Advantages and Disadvantages of Different Coupling Methods of Plasma Antennas

: One of the important challenges in plasma antennas, is the coupling of RF signal to the plasma column. RF signal coupling has a significant effect on antenna efficiency, antenna implementation cost, structure implementation complexity, antenna pattern shape, and final structure weight and volume. In this article, firstly the various methods of coupling were introduced. Then capacitive coupling, direct coupling and sleeve coupling were presented and their advantages and disadvantages were mentioned. As a sample, a plasma folded monopole antenna with sleeve coupling was fabricated and measured. By comparison of the different coupling methods and as a result, one can conclude that the sleeve coupling method is the most suitable method. This method has the least sensitivity to change the dimensions. It is also easy and cheap to implement. In this type of coupling, the efficiency of the Nesta antenna is suitable and the coupling structure adds small weight and volume to the antenna structure.


INTRODUCTION
The controllable conductive-dielectric property of plasma has been known for decades, and makes it practical in many microwave applications, such as stealth reconfigurable antennas [1][2][3][4], frequency selective surfaces [5], lenses [6], waveguides, reconfigurable cavities [7], phase shifters [8] and attenuators [9]. Plasma elements can be reconfigured electrically, which is impossible to be done by a metal. Plasma antennas have a higher degree of freedom than metal antennas, which 2 provides a variety of capabilities for plasma antennas. Plasma antennas use ionized gas as an electron conduction medium. The advantages of plasma antennas are that they are highly reconfigurable and can be turned on and off. [10].The plasma antenna can be classified into two groups: plasma antennas that the plasma is used in as a parasitic element and plasma antennas that the plasma is used as a driven element. Samples of the first group have been implemented. The most famous ones are [1], [11], and [12]. In the second group of plasma antennas, first the tube gas must be ignited to produce the plasma in it [13][14][15][16][17], then the RF signal should be coupled to the plasma column with another equipment. For coupling RF signal to the plasma column, these questions must be answered: What are the methods of RF coupling to the plasma column? What are the properties of these methods? What is the best method for the coupling? What are the optimized dimensions for the coupler?

PLASMA THEORY
Gas-discharge plasmas are weakly ionized plasmas [18,19] that are one of the most used forms of plasmas [20]. The word "plasma" originates from blood plasma by I. Langmuir in 1923 [21]. A gas-discharge plasma is the result of passing an electric current through a gas under the presence of an external electric field [22]. Plasma is highly nonlinear and its detailed description requires a highly accurate computer model. However, its behavior can be described by continuity equations.
Plasma is a dispersive medium. The motion of electron in plasma medium is based on the following second order nonhomogeneous differential equation [11]: Where and are the electric charge and mass of electrons, respectively and E is the applied electric field. Also is the collision frequency. In plasmas with industrial applications energy transfer is neutralized by collisions of electrons and particles. Collision frequency indicates this conflict. The collision frequency plays an important role in determining the amount of dispersion and attenuation. This quantity varies in different gases.
The solution of equation (1) shows the place of electrons versus time. Assume time harmonic electric field is applied to the plasma. Then the phasor solution of this equation is: By involving this solution in the polarization equation = − (where is the density of electrons) and using = 0 + the following equation can be obtained: From this equation, and constitutive relation = the dielectric relative permittivity of a nonmagnetic, non-thermal plasma can be obtained through the following equation and is known as cold-plasma or Drude dispersion model, which is plotted in Fig. 1 versus normalized frequency.
Where and are the operating frequency and electron plasma frequency, respectively. In fact, is the frequency with which the electrons fluctuate between the ions. If the frequency of the incident wave to the plasma region is less than the plasma frequency, the reaction of the electrons in the plasma to the electric fields of the electromagnetic wave is in the form of energy absorption.
Conversely if the frequency of the incident wave to the plasma region is greater than the plasma frequency, the electrons will be unable to react and will be fixed. So, the wave will pass without much reflection or loss. This phenomenon occurs in earth's ionosphere when signals are in FM and TV bands greater than 90 MHz.
It is obvious that for and >> the equation (4) can be written as the following equation: So, the plasma acts like a metal and its conductivity is obtained by: According to this equation, the conductivity of plasma can be altered by changing the frequency and collision frequency of the plasma [24].

