Toward the theory of a loop antenna in an anisotropic plasma

We consider the problem of determining the current distribution along a loop antenna consisting of an infinitely thin perfectly conducting strip coiled into a ring. The antenna is immersed in an anisotropic plasma medium perpendicular to the external magnetic field and is excited by a given EMF. Primary attention is focused on the frequency band in which the excitation of electrostatic waves is possible. The problem is reduced to solving a system of integral equations with logarithmic and singular kernels. Using the solution of these equations, we found expressions for the antenna current distribution and input impedance. The analysis of these expressions is presented. Radiophysical Research Institute, Lobachevsky State University, Nizhny Novgorod, Russia. Translated from izvestiya Vysshikh Uchbnykh Zavedenii, Radiofizika, Vol. 41, No. 3, pp. 358–373, March, 1998.     

Quasi-static field of an elementary electric dipole in a moving,isotropic, warm plasma

We have investigated the field of an elementary electric dipole in a medium moving at nonrelativistic velocities. We used a quasi-static approximation and a hydrodynamic model of the plasma, taking into account the thermal motion of the electrons. The plasma is assumed to be isotropic, uniform, and infinite. We demonstrate that the intrinsic spatial dispersion of the medium (in the associated reference frame) produces a change in the plasma wave part of the source field.Kirovskii State Teachers Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedeni Radiofizika, No. 10, pp. 1227–1236, October, 1994.     

A theory of the successive production of moving striations in the plasma of inert gases

On the basis of results already published of experiments carried out by the method of excitation of transient processes with small perturbation, a theory is elaborated on the successive production of moving striations (waves of stratification) in an inert gas. The stratification of the plasma is interpreted as the successive production of regions with an alternately positive and negative space charge, i. e. as the producti n of a characteristic macroscopic periodic polarization of the plasma. The basic assumption of the theory is the relative independence of the chain of processes in each dark or light region of the striations, so that interaction between the regions occurs as a result of the electric field of the space charge in the neighbouring region.Equations are derived expressing the chronological order of the processes leading to the production of a space charge in each individual region and the interaction of the regions. The solution of the equations leads to functions, some of which are in agreement with experimental data while others cannot be verified on the basis of the experimental material at present at our disposal and require the carrying out of new experiments.The main results contained in this paper were reported on at the Conference on the Physics of Plasma in Leipzig on October 8th, 1956.     

Characteristics of receiving antenna arrays measured in a shallow sea

A diagnostic technique for receiving hydroacoustic antenna arrays operating in a shallow sea is presented. The technique reconstructs the hydrophone transfer coefficients, the array profile, and its position relative to the surface and the bottom. A stepped-frequency source and a special receiving element with a known transfer coefficient are used. The technique is illustrated by experimental hydroacoustic data, and the error in reconstructing each of the parameters is estimated.     

The theory of moving striations in a D-C discharge plasma II. High current approximation

The integrodifferential equation of striations, found in the preceding part [1] of this theory, is simplified for the case when the Debye lengthl _D is vanishingly small in comparison with the wave-length of the striations. It then takes the form (51b). The still non-zero space charge field then influences the motion of the charge carriers in such a way that it takes on the character of ambipolar diffusion in the axial direction. This is expressed by the first term on the right-hand side of Eq. (51b). The second and third terms describe the influence of the space charge field on the ionization rate through the changes in the electron temperature. Thus the third (integral) term causes the oscillatory behaviour of the transient process excited by a pulse disturbance, while the second term can lead to growth of the amplitude (i.e. to amplification) of the transient wave.The transient solution of Eq. (51b) is given by the formula (73). It is in full qualitative agreement with the experiment and the quantitative agreement is also sufficient. This shows that processes found to be decisive for the very nature of moving striations [11] and for their amplification [16] do determine with sufficient accuracy even other finer properties of striations. The choice of optimum wave-length, in the conditions studied in this paper, is fulfilled by the ambipolar diffusion in the axial direction, which damps the short wave-length striations, and by the final value of the relaxation length of the electron temperature [1/a ₁, see Eq. (4)] which limits the long-distance effect of the electric space charge field on the ionization rate.In conclusion, the authors thank F. Kroupa and M. Novák for carefully reading the paper and for valuable remarks, and S. Vepek for help in the calculations.     

