surface electric current on the electrohydrodynamic flow inside and outside a spherical drop

The problem of electrohydrodynamic flow of a viscous, low-conducting, polarizable liquid inside and outside a spherical drop in an applied homogeneous constant electric field is analytically solved with account for the effect of both surface conduction current and surface convection current. The influence of the drop deformation on the field and the flow is neglected. The solution is obtained in the form of asymptotic expansions in a small parameter corresponding to weak surface convection electric currents.     

Spreading of a liquid over a plane rigid substrate in an electric field

The influence of an electric field on spreading of a thin conducting liquid layer over a plane rigid substrate is investigated theoretically. The conductivity of the liquid is assumed to be so low that the effect of the magnetic field of the currents generated in the liquid under the action of the electric field can be neglected. The spreading is assumed to be so slow that the quasi-steady approximation can be used to calculate the electric field strength which can be considered to be equal to zero inside the liquid. Equations that describe variations in the layer shape are obtained in the lubrication theory approximation. The general formulation of the problem is considered. The solution of the problem is obtained in parametric form when the effect of the gravity force and the surface tension can be neglected. Variations in the layer thickness along the substrate are so smooth that the charge distribution over its surface can be assumed to be the same as that over the substrate surface in the absence of the liquid.     

Plasma oscillations of an electron beam in an external electric field

Many papers have been devoted to the problem of the interaction of beams of charged particles with a plasma (a detailed bibliography is given, for example, in [1]). Analysis of the dispersion equation shows that in the case of a sufficiently slow monoenergetic electron beam of low density, growing longitudinal waves are not excited in a system consisting of such a beam and a plasma [2–4].The problem of the penetration of an external longitudinal electric field into a semiconfined plasma with an electron beam in the absence of instabilities in the system is studied (the boundary-value problem for growing waves was examined in [5]). This problem is, in a certain sense, an extension of the second part of L. D. Landau's well-known work [6] to include the case of a plasma with a beam. On the other hand, in the absence of an external electric field, this problem may be considered a boundary-value problem of the interaction of a weakly modulated electron beam with a plasma.The authors thank M. L. Levin for his useful comments.     

Features of the electric current and field distributions in flows with narrow layers of highly conductive gas

A solution obtained by Fourier's method provides the basis for analyzing the influence of a narrow gas layer, of higher conductivity than the rest of the flow, on the Joule dissipation and current distribution in the terminal zone of a plane magnetohydrodynamic channel with nonconducting walls. The MHD interaction parameter, Reynolds magnetic number, and Hall parameter are assumed small. It is shown that a narrow, highly conductive layer can on occasions be replaced by a surface of discontinuity, on which well-defined relations between the electric quantities are satisfied. The presence of such a layer leads to an increase in the Joule dissipation and a reduction in the lengths of the current lines. A hopeful arrangement for a magnetohydrodynamic energy converter is one in which an inhomogeneous flow is used, consisting of a continuous series of alternating very hot and less hot zones [1,2]. For this arrangement, it is worth examining the influence of the stratified conductivity distribution of the working body on the Joule dissipation and the electric currents in the channel. Numerous papers have discussed the case of inhomogeneous conductivity in the context of MHD system electrical characteristics. A general solution was obtained in [3] for the stationary problem on the electric field in a plane MHD channel with nonconducting walls when the magnetic field and conductivity are arbitrary functions of the longitudinal coordinate. In [4], where the braking of undeformed conducting clusters was investigated, the Joule dissipation, linked with the appearance of closed eddy currents in the cluster as it enters and leaves the magnetic field, was evaluated. The relationships between the electrical quantities, on moving through a narrow layer of low-conductivity liquid, were considered in [5].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 9, No. 1, pp. 39–43, January–February, 1970.In conclusion, the author thanks A. B. Vatazhin for valuable advice and discussion.     

