Application of Telegraph Equations for Modeling of Plasma Antenna Characteristics
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LLATIONS AND WAVES IN PLASMA
Application of Telegraph Equations for Modeling of Plasma Antenna Characteristics A. S. Kovaleva, V. A. Vozhakovb, c, N. V. Klenova, b, c, d, *, S. S. Adjemovc, and M. V. Tereshonokc, d a Skobeltsyn
Institute of Nuclear Physics, Moscow State University, Moscow, 119991 Russia State University, Faculty of Physics, Moscow, 119991 Russia c Moscow Technical University of Communication and Informatics, Moscow, 111024 Russia d Moscow Technological University (MIREA), Moscow, 119454 Russia *e-mail: [email protected] b Moscow
Received February 13, 2017; in final form, July 7, 2017
Abstract―A method is proposed to calculate the characteristics of a plasma antenna analytically. The method allows one to simply take into account the finiteness of the region occupied by the ionized gas and find the distributions of the main plasma parameters along the antenna. DOI: 10.1134/S1063780X18020071
1. INTRODUCTION During the past decade, the number of publications devoted to designing and studying new types of devices intended to receive and transmit electromagnetic radiation in different frequency ranges has increased substantially. Among such devices, plasma antennas (PAs), in which an ionized gas is used as the working substance instead of metals, have attracted considerable interest [1–9]. Antennas of this kind have a number of advantages: a PA can be abruptly “switched off,” due to which its effective scattering area is reduced radically; its characteristics can easily be varied by varying the plasma parameters; it can also operate as a filter, i.e., it can transmit high-frequency signals and simultaneously receive lower frequency signals; etc. We note that, along with PAs, metal antennas covered with a plasma layer were also studied [1, 10, 11]. The goal of this work was to develop methods for calculating the characteristics of these promising devices intended to be used in radars and communication systems. 2. CALCULATION OF THE CHARACTERISTICS OF A SURFACE WAVE IN A PLASMA COLUMN BY SOLVING MAXWELL’S EQUATIONS To date, there is no general theoretical method to describe even such a simple physical model of a PA as a finite-length dielectric tube filled with a noble gas (Fig. 1). The solution to Maxwell’s equations in the form of an azimuthally symmetric surface wave propagating along an infinitely long cylinder filled with a uniform plasma has been known for a long time [12].
This solution can also be obtained from the equations for a waveguide with dielectric insertions after substituting the expressions for the plasma permittivity into them [13]. Let us consider a plane wave, exp{i(ωt – kz)}, which propagates along the Z axis. The wave electric field has two components Ez and Er, directed along the Z axis and the radius, respectively, while the magnetic field has only one component Hθ, directed azimuthally. The wave equation for the complex amplitude of the magnetic field can be written in the form [12] 2
d H θ 1 dH θ ⎛ 2 + + ⎜ ω ε0μ0ε − k 2 − 12 ⎞⎟ H θ = 0. 2 ⎝ r dr dr r ⎠
(1)
Here, ε is the
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