Screening of a moving charge in a nonequilibrium plasma

Based on the model of point sinks, we consider the problem on the screening of the charge of a moving macroparticle in a nonequilibrium plasma. The characteristic formation times of the polarization cloud around such a macroparticle have been determined by the method of a three-dimensional integral Fourier transformation in spatial variables and a Laplace transformation in time. The screening effect is shown to be enhanced with increasing macroparticle velocity. We consider the applicability conditions for the model of point sinks and establish that the domain of applicability of the results obtained expands with decreasing gas ionization rate and macroparticle size. We consider the problem of charge screening at low velocities and establish that the stationary potential of the moving charge has a dipole component that becomes dominant at large distances. We show that the direction of the force exerted on the dust particle by the induced charges generally depends on the relationship between the transport and loss coefficients of the plasma particles in a plasma. When the Langevin ion recombination coefficient β _iL = 4πeμ _i exceeds the electron-ion recombination coefficient β _ei , this force will accelerate the dust particles in the presence of sinks. In the absence of sinks or when β _ei > β _iL , this force will be opposite in direction to the dust particle velocity. We also consider the problem on the energy and force of interaction between a moving charged macroparticle and the induced charges.     

Screening of a moving charge in a nonequilibrium plasma

The problem of screening a moving charged dust particle is analyzed in the model of point sinks. Typical time scales for the formation of a polarization cloud around the moving macroscopic particle are found using the three-dimensional integral transform with respect to the spatial coordinates and the Laplace transform in time. It is shown that the stationary potential of a moving charge has a dipole component dominating at sufficiently large distances. The force exerted on a moving charged macroscopic particle by the electric field of induced charges is calculated. It is shown that, in general, the direction of this force depends on the ratio between the transfer coefficient and the decay rate of plasma particles in the plasma. In the presence of sinks, a dust particle is accelerated by this force if the Langevin recombination rate for ions, β _iL = 4πeμ _i , exceeds the electron-ion recombination rate β _ei . In the absence of sinks or if β _ei > β _iL this force is antiparallel to the dust-particle velocity.     

Schwarzschild black hole as moving puncture in isotropic coordinates

The success of the moving puncture method for the numerical simulation of black hole systems can be partially explained by the properties of stationary solutions of the 1 + log coordinate condition. We compute stationary 1 + log slices of the Schwarzschild spacetime in isotropic coordinates in order to investigate the coordinate singularity that the numerical methods have to handle at the puncture. We present an alternative integration method to obtain isotropic coordinates that simplifies numerical integration and that gives direct access to a local expansion in the isotropic radius near the puncture. Numerical results have shown that certain quantities are well approximated by a function linear in the isotropic radius near the puncture, while here we show that in some cases the isotropic radius appears with an exponent that is close to but unequal to one. This paper is dedicated to the memory of Jürgen Ehlers. I have known JE for a number of years, in particular during his time as founding director of the Albert Einstein Institute in Potsdam. JE was the mentor of my habilitation thesis in 1996, and I am deeply thankful for many insightful discussions. JE combined great breadth and physical intuition with sharp analytical thought. His example inspired me to look beyond the numerical methods and results of numerical relativity to the analytic foundations. For example, while at the AEI, S. Brandt and I introduced “puncture initial data” for the numerical construction of general multiple black hole spacetimes [3]. While the puncture construction starts with an analytic trick of the sort that numerical relativists may devise, it is fair to say that the keen interest in analytical relativity created by JE at the AEI induced us to push our analysis one step further. As a result [3] connects to [26] for an existence and uniqueness proof for such black hole initial data, using weighted Sobolev spaces (see also [4–6]). The present work and its predecessors [9–12] represent an example where numerical experiments led to the discovery of an analytic solution for the 1 + log gauge for the Schwarzschild solution, and the present result, although modest, is of the type which I believe JE would have appreciated.