Limit currents in a plasma betatron

The radial motion of a plasma column is considered for electron acceleration in a plasma betatron. The limit value of the relativistic currents which can be obtained in devices of this type is computed.G. I. Budker [1] proposed using the runaway effect in a plasma with a strong electric field for converting a cold ring plasma into an intense compensated beam of relativistic electrons. To confine such a beam within an annular vacuum chamber one can use either a betatron-type magnetic field or the field of the image currents produced in the metal shell enclosing the vacuum chamber with the electron beam. In the latter case, as estimates show, the number of accelerated electrons must already be considerable; this leads to an increase in the difficulties which impede the successful acceleration of all plasma electrons.Accordingly, most of the experiments on accelerating plasma electrons have employed betatron fields in devices called plasma betatrons [2–4], A feature of these accelerators is total compensation of the space charge of the accelerated electrons and hence an increased possibility of obtaining high accelerated currents. In this article, we compute the magnitude of the limit currents which may be obtained in a plasma betatron as a function of its parameters and operating conditions.The first results in this direction, published in 1949 [5], were rough estimates. Subsequently, other more accurate calculations were published [6], but these, in our opinion, did not give sufficient information on the characteristic quantities.The author thanks A. E. Bazhanov for his help in interpreting Eq. (16).     

Heating of a medium as a result of Joule energy dissipation

It is well known that when a magnetic field is present and electric currents flow through a gas, terms over and above those present in the case of ordinary thermal conductivity appear in the heat flux density vector. If the gas is dense enough and the magnetic field not over large, then the anisotropy caused by the magnetic field may be neglected. However, for a sufficiently large electric current a term proportional to the temperature and to the current density vector remains in the heat flux density vector. This effect explains, for example, the asymmetry of heat fluxes in the electrodes of a continuously operated electromagnetic accelerator (1).We shall consider this situation in relation to the example of a fully ionized quasineutral gas with identical electron and ion temperatures.     

Optimal form of shielding for polychromaticγ-radiation

In [1] the problem of the construction of the optimal form of shielding (in the sense of minimum weight) for the monoenergetic-radiation of linear, disc and cylindrical sources was considered. Below, for the same source geometries, the problem of optimal form of shielding is solved for the case of polychromatic radiation. As in [1], radiation scattering in the environment is neglected, and the sources are assumed to radiate isotropically. Multiple scattering in the shielding is taken into account by using an analytical expression for the build-up factor.     

Charging of disperse particles in two-phase media with unipolar charge

Charging of disperse particles with good conduction in two-phase media with unipolar charge is considered in the case when the volume concentration of the particles is low. For this, in the framework of electrohydro-dynamics [1, 2], a study is made of the charge of one perfectly conducting liquid particle in a gas (or liquid) with unipolar charge in a fairly strong electric field. The influence of the inertial and electric forces on the motion of the gas is ignored, and the velocities are found by solving the Hadamard—Rybczynski problem. We consider the axisymmetric case when the gas velocity and electric field intensity far from the particle are parallel to a straight line. The analogous problem for a solid spherical particle was solved in [3–6] (in [3], the relative motion of the gas was ignored, while in [4–6] Stokes flow around the particle was considered). The two-dimensional problem of the charge of a solid circular, perfectly conducting cylinder in an irrotational flow of gas with unipolar charge was studied in [7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 108–115, November–December, 1980.We thank L. I. Sedov and V. V. Gogosov for a helpful discussion of the present work.     

Electric characteristics of a probe in a subsonic plasma flow

Lam [1] and Su [2] have formulated and given some results of the solution to the problem of the concentration distributions of the charged particles and electric field in a weakly ionized plasma that flows past a conducting body (an electric probe) under the condition that the Reynolds number of the oncoming flow is high. In the present paper, this problem is solved by the method of exterior and interior asymptotic expansions with respect to a small parameter [3]. The form of the current-voltage characteristics of the probe is found as a function of the determining parameters of the problem. Data of an experimental verification of the obtained results for the case of a cold probe in a flowing air plasma containing added potassium are given.     