METHODS OF COUPLING
The RF signal can be coupled with a plasma column by different methods but, the most famous methods are capacitive coupling [11,12], direct coupling [13] and sleeve coupling [14,15]. These methods are explained in the following sections.
A. Capacitive Coupling Fig. 2 shows a plasma antenna with capacitive coupling. In this coupler, the outer conductor of RF coaxial cables connected to a cylindrical metallic box and inner conductor of RF coaxial cable is connected to a metallic sleeve that surrounds the plasma column. For analyzing this coupler, it can be assumed that this coupler resembles a cylindrical resonant cavity that is perturbed by the plasma column. By calculating the cavity resonance frequencies, resonance frequencies of the capacitive coupler and therefore resonance frequencies of the plasma antenna are calculated. In some cases, the effect of such perturbations on the performance of the cavity can be calculated exactly, but often approximations must be made. One useful technique accomplishing this goal is the perturbation method, which assumes that the actual fields of a cavity with a small shape or material perturbation are not greatly different from those of an unperturbed cavity. In [7] resonance frequencies of a cylindrical cavity that perturbed with a plasma column is calculated. Comparing approximated results acquired from perturbation method [7] with CST software results shows a good agreement between them. For example, in Fig. 3 variations of resonance frequency versus inner radius of cavity ( 1 ) are shown in both simulated and approximated results.

B. Direct Coupling
As shown in Fig. 4, in this method, RF signal is connected to the ends of a plasma element, directly.
For igniting of the plasma, a high voltage must be applied across two ends of the plasma element.
Therefore, equipment for insulating RF signal from igniting power is needed. Using a high pass filter before the RF signal and a low pass filter before igniting power is one of the simplest solutions for this problem. In practice we can use a duplexer for this purpose.    The other coupling method of the plasma antenna is sleeve coupling. In this method for coupling of the RF signal to the plasma column, two sleeves are placed at the plasma tube, as shown in Fig.   7. A structure shown in Fig. 8 is suitable for simulating of this coupler.  Fig. 7]. Therefore, the effect of these three parameters on the antenna resonance 9 frequency must be investigated. After the run of different simulations, it is found that the antenna resonance frequency is not sensitive to the distance of two sleeves ( 1 ). Fig. 9 shows this property.
Also, by varying the X_min_C, the resonance frequency doesn't change noticeable. (Fig. 10 As shown in Figs. 9 and 10, it is concluded that the resonance frequency of the plasma antenna with sleeve coupling has a low sensitivity to the dimensions of structure. Similar to the metallic dipole antenna, it can be found that the length of the dipole for the first resonance is related to the wavelength (Equation 9). There is a constant term in this relation because the plasma parameters are not scaled whereas other parameters (frequency and length) are scaled [15]. = 0.8487 + 127.11 (9) Where the wavelength of the first resonance of the antenna and L is the antenna length.
The simulated results for 11 of the plasma antenna with sleeve coupling in different antenna lengths is shown in Fig. 11. Three-dimensional radiation pattern of this antenna with sleeve coupling is shown in Fig. 12, which collision frequency is = 900 and electron plasma frequency is =7 GHz. It can be found that this pattern, approximately, is similar to the pattern of a metallic dipole antenna.
Both patterns are omnidirectional and the main lobe occurs in the normal plane to the antenna.
Also, the radiation efficiency of this antenna is about -0.34 dB that is suitable enough. Another advantage of the sleeve coupling method are that, this method is easy for implementation and has low cost.

A. Comparison of Complexity and the cost of Implementation
Because of the capacitive coupling structure, this method is the most complex and the most expensive method. Direct coupling needs the isolation circuit that must be designed and fabricated.
So, this method is more complex than the sleeve coupling method. There it is concluded that the sleeve coupling method is the simplest and cheapest method for RF coupling in the plasma antenna.

