Acta Polytechnica doi:10.14311/AP.2015.55.0034 Acta Polytechnica 55(1):34–38, 2015 © Czech Technical University in Prague, 2015 available online at http://ojs.cvut.cz/ojs/index.php/ap OPERATION MODES AND CHARACTERISTICS OF A PLASMA DIPOLE ANTENNA Nikolay N. Bogacheva, b, ∗, Irina L. Bogdankevichb, c, Namik G. Gusein-zadeb, c, Konstantin F. Sergeychevb a Moscow State Technical University of Radio Engineering, Electronics and Automation, Moscow, Russia b Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, Russia c Pirogov Russian National Research Medical University, Moscow, Russia ∗ corresponding author: bgniknik@yandex.ru Abstract. The existence modes of a surface electromagnetic wave on a plasma cylinder, and the operating modes and characteristics of a plasma antenna are studied in this paper. Solutions of the dispersion equation of the surface wave are obtained for a plasma cylinder of finite radius for different plasma density values. The operation modes of a plasma asymmetric dipole antenna of finite length and radius are researched by numerical simulation. The electric field distributions of the plasma antenna in the near field and the radiation pattern are obtained. These characteristics are compared with the characteristics of a similar metal antenna. Numerical models are verified by comparing the counted and measured metal antenna radiation patterns. Keywords: plasma antenna, surface electromagnetic wave, numerical simulation, operation modes, metal monopole, radiation pattern. 1. Introduction In recent years much plasma antenna research has been done by theoretical, numerical and experimental methods [1–11]. The most popular plasma antenna type is the Plasma Asymmetrical Dipole (monopole) antenna (PAD) [1, 2, 4–11]. Some little explored prob- lems of plasma antennas are: the noise performances of the plasma antenna; non-linear distortions and cur- rent instabilities in the plasma of gas discharge, the choice of optimum plasma parameters for PAD op- eration, and the role of the surface electromagnetic wave (surface wave) [12] in antenna operation. Our research was focused on the determining the influence of plasma density on the radiation modes of PAD and the interrelation surface wave with antenna operation modes. Previous papers [2, 4, 5, 8–11] have reported nu- merical simulation results. In the context of the simu- lations, some characteristics of plasma antennas have been determined. In these simulations such plasma density values ne were used that plasma antenna func- tioned like metal antenna (ωP e > 10 ·ωew0). However, in experimental studies the plasma density values may be very different, and the plasma frequency may be close to the threshold ωP e ≈ √ 2 ωew0. In this case, the radiation antenna fails, or nonlinear distortions appear in the transmitted signal. For example, it was shown in [7] that at a frequency of 400 MHz, the radiated power dependence P(ne) represents a nonlinear func- tion. Our task was to study the interrelation between the surface electromagnetic wave and the operation modes of a plasma antenna for plasma frequency val- ues in the range of √ 2 ωew0 ≤ ωP e ≤ 15 ·ωew0, where ωew0 = 2πf0 = 2π · 1.7 GHz = 1.07 · 1010 rad/s. 2. Surface electromagnetic wave on a cylindrical plasma column We will consider in this section distribution conditions of the existence modes of a surface electromagnetic wave on the boundary of a plasma cylinder of infi- nite length and fixed radius r0. For this, we use the dispersion equation for an azimuthal symmetric sur- face wave on the cylindrical surface of a conducting medium of radius r0 [13]: ε √ kz 2 − ω2ew c2 K0 (√ kz 2 − ω 2 ew c2 r0 ) K′0 (√ kz 2 − ω 2 ew c2 r0 ) − √ kz 2 − ω2ew c2 ε I0 (√ kz 2 − ω 2 ew c2 εr0 ) I′0 (√ kz 2 − ω 2 ew c2 εr0 ) = 0, (1) where plasma dielectric permittivity ε is defined as ε(ω) = ε0 − ω2P e ωew (ωew + iνe) = ε0 − ω2P e ν2e + i ω2P e ωew νe if ωew � νe, ε0 − ω2P e