Nonlinear regimes of current flow through a weakly ionized boundary layer and their stability

The problem of steady states and stability of current flow in low-temperature plasma with allowance for the Joule heat release have been considered repeatedly for the case of confined stationary plasma (see, for example, [1]). The present paper is devoted to the asymptotic solution of this problem for the case of a laminar boundary layer of weakly ionized plasma. A similar problem was previously considered in [2] in a zero-dimensional approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 153–163, July–August. 1986.The author thanks G. A. Lyubimov and the participants in the seminar he directs, I. M. Rutkevich and V. D. Khait for their discussion of the work and their useful observations.     

Evolution of Packets of Surface Gravity Waves over Strong Smooth Topography

Wave packets in a smoothly inhomogeneous medium are governed by a nonlinear Schrödinger (NLS) equation with variable coefficients. There are two spatial scales in the problem: the spatial scale of the inhomogeneities and the distance over which nonlinearity and dispersion affect the packet. Accordingly, there are two limits where the problem can be approached asymptotically: when the former scale is much larger than the latter, and vice versa. In this paper, we examine the limit where the spatial scale of (periodic or random) inhomogeneities is much smaller than that of nonlinearity/dispersion (i.e., the latter effects are much weaker than the former). In this case, the packet undergoes rapid oscillations of the geometric-optical type, and also evolves slowly due to nonlinearity and dispersion. We demonstrate that the latter evolution is governed by an NLS equation with constant (averaged) coefficients. The general theory is illustrated by the example of surface gravity waves in a channel of variable depth. In particular, it is shown that topography increases the critical frequency, for which the nonlinearity coefficient of the NLS equation changes sign (in such cases, no steady solutions exist, i.e., waves with frequencies lower than the critical one disperse and cannot form packets).     

Asymptotic theory of boundary layers of weakly ionized thermalplasmas on emitting electrodes

The paper deals with collision-dominated boundary layers of weakly ionized thermal plasmas on emitting electrodes. The case considered is when the dominating ionization mechanism in the plasma is ionization by electron impact, and the dominating recombination mechanism is recombination with an electron as a third body. The ratio of the Debye length to the recombination length is treated as a small parameter, and the method of matched asymptotic expansions is employed. Analytical formulas have been obtained for the distributions of the number densities of ions and electrons and of the electrostatic potential in each asymptotic zone. Formulas have been obtained describing the voltage drop in the boundary layer as a function of the density of the electric current coming from the plasma to the electrode     

Nonlinear waves in weakly dispersive random media

The propagation of nonlinear waves in random media is an important aspect of nonlinear wave theory and has a long and informative history. This paper describes the basic ideas of the approaches that have been applied. The average-field method, which has been used most extensively in linear problems, is considered. This approach is then shown to be incorrect as far as nonlinear processes are concerned. Finally, a new scheme is proposed average-form the method, which allows consistent evolution equations to be obtained for nonlinear waves in random media.Institute of Applied Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 8, pp. 760–766, August, 1993.     

The perturbed region of a weakly ionized plasma near a cold electrode

An asymptotic theory of the perturbed region of a weakly ionized plasma of molecular gases with allowance for the separation of the charges and the gas-phase ionization and recombination reactions was developed earlier by the author of the present paper for the limiting case of a hot electrode [1], when the ratio (calculated using the electrode temperature) of the chemical-equilibrium molecular concentration of the charged particles to the unperturbed concentration is in order of magnitude equal to unity. In the present paper, the opposite limiting case of a cold electrode, when this ratio is small, is considered.     

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.     

Exploding solutions for three-dimensional rimming flows

We examine the linear stability of a thin film of viscous fluidon the inside of a cylinder with horizontal axis, rotating aboutthis axis. Unlike previous models, both axial and azimuthalcomponents of the hydrostatic pressure gradient are taken intoaccount, which yields solutions which collapse in both dimensions.Two types of such solutions are found: disturbances with zeroand non-zero net mass (the former have greater explosion rates,that is, their amplitudes grow faster than those of the latter).It is also shown that, despite the existence of exploding disturbances,all solutions with harmonic dependence on time (eigenmodes)are neutrally stable