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Notes: Abstract Hall phenomena in an electrically conducting fluid with a variable magnetic field were considered in [1]. In that paper the basic characteristics of the above-mentioned phenomena are determined, with certain unimportant constraints, for the case of fluid motion along a channel of rectangular cross section in a traveling magnetic field. The magnetic Reynolds number was assumed to be small, and a solution was given for the induction field in the form of a series in powers of the indicated parameter. Quantitative estimates based on the data of [1] are impossible in the case of relatively high electrical conductivity of the fluid, although certain conclusions of a qualitative nature remain valid. There is thus reason to consider the case of high magnetic Reynolds numbers. This will also allow a fuller picture of the characteristic Hall effect phenomena to be constructed for a variable magnetic field.

Notes: Abstract A formulation is given of the problem of the stability of piston-flow motion in a traveling magnetic field. It is shown that this question reduces to the problem of stability of motion in the presence of constantly acting perturbing forces. The second Lyapunov method is used as the basis to present the sufficient criteria for stability of the flow motion with respect to certain specified quantities.

Notes: Abstract Interferometric measurement of the air density in a supersonic nozzle of rectangular cross section is described. The flow structure is studied in a real Laval nozzle. It is shown that the core flow follows the laws of motion of an ideal gas and has a wave nature. The relation δZ=(3−4)δy is obtained for the boundary layer thickness on the nozzle walls for nozzle width-height ratio L/h=3.75–7.5. The flow structure in a real supersonic nozzle may differ significantly from the theoretical structure, both because of defects in nozzle fabrication and because of boundary layer growth on the nozzle walls. In many casesitis important to know the param'eters of the supersonic flow in the actual nozzle. The determination of these parameters (density ρ, pressure ρ, temperature T, velocity u, Mach number M) at any section of the nozzle in question is the objective of the present investigation.

Notes: Abstract 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” Ep is introduced in [2], which is determined for an Isotropic plasma by the relation $$E_R = \sqrt {3kTme^{ - 2\delta } (\omega ^2 + v_0 ^2 )} .$$ Here k is the Boltzmann constant, T is the plasma temperature in the absence of a field, m and e are the electronic charge and mass, & is the mean fraction of energy transferred to a heavy particle by an electron on collision,ω is the frequency of field variation, ν0 is the electron-ion collision frequency in the absence of a field. In weak electromagnetic fields (E≪Ep) the plasma maintains thermodynamic equilibrium, and the electrical conductivity of the plasma is independent of the field. In strong electric fields (E≫Ep) there is a sharp difference of electron temperature and the voltage-current characteristics of the plasma become nonlinear. The question of nonequilibrium electrical conductivity has been fairly fully studied [3–5] as regards monatomic gas plasmas like argon and potassium mixtures. It was shown in [3] that for the plasmas which were considered the dependence of the electrical conductivity on the electric field with no magnetic field present could be satisfactorily described by a power function of the absolute current density, i.e., σ =c∣j∣ γ , where c is a function of the atomic temperature. This function has also been confirmed experimentally for an argon-potassium plasma for a temperature of the order of 0.2 eV and a pressure of the order of 1 atm. [3]. In the following we consider electromagnetic phenomena in a dense plasma with an electrical conductivity of the type σ =c∣j∣γ when it is in motion in a traveling magnetic field. It is assumed that the plasma parameters and limits of variation of the independent quantities (j, Te) are such that the function σ =c∣j∣γ is stable [4]. In addition the plasma is taken as having the properties of an ideal incompressible fluid. These last assumptions together with the assumption that the gradients of static pressure and pondermotive forces are only in the direction of plasma motion allow us to commence from the equations of electrodynamics.

Notes: Abstract In a lightly ionized plasma, charged-particle drift due to collisions with neutral atoms occurs at different velocities: $$\begin{array}{*{20}c} {v_{Ea} = \mp \frac{{b_a E}}{{1 + (\omega _a \tau _a )^2 }},v_{ \bot a} = \frac{{b_a E(\omega _a \tau _a )}}{{1 + (\omega _a \tau _a )^2 }}} \\ {\left( {b_a = \frac{{|e|\tau _a }}{{m_a }},\omega _a = \frac{{|e|\tau _a }}{{m_a }}} \right),} \\ \end{array} $$ where ba is the mobility of particles of the type a;ωa is the Larmor frequency; the upper sign refers to electrons and the lower sign to ions. A difference in the charged-particle drift velocities can cause instability of an inhomogeneous lightly ionized plasma. Let us consider the following example. Assume that in the initial state of the plasma there is a concentration gradient along the x-axis, that the external electric field is directed along the x-axis, and that the magnetic field coincides with the z-axis. In this system, under the influence of a Lorentz force the charged particles will move in a direction opposite to the y-axis. Since electrons have a higher velocity than ions, an electric field is induced in this direction. This electric field, together with the magnetic field, causes particle drift in the negative direction of the x-axis. Consequently, if the concentration gradient in the initial state is directed opposite to the x-axis this state cannot be stable. Instability of this kind has been examined by Simon [1]. On the basis of studies by Kadomtsev and Nedospasov [2], as well as by Rosenbluth and Longmire [3], Simon developed a theory of instability of a lightly ionized plasma in crossed fields with an inhomogeneous density distribution in the direction of the external electric field. Somewhat later, Simon's theory was developed [4]. In devices with inhomogeneous plasma flow in which the plasma (conducting) layers alternate with nonconducting layers, the external electric field and concentration are normal to one another. We shall bear this case in mind below and shall examine the instability of a lightly ionized plasma in crossed fields when the concentration inhomogeneity is in a direction perpendicular to the external electric field.