ω2ew ( 1 − i νe ωew ) if ωew � νe, (2) and ωP e = √ nee2/meε0 — electron plasma frequency, I0, K0 and I′0, K′0 — modified Bessel functions and their derivatives respectively, kz — a wave number, ωew = 2πf — the cyclic frequency of an electromag- netic wave, c — velocity of light, νe — electron colli- 34 http://dx.doi.org/10.14311/AP.2015.55.0034 http://ojs.cvut.cz/ojs/index.php/ap vol. 55 no. 1/2015 Operation Modes and Characteristics of a Plasma Dipole Antenna sion frequency, ε0 — relationship dielectric permittiv- ity, ne — electron plasma density, me and e — mass and charge of an electron. The real part of the solution of the dispersion equa- tion (1) is given in Fig. 1 for the parameters of the plasma used in the simulation part of our studies. Note that νe = 107 s−1, for argon in a tube with pres- sure p0 = 3·10−2 Torr = 4 Pa [4], r0 = 0.5 cm, and the angular frequency on the vertical axis of the graphs in Fig. 1 normalized ω = ωew r0 c , so ω0 = ωew0 r0c = 0.18 and k = kzr0 Fig. 1,a shows for ωP e = √ 2ωew0 = 1.58 · 1010 rad/s (ne = 8.0 · 1010 cm−3) that frequency ω0 misses the asymptotic part of the dispersion curve. In this case, the surface electromagnetic wave propa- gates along the plasma column and does not radiate into the surrounding space (nonradiative mode). If ωP e = 5.35 · 1010 rad/s (ne = 9.1 · 1011 cm−3) (see Fig. 1,b) wave frequency ω0 falls on the nonlinear part of the dispersion curve. At such settings, the electromagnetic wave radiated in space, although the emitted characteristics wave are suboptimal. In this sub-optimal (or transition) mode any small change in the wave parameters can lead to a change in the characteristics of the radiation. For plasma ωP e = 1.07 · 1011 rad/s (ne = 3.6 · 1012 cm−3) (see Fig. 1,c), wave frequency ω0 is near the border of the linear part and the radiation charac- teristics are close to optimal. This will be called the linear mode. 3. Model verification In this section, we compare the results of numerical simulations and experimental measurements of the radiation pattern for verification. We investigated the Metal Asymmetric Dipole (monopole) antenna (MAD) with la = 4.1cm; da = 0.3cm; Ds = 18cm at frequency f0 = 1.7GHz. The radiation pattern in the far field of MAD was obtained by numerical simulation in KARAT code [14] and CAD EMpro [15] and experimental measurements were carried out in an anechoic chamber. The general scheme of the quar- terwave asymmetric dipole with length la, diameter da = 2Ra metal screen diameter Ds = 2Rs is shown in Fig. 2. The MAD model was implemented in full electro- magnetic KARAT code [14] in the 2.5D version. We consider the axisymmetric case with a perfect match- ing layer (PML) on the borders of the counting area. The metal screen and the pin of MAD were given as perfectly conducting surface. Simulation was car- ried out by the finite difference time domain (FDTD) method. The model in EMpro was created in three-dimen- sional geometry in the xyz coordinate system, with a resizable and perfect matching layer at the edges of the counting area. The calculation was performed using the finite element method (FEM) in the block Agilent FEM Simulator. (a) (b) (c) Figure 1. Real parts of dispersion equation solutions for plasma: a) ωP e = 1.58 · 1010 rad/s (ne = 8.0 · 1010 cm−3), b) ωP e = 5.35 · 1010 rad/s (ne = 9.1 · 1011 cm−3), c) ωP e = 1.07 · 1011 rad/s (ne = 3.6 · 1012 cm−3). Fig. 2 shows the results of a numerical simulation and measurement of the radiation patterns for MAD with la = 4.1 cm; da = 0.3 cm and Ds = 18 cm at the frequency f0 = 1.7 GHz. As can be seen from the graphs, the radiation patterns coincide on the main lobe. The side lobes have differences in level and in position. The radiation pattern obtained in KARAT code differs from the measured radiation pattern because the absorber layer is very near to the back surface of the metal screen in the model. The differences in the radiation pattern of the EMPro model is due to the fact that the FEM method are not very correct for devices with a small Q-factor (gain–bandwidth) [15]. 