A self-consistent solution for nonlinear theory of the positive column in a magnetic field

Only the electron and ion gases were taken into account in all previous theories of the positive column of intermediately-low-pressure arc discharge with or without the longitudinal magnetic field, while the motion of neutral gas was neglected. In 1982, the authors^[1] presented a nonlinear theory of a positive column which indicated that the rotating velocities of neutral gas and ion gas were nearly equal, and the motion of neutral gas could not be ignored. They further discussed the problem of validity of Bohm's criterion. However, some of the parameters with which the computation was worked out in Ref. [1] were not correlated to the initial discharge parameters. In the present paper, two integral relations are supplemented, so that a complete mathematical formation of the problem is given. A convergent numerical solution is obtained by iteration and the solution of Ref. [1] turns out to be the first iteration approximation. It is shown that both functions and parameters obtained by self-consistent solution differ significantly from those obtained in the first iteration approximation. According to this paper the computation can be conducted when the initial discharge parameters are given, so this method could have certain practical applications.     

Electroconvective jets in liquid dielectrics

The principal feature of electroconvective jets in liquid dielectrics developing under the influence of a high-voltage external field is the large value of the EHD interaction parameter. This leads to the coupling of the hydrodynamic and electric problems. As formulated in [1, 2] the situation is reversed: the EHD interaction parameter is small. In these problems the interest is usually confined to finding the electric characteristics of the jet for a given velocity field. In [3] flows from sharp electrodes in liquid dielectrics were analyzed under two principal assumptions: nonlinear ohmic conductivity and point EHD interaction. This paper deals with the calculation of submerged electroconvective jets with ionic conductivity on the basis of the boundary-value problem formulated in [4]. In this case point EHD interaction is not assumed. It should be noted that in this formulation the problem is of practical as well as theoretical interest, for example, in connection with the problem of designing throttle EHD converters [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 13–19, November–December, 1984.     

Numerical simulation of an electric discharge in supersonic flow

The two-dimensional problem of supersonic air flow past a spherical electrode is considered on the basis of a joint solution of the Navier-Stokes equations for a neutral gas and the charged-particle transport equations in the diffusion-drift approximation. The self-sustained discharge is considered in the cathode regime of operation of the test electrode in a formulation analogous to that of the experimental study [1]. The thermal and non-thermal (action of the electrostatic force in the cathode layer of the space charge) mechanisms of action of the discharge on the flow field are investigated. Within the framework of the numerical model considered the effect of the electrostatic force turns out to be negligibly small and the main effect of the action on the flow is the heat release driven by the electric currents. The influence of the discharge on the flow field was manifested itself in a reduction of the aerodynamic drag by up to 25%.     

Joule loss due to compressibility of gas in a channel of variable section

It is known that closed electric currents arise in a conducting medium moving in a non-uniform magnetic field. These currents lead to additional energy loss and adversely affect the characteristics of magnetohydrodynamic channels. (The numerous investigations of these effects are dealt with in the review [2, 3].) Eddy electric currents are also formed, however, when a medium flows in a uniform magnetic field perpendicular to the to the plane of motion if the channel has a variable cross section and the medium is compressible [1], This paper is devoted to an investigation of some features of these flows. It is assumed in the analysis that the gas flows in channels whose geometry varies slightly.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 9, No. 4, pp. 3–9, July–August, 1968.     

The plane contact problem in the electrodynamics of continuous media in the presence of the Hall effect

Solutions are given for the distributions of current density, field strength and electric field potential in the neighborhood of the point of contact of two conducting media with different scalar electrical conductivities a and Hall constants R_H. Problems of this type are encountered in magnetohydrodynamic theory, and in semiconductor physics, for example, in investigating the fields in piecewise-inhomogeneous media or on the electrodes in magnetohydrodynamic channels and electrical engineering apparatus. If one of the two media has ideal properties =, R_H=0, then within the framework of the approximate theory (the induced magnetic field is neglected) the problem reduces to finding an analytic function in the region occupied by the second medium, and this can often be solved by carrying out a conformal mapping of the region onto a polygon [1, 2]. In other cases the electric field in each medium depends jointly on the physical properties and geometries of regions of the two media, and a solution must be found which is joined at the contact. The theory of singular integral equations [3,4] is a convenient mathematical tool for solving such problems.     

