#### What is in this article?:

- Analyze The RCS Of A Plasma Antenna
- Achieving A Stealth State

For systems where detection must be minimized, plasma antennas can provide a small radar cross section (RCS).

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Plasma antennas offer some special qualities that make them attractive for electronic-warfare (EW), radar, and other applications that may require stealth operation. The plasma in these antennas is essentially a blend of electrons, ions, and neutrons. When the density of the plasma is high enough, an electromagnetic (EM) wave will travel on its surface rather than deep into it. The plasma will exhibit the properties of a conductor, serving as an antenna for transmitting and receiving signals.

Consequently, a plasma column can be used as a radiative element in place of a metallic conductor. The plasma becomes conductive when energized by an RF source, and nonconductive once the source is removed. As a result, it can be made to have a radar cross section (RCS) that virtually disappears to an enemy radar once the RF source is removed.^{1} Another advantage of a plasma antenna compared with its metal counterpart is that it can be reconfigured; its radiation characteristics can be changed conveniently by electrical rather than mechanical control.^{2}

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Much study has focused on plasma antennas—mainly to understand their radiation characteristics, including the input impedance, the radiation pattern, and the loss of the plasma column by means of analytical solutions or numerical simulations.^{3-5} Because a plasma antenna has little or no RCS when it is turned off, it has had great appeal for defense applications. But when it is on, whether transmitting or receiving, it does have an RCS and can be detected by an enemy radar. Understanding its RCS characteristics when it is powered on is important for applying these antennas to stealth applications.

Unfortunately, of the studies performed so far on plasma antennas, none has addressed the RCS characteristics of these antennas. As is known, plasma is a dispersive media for which the relative permittivity is dependent upon frequency. Various approaches can be used to simulate the interaction of EM waves with a plasma antenna. The two main methods based on finite-difference-time-domain (FDTD) analysis are the direct integration and the recursive convolution methods. Yoonjae Lee^{6} and Fan Luo^{7} studied the radiation characteristics of plasma antennas using the former method. Xue-Shi Li^{8} investigated the input impedance and radiation patterns of plasma antennas with nonuniform distribution of the plasma using the latter method. But neither addressed scattering fields from plasma antennas.

In the present study, FDTD analysis using the Z-transform will be applied for simulating the interaction of EM waves and an unmagnetized plasma antenna. Considering a plasma antenna as an infinite square column with a dielectric tube, it can be simulated by means of iterative formulas. The simulations can be applied to analyze the antenna’s RCS characteristics in terms of inhomogeneous plasma density, different EM incident frequencies, different plasma collision frequencies, and different relative dielectric constants for the tube containing the plasma.

Unmagnetized cold plasma is a dispersive material, with an effective relative dielectric constant, ε_{r}, given by Eqs. 1 and 2^{9}:

where:

v_{c} = the electron-neutral collision frequency;

w_{pe} = the plasma angle frequency;

w = the angle frequency of the incident EM wave;

n_{e} = the plasma density;

e = the electron charge; and

m_{e} = the mass of the electron.

The complete set of Maxwell’s equations forunmagnetized cold plasma is given by Eqs. 3-6:

Note that Eq. 3 is written in the frequency domain and must be translated into the time domain for implementation into FDTD analysis. Substituting Eq. 1 into Eq. 5 yields Eq. 7:

By the convention theorem,^{10} the Z transform of Eq. 5 becomes Eq. 8:

Introducing an auxiliary term:

E(z) can be solved as shown in Eqs. 10 and 11:

As a result, the iterative formulas for FDTD are shown in Eqs. 12 and 13:

Equation 12 and 13 apply to one-dimensional space. They can be extended to two-dimensional use by means of Eqs. 14 and 15:

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