35 Nikolay Bogachev, I. Bogdankevich, N. Gusein-zade, K. Sergeychev Acta Polytechnica Figure 2. Scheme of an asymmetric dipole (monopole) antenna (left side) and the experimental and modeling radiation pattern (right side) of metal asymmetric dipole antenna. Figure 3. Plasma antenna model in KARAT code: 1 — coaxial cable, 2 — plasma column, 3 — metal screen, 4 — absorber (PML). 4. Numerical simulation results and discussion This section presents the results of a numerical sim- ulation of the plasma and metal asymmetric dipole (la = 4 cm, da = 1 cm) with an infinite size of the screen Ds = ∞. The plasma in the model was set as the medium described by the Drude theory, where the dielectric permittivity of the plasma was determined by formula (3) [16]: ε(ω) = 1 − ω2P e ωew (ωew − iνe) , (3) In this model (see Fig. 3.), the Gaussian pulse with τi = 15 ns and frequency f0 = 1.7 GHz reached the plasma (metal) antenna through a coaxial ca- ble. The plasma parameters were changed by varying the plasma density ne (the electron collision frequency remained constant νe = 107s−1). The field of the quarterwave dipole has structure of a TM-mode. So we consider the functions Ez (r) and No. Ratio ωp ne ωp vs ωew0 vs f0 [rad/s] [cm−3] 1 √ 2 ·ωew0 = √ 2 · 2πf0 1.58 · 1010 8.0 · 1010 2 5 ·ωew0 = 5 · 2πf0 5.35 · 1010 9.1 · 1011 3 10 ·ωew0 = 10 · 2πf0 1.07 · 1011 3.6 · 1012 Table 1. Parameters of the plasma. Er(z) to be the most informative. In addition, the selection function Er (z) is due to the proportionality of this component to the distribution of charge Q along the antenna. The spatial structure of the field components Ez (r) and Er (z) (Fig. 4 and Fig. 5) was plotted for the plasma and metal antennas la = 4 cm, da = 1 cm, Ds = ∞ according to the simulation results of code KARAT at frequency f0 = 1.7 GHz. In Fig. 4, function Er (z) are presented in the three operating modes of PAD. In the first mode (the param- eters correspond to point No. 1 in Table 1) there is a surface wave distribution with wavelength λ ≈ 1.5 cm along a plasma column of the antenna (curve 1). This wavelength matches the wavelength calculated in Sec- tion 2 for the same parameters. This case is a nonradia- tive mode. The second mode (No. 2 in Table 1) is sub- optimal transition mode (curve 2). The third mode (No. 3 in Table 1) of the plasma antenna (curve 3) is close to the operation mode of the metal asymmetrical dipole (curve 4). In Fig. 5, the graphics Ez (r) are for the same plasma concentration values as in Fig. 4. Three qualitatively different operation modes of the plasma antenna are also clearly visible. In the first mode (curve 1), can be seen as Ez (r) fades out in both directions from the boundaries of the plasma-vacuum at a different speed 36 vol. 55 no. 1/2015 Operation Modes and Characteristics of a Plasma Dipole Antenna Figure 4. Distributions of Er (z): 1–3 — modes of the plasma antenna, 4 — the metal antenna. Figure 5. Distributions of Ez (r): 1–3 — modes of the plasma antenna, 4 — the metal antenna. Figure 6. Radiation patterns: 1–3 — modes of the plasma antenna, 4 — the metal antenna. and in a vacuum it fades out at the distance a = 1cm, which is much smaller than the wavelength supplied to the antenna (λ ≈ 18 cm). This indicates that when ωP e = √ 2ωew0 the antenna operates as a surface wave line, without radiation of the surface wave into the surrounding space. This mode of operation of the antenna is nonradiative, and it coincides with the existence mode of the surface wave on the plasma column (see Section 2). The second mode is characterized by the presence of a surface wave component and a radiated volumetric wave component in the distribution of Ez (r) (curve 2). The surface component of the wave slowly fades in the depth of the