Field of an electric dipole surrounded by a nonuniform cylindrical plasma sheath

Abstract

We analyze and solve the problem of the field of a dipole surrounded by a cylindrical plasma sheath with a piecewise-linear profile of dielectric permittivity ε including the point at which ε = 0. The predominant influence of the region in which ε = 0 on the formation of the dipole field is shown. The resonant properties of the solution in the case of a small cross-sectional size of the cylindrical sheath are studied.An increase in the radiation from antennas sura Fig. 1.rounded by plasma sheathes of various shapes (circular or elliptic cylindrical, spherical, and spheroidal) for the same current as in the sheathless antenna was considered for the model of a plasma sheath in the form of a homogeneous or piecewise-homogeneous medium with a step-like transition of dielectric permittivity between a vacuum layer (ε = 1) and a plasma layer with the negative real part of dielectric permittivity [1][2][3][4][5][6]. In those works, the region in which the real part of dielectric permittivity went to zero was not considered, although this region predominantly affects the formation of the source field in the cases analyzed in [7,8]. In this paper, we study the influence of a plasma sheath on the source field within the framework of a model allowing for the transition region between a vacuum cavity and a plasma sheath. At first, we consider a model in which the transition is described by a piecewise-constant profile of dielectric permittivity with a zero real part. Then we study another plasma-sheath model in which the transition between a vacuum layer and a uniform plasma sheath is described by a linear profile of dielectric permittivity with the real part crossing zero.Let us pass to solving the first problem. Consider the radiation from an electric dipole located at the center of the cross section of an infinitely long cylindrical plasma column ( Fig. 1) with radius a such that the cross-sectional size of the cylinder is small (ka 1, where k = ω/c, ω is the angular frequency, and c is the speed of light). We assume that the dipole moment of the source located at the origin of a system of cylindrical coordinates (r, ϕ, z) is aligned with the column radius for z = 0 and ϕ = 0, i.e., the electric dipole is horizontal. Note that in the case of a dipole moment parallel to the axis of a plasma column, a resonant increase in the radiation field is absent [9]. The relative dielectric permittivity of the medium filling the cylindrical column is described by a piecewise-constant function ε p (r) (Fig. 2a) such that * Yulia.Afanasyeva@paloma.spbu.ru