Spectral Characteristics of Waveguide Systems

The existence of waveguide trapped modes is considered. We prove that trapped modes embedded in a continuous spectrum are unstable in the presence of small real perturbations of the waveguide filling.     

Geometric interpretation of the tensor of an electromagnetic field with orthogonal components E and B

An electromagnetic field with (B, E) = 0 is interpreted geometrically as associating with each point (x, y, z, t) of the projective line ?³. For this field, the general solution to the first four Maxwell equations, ?\(\mathfrak{o}\mathfrak{t}\) F = 0, is obtained. The remaining four equations are reduced, in a field with no charges and currents, to a problem which is bound up with the scalar wave equation.     

Effect of unstable MHD modes on the confinement of a stellarator plasma

The results of an experimental study of the influence of unstable MHD modes on plasma confinement in an L-2M stellarator are presented. The spectral and statistical characteristics of turbulent plasma simultaneously at both the edge and center of the plasma are investigated. It is shown that at constant power of electron-cyclotron heating of the plasma the energy content of the plasma depends strongly on the strength of the externally applied vertical magnetic field used to adjust the position of the plasma column. Appreciable degradation of plasma confinement is observed for values of the vertical field such that ideal MHD modes become unstable in the greater part of the plasma column. This in turn is due to the formation of a magnetic configuration with a magnetic “hump.” At the same time, in the edge plasma the instability of resistive-balloon modes grows, and turbulent particle transport increases. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 6, 407–412 (25 March 1999)     

A Numerical Method for Constructing a Self-Similar Isolated Wave Solution

An efficient numerical algorithm is developed for constructing self-similar isolated wave or switching wave solutions. The algorithm is developed for the well-known Kolmogorov–Petrovskii–Piskunov (KPP) problem, which has a switching-wave analytical solution, and is applied to construct an isolated traveling pulse in the four-component reaction–diffusion model.     

Sampling Errors in Monitoring the Pollution of Environmental Samples

Designs of experiments were proposed for estimating random sampling errors in ecological monitoring and errors due to sample delivery to the laboratory. The designs were tested in controlling pollutants in gas and dust atmospheric emissions, atmospheric aerosols, insoluble snow cover residues, soils, and plants. It was found that the contribution of random sampling errors was often dominant as compared to the errors introduced in the course of analysis of laboratory samples.