Self-similar magnetogasdynamic flows accompanied by detonation and combustion waves

Magnetogasdynamic (MGD) flows with detonation waves and combustion fronts have attracted more and more attention in recent years. Intensive heat supply assures such a significant increase in the temperature and pressure behind the heat liberation fronts that the gaseous combustion products become conductive so that the flow map in the electric and magnetic fields can vary substantially as compared with ordinary gasdynamics. In the case of finite gas conductivity, when the magnetic Reynolds numbers R_m are low, the asymptotic laws of detonation wave propagation which either go over into the Chapman-Jouguet (CJ) mode (in a number of cases at a finite distance from the initiation source) or remain overcompressed, have been studied [1]. Stationary flow modes behind detonation waves have been investigated in [2] and the problem of the detonation wave originating at the closed end of the tube emerging in the stationary mode in crossed homogeneous magnetic and electric fields has been examined. Results are presented in this paper of an investigation of one-dimensional self-similar flows caused by piston motion in a hot gas mixture in which a detonation wave or combustion front is propagated. The motion is realized in external electric and magnetic fields which exert a substantial effect on the flow of the conductive combustion products. Domains of application of the governing parameters in which the various flow modes are realized are found by using a qualitative and numerical analysis. The results obtained are used to solve problems about the hypersonic gas flow around a thin wedge in an axial magnetic field.     

Influence of the hall effect on hypersonic flow past a wedge

This paper deals with the problem of the steady-state hypersonic flow of an inviscid compressible gas past a wedge. Inside the wedge a magnetic field is excited in a direction perpendicular to the generator. The flow in the region of perturbation is investigated on the basis of the ordinary equations of magnetohydrodynamics and Ohm's law, written for the case where the Hall effect is taken into account. The system of equations obtained has been solved numerically on a computer by the method of finite differences. The results show that for the given problem the Hall effect intensifies the magnetohydrodynamic action of the magnetic field on the flow. M. D. Ladyzhenskii [1] has also studied hypersonic flow past bodies from inside which a magnetic field is excited. He has investigated the influence of a strong magnetic field on the flow for the case where the Hall effect is neglected. The object of the present study is to determine the importance of the Hall effect.The author wishes to thank M. D. Ladyzhenskii for formulating the problem and discussing the progress of the work.     

Nonlinear electromagnetic phenomena in a liquid with nonequilibrium electrical conductivity in an alternating magnetic field

On the basis of [1] this note examines nonlinear electromagnetic phenomena in a dense plasma brought about by the variation in its electrical conductivity as the electrical field changes. It is well known that the electrical conductivity depends on the electric field strength due to the following causes. The electrons in moving in the electric field receive energy from the field which may be considerable over the free path length. However it is difficult for this energy to be transferred to the heavy particles. In monatomic gases the energy exchange between electrons and heavy particles comes about basically as a result of elastic collisions. Thus a noticeable difference in electron and ion temperature, determined by the electron energy balance taking radiation losses into account, turns out to be possible even for relatively weak electric fields. In molecular gases, on the other hand, the fundamental energy exchange mechanism is the excitation of the rotational and oscillatory degrees of freedom of the molecules. Thus the electron energy in these gases is dissipated relatively easily, and the electron temperature is not observed to be noticeably higher than the atomic temperature. The concept of the characteristic “plasma field” E_p is introduced in [2], which is determined for an Isotropic plasma by the relation

$$E_R = \sqrt {3kTme^{ - 2\delta } (\omega ^2 + v_0 ^2 )} .$$