International Journal of Antennas and Propagation

Volume 2015, Article ID 736090, 5 pages

http://dx.doi.org/10.1155/2015/736090

## Modeling of a Plasma Antenna with Inhomogeneous Distribution of Electron Density

^{1}State Key Laboratory of Pulsed Power Laser Technology, Electronic Engineering Institute, Hefei, Anhui 230037, China^{2}Institute of Information Ammunition, Academy of Army Officers, Hefei, Anhui 230031, China

Received 16 October 2014; Accepted 26 January 2015

Academic Editor: Atsushi Mase

Copyright © 2015 Zong-sheng Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The distribution of the electron density along a plasma antenna can influence the antenna’s performance. But little has been done in this regard in former studies. In this paper, a model of a practical plasma antenna with an inhomogeneous distribution of electron density is founded according to the transmission-line equivalent theory of a metal monopole, from which the current distribution and the radiation pattern of a plasma antenna with appropriate parameters are calculated. The results show that the electrical current distribution, the maximum radiation direction, and the beamwidth of a plasma antenna vary with electron density distributions. To validate the model, the plasma antenna with the same parameters is also simulated based on electromagnetic software HFSS. It is found that the results from the two ways are almost consistent.

#### 1. Introduction

Compared with the conventional metal antenna, plasma antennas use ionized gas as the conducting medium instead of metal, which have excellent potentials for applications and have attracted intensive interest of researchers [1–3]. Models of the plasma antenna and simulations of the radiation pattern by using different numerical methods have been provided [4–7], and some significative results have been achieved. A number of the models were founded on the dispersion relation of surface wave along ideal plasma columns in vacuum [1, 4–6]. But for practical plasma antennas, the plasma is restricted in a tube. So the outer and inner radius of the tube, the dielectric constant of the tube material, and the density distribution of the plasma should be also taken into account in the computation. Zhao et al. [7] examined influences of the dielectric constant and the radius of the tube on the far-field radiation pattern of the plasma antenna. However, the model assumed that the density distribution of the plasma in the tube is homogeneous, other than the linear distribution in the actual tube [3, 8]. In the present paper, we developed a model of the plasma antenna with inhomogeneous distribution of the electron density. From the model, electrical current distributions and radiation patterns of plasma antennas can be calculated. Moreover, another model of the plasma antenna was constructed using electromagnetic software HFSS, which is an interactive software package for calculating the electromagnetic behavior of a structure [9]. Results from the software could attest the validity of the first model.

#### 2. Theoretical Model

The electrical current distribution of the plasma antenna can be expressed mathematically and analogously to that of a monopole. According to the transmission-line equivalent theory of a metal monopole, the current distribution along the antenna can be written aswhere is the magnitude of the current, is the length of the antenna, is the axial distance from the bottom of the antenna, is the real part of the wave vector , while is the imaginary part.

For a metal monopole, the far-field radiation is well known aswhere is the maximal value of the current on the antenna.

Using (1) and (2), the normalized radiation pattern of the plasma antenna can be calculated if the wave vector is known.

For a practical plasma antenna, the plasma column of a radius is contained in a dielectric tube of a thickness . A communication signal with an angular frequency is launched at one end of the antenna. The electron plasma angular frequency is . If , the communication signal propagates as a surface wave. There have been many researches on the surface wave both theoretically and experimentally [8]. IVAN and EVGHENIA investigated its characteristics detailedly when they examined plasma resources produced and sustained by a travelling electromagnetic surface wave [10]. From their study, provided that the plasma density is radially constant, the dispersion relation of the surface wave along a plasma column can be written aswhereand , , , , , , is the collision frequency of plasma, and are the Bessel functions, , , , and are the modified Bessel functions, and are the Hankel functions, and is the dielectric constant of the tube material.

If we assume , (3) becomes where , , . Equation (5) is just the dispersion relation of surface wave along plasma column in vacuum as shown in former studies [4–6].

The electron density along the plasma antenna decreases almost linearly and can be expressed approximately as [3, 8, 11]where is the density at the bottom of the plasma antenna while is that at the top.

#### 3. Numerical Results and Discussion

Using (1) to (3) and (6), the normalized radiation pattern of the plasma antenna and its electrical current distribution were calculated with , , , , , , , and a communication signal frequency . These parameters are consistent with the cases of our experiments, which have been proven reasonable for the practical plasma antenna. With other appropriate values, the model founded in our paper can be also applicable. Figure 1 is the normalized radiation pattern of the plasma antenna with different distributions of electron density. Comparatively, the normalized radiation pattern of a metallic antenna with the same length is also presented. The calculating results show that the normalized radiation pattern of the plasma antenna is markedly influenced by the electron density distribution and has great difference from that of a metallic antenna with the same length. In spite of the same collision frequency and length, the maximum radiation direction and beamwidth of the plasma antenna vary due to different density distributions. The main reason for this phenomenon is that the plasma density and its collision frequency determine the wave vector , which impacts the electrical current distribution along the plasma antenna. Figure 2 gives the real part and the imaginary part of the wave vector along the plasma antenna.