B. Similarity to the Metallic Dipole Antenna
The maximum value of the metallic dipole pattern occurs at θ=π/2 but in the capacitive coupling, there is a null at θ=π/2 [11,12]. Therefore, the radiation pattern of the capacitive coupling method is different from the metallic dipole. In the sleeve coupling, the pattern is a little different from the metallic dipole because of the T-match network and in the direct coupling the pattern is similar to the metallic dipole completely.

C. Comparison of the Radiation Efficiency
Radiation efficiency of the capacitive coupling is insufficient (Typically is about -10 dB) but the radiation efficiency of the direct and the sleeve coupling is sufficient (Typically is about -1 dB).

D. Comparison of the Coupler Dimensions and Volume
One of the attractive capabilities of plasma antennas is its camouflage from waves. The antenna coupler is metallic and is in conflict with this important property of plasma antennas. Therefore, the antenna with a small coupler is better. Moreover, the size and weight of antenna structure must be small as possible. The capacitive coupling coupler is large but the sleeve coupler includes less metal than the capacitive coupler and the direct coupler has the least metal [11][12][13][14][15].

E. Comparison of Dimension Sensitivity
Dimension sensitivity of the capacitive coupling is high but the sensitivity of the two other methods is low. Now, comparison of advantages and disadvantages of the different coupling methods are shown in Table 1. Based on the topics discussed, it is concluded that sleeve coupling is the best method for coupling of RF signal to the plasma column and the capacitive coupling is the worst method.   Table 2.  2-The electron-electron interaction is ignored.
3-The electron-ion interaction is ignored.

4-
The electrons reach thermal equilibrium in contact with the ion network and after collision in a random direction, they move at a speed corresponding to the ambient temperature. In the warmer environment, the temperature and energy of these electrons increase.

5-
The system memory disappears after each collision and the electrons are under no external force when moving.
Although this model is valid for analysis of the metallic environments, with proper approximation it can be used for gas environments and electron plasmas.
In this model we substitute 900 MHz for electron-neutral collision frequency and 7 GHz for plasma frequency [9]. The metal is set as aluminum with conductivity equal to 3.56 10 7 S/m.

Results and Discussion
Fig. 14 shows the fabricated folded monopole plasma antenna with sleeve coupling. The amplitude of S11 is measured in frequency range 400 MHz to 6 GHz and is shown in Fig. 15. In the measurement process, by switching plasma on, one resonance appears at 1.4 GHz and receiving waves to the antenna are absorbed but by switching plasma off, any resonance appears in plasma and the waves are not absorbed, exactly, similar to when any antenna is present (Fig. 15).

CONCLUSION
In this paper, the different coupling methods of RF signal to the plasma antenna were investigated. Three methods were introduced: capacitive coupling, direct coupling and sleeve coupling. It is shown that each method has advantages and disadvantages. Capacitive coupling method suffer from bigness, complexity, bad pattern, high sensitivity and has one benefit, good shielding for RF signals. Direct coupling suffers from additional equipment for isolation and has some benefits, good radiation efficiency, and pattern similar to dipole, low weight and volume.
Sleeve coupling has some benefits, good radiation efficiency, low weight and volume, low cost and simplicity of implementation. It is concluded that the sleeve coupling is the best method. A folded monopole plasma antenna with this coupling was fabricated and measured. An important result was observed that when plasma is turned on, a resonance for the antenna can appear. By this method, the antenna parameters can be changed electrically, without any mechanical changes in the antenna structures.

ACKNOWLEDGEMENT
The data that support the findings of this study are available from the corresponding author . The authors declare that they have no conflict of interest upon reasonable request.

DECLARATIONS
We declare that, there is no funding to report for this submission. Also, we wish to confirm that there are no known conflicts of interest associated with this publication and there has been no financial support for this work. Also, the data and code that support the findings of this study are available from the corresponding author upon reasonable request.