plasma, and the radiated component of the wave for the case ωP e = 5ωew0 differs in phase by more than 60° from the radiation of the metal antenna (curve 4). This is a transition mode, and it is also associated with the regime of the existence of a surface wave on the plasma column. In the third mode (curve 3) Ez (r) consists of a surface part and a volumetric wave part, but the surface wave is attenuated rapidly in the plasma and the volumetric portion is different from the MAD case (curve 4) is only 20° in phase. The difference in the phase of Ez (r) for the real PAD and MAD of imperfect conductors may be less, due to the finiteness of the skin layer. This mode is linear (radiative). The radiation patterns were plotted in the consid- ered cases of PAD and MAD (see Fig. 6). The plasma antenna radiation patterns (curves 1-3) are normal- 37 Nikolay Bogachev, I. Bogdankevich, N. Gusein-zade, K. Sergeychev Acta Polytechnica ized to a metal antenna radiation pattern (curve 4), and are plotted in a rectangular coordinate system for θ values from 0° to 90° (0° coincides with the antenna axis). As the graph shows, in the case of ne = 8.0 · 1010 cm−3, curve 1 is close to 0, i.e. when ωP e =√ 2ωew0, as noted above, the antenna does not radi- ate energy waves into the surrounding space, and all the energy goes to surface wave propagation along the plasma tube. In the transitional mode (curve 2) ne = 9.1 · 1011 cm−3 and ωP e = 5ωew0 the radiation pattern is smaller in amplitude than radiation pat- tern of the metal antenna, which means no optimum plasma antenna operating compared to MAD. The ra- diation pattern of the linear mode (ne = 3.6·1012 cm−3 and ωP e = 10ωew0, curve 3) is very close to curve 4, which implies that the plasma antenna is near to the characteristics of the metal. 5. Conclusions We have obtained the following results by using the solution of the dispersion equation and a numerical simulation: (1.) Three existence modes of the surface wave on an infinite plasma cylinder of finite radius. (2.) The operation modes of a plasma asymmetric dipole antenna. They are nonradiative, transition and linear (radiative). (3.) The relationship between the modes of the exis- tence of a surface wave on an infinite plasma cylinder and the operation of a plasma asymmetric dipole antenna. (4.) The dependence of the operation modes of a plasma asymmetric dipole antenna on the ratio of the plasma frequency and the electromagnetic wave frequency. (5.) The plasma antenna characteristics in the linear mode are close to the characteristics of the metal antenna. In addition, the models used here were verified by experimental measurements. Acknowledgements This work has been supported by the Russian Foundation for Basic Research (RFBR) project N14-08-31336. The authors are grateful to Professor A.A. Rukhadze and Pro- fessor A.M. Ignatov for discussions and useful comments. The measurement patterns were carried out in an ane- choic chamber in the JSC Kulon Research Institute. 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IEEE Transactions on Plasma Science 3(2):55, 1975. [13] A. Aleksandrov, L. Bogdankevich, A. Rukhadze. Principles of Plasma Electrodynamics. Springer Verlach, Heidelberg, 1984. [14] V. Tarakanov. User’s Manual for Code KARAT. VA, Springfield, 1992. [15] Keysight Technologies. About EMpro. http://www.keysight.com/en/pc-1297143/empro. [16] Drude. Zur elektronentheorie der metalle. AnndPhys 1:566, 1900. 38 http://dx.doi.org/10.1063/1.874041 http://dx.doi.org/10.1109/TPS.2004.826019 http://dx.doi.org/10.1109/TPS.2006.872180 http://dx.doi.org/10.1134/S1063780X06050047 http://dx.doi.org/10.1109/ICMMT.2008.4540404 http://www.keysight.com/en/pc-1297143/empro Acta Polytechnica 55(1):34–38, 2015 1 Introduction 2 Surface electromagnetic wave on a cylindrical plasma column 3 Model verification 4 Numerical simulation results and discussion 5 Conclusions Acknowledgements References