Mutual Impedance ofPlasma Antennas
Bo Yin, FengYang Bin Wang, HonggangHao
School of Electronic Engineering, College of Electronic Engineering,
University of Electrnic Scienic and Technology of China, ChongqingUniversity of Posts and Telecommunications,
Chengdu, 610054, China Chongqing, 400065,China
E-mail:
Abstract-- the concept of plasma antennas array has been put forward for a long time, but the study on the mutual coupling between elements of the array is very little. In this paper, a model for antennas array involving two plasma elements is set up, where the density of element 1 is assumed to be very high and could be used as metal, and the mutual impedance between plasma elements is derived detailedly. Then, considering that the density of the plasma element 2 is uniform or non-uniform distribution, we analyse mutual impedance of the two plasma column antennas which vary with the plasma density, collision frequency inside element 2 and the distance of two elements. The result of experiment shows, under normal circumstance, theamplitudes of mutual resistance and reactance between two plasmaantennas are smaller than those between two metallic antennas which has the same configure and size, and the plasma density, collision frequency inside element 2 will impact the impedance. This is very useful for beam forming and directional reconfiguration among of plasma antenna’s application.
Keywords- mutual impedance; plasma column antennas; plasma density; collision frequency
I．INTRODUCTION
Plasma consists of electrons,ions and neurons. When the density of ionized gas is very high enough, theelectromagnetic wave can not go deep into the plasma, and the skin depth is quite small, then plasma exhibits properties of a conductor. Therefore, plasma can be used as a radiator element instead of metallic conductors.By using RF source,the plasma antenna works immediately once it is energized, and will stop instantly with the source removed. When de-energized, plasma is non-conducting, and causes little return wave to radar.Another advantage of plasma antenna is that it can be reconfigured, to change the radiation pattern, conveniently by electrical rather than mechanical control [1] [2].
The previous experiments have demonstrated that the directivity of monopole plasma column antenna is very weak [3], and smaller than that of metallicantennawith the same configuration. However, in the communication, especially the communication from point to point, it needs the antenna with the powerful directivity. This can accomplish through a consideration of plasma antenna array[4]. Although studies on plasma antennas have received considerable attention over the past 30 years, a full set of plasma column antenna has not been extensively studied experimentally and theoretically[5][6]. To the best of our knowledge, there has been no report on the study of the array properties of the plasma antenna so far. Antenna engineers arefrequently faced with the problemof predetermining the input impedance of each element of a directional array. In addition, they must often find theinterference pattern due to the parasitic antennas adjacent to the fed antenna.The same problemhas to be solved when we use more than one plasma antenna at one time which the distance between antennas can not be neglected. To determine the impedance or determine the induced current on the other plasma columns, it is necessary to find the mutual impedance between elements.So the study on mutual impedance of plasma column antennas is very important toanalyse the array properties of plasma antennas.
In this paper, a theoretical model of two center-fed parallel plasma columns of any length is set up based on the physical properties of the plasma.The mutual impedance between plasmaantennas is calculated for the uniform and nonuniform distribution of plasma column, and the results are compared with the mutual impedance of metallic antennas.The data shows that the mutual impedance between two plasmaantennas is smaller than that between two metallic antennas,whetherthe plasma distribution forthe antenna 2 is uniform or non-uniform.And the impedance curves are altered as the plasma frequency or collision frequency varies.
II．Determination of mutual impedance between plasma column antennas
- modeling
Referring to Fig.1, two center-fed plasma column antennas 1 and 2 which lengths are 2l1and 2l2 respectively, are separated by a distance d. Such antennas are constructed from insulting tubes filled with low pressure gases. In circuit theory, The mutual impedance of two coupled circuits is defined as the negative of the radio of the emf V21 in circuit 2 to the I1 flowing in circuit 1 with circuit 2 open[7].The mutual impedance of plasma antennas is
(1)
where V21is the emf induced across the terminals of plasma antenna 2 by the conference current I1 in the plasma antenna 1. The open-circuit voltage of terminal 2 which results from voltage induced by the antenna 1 may be found.
(2)
Fig.1 Two parallel plasma column antennas
For signal frequencies well below the plasma frequency,the surface wave will propagate along cylindrical plasma column. However, thewave vector of surface wave should vary with the plasma density inside the dielectric tube[8][9].For a uniform density and infinitely long plasma column, we may obtain the plasma surface wave dispersion relation by Helmholtz’s wave equation and the boundary condition, that is[10]
(3)
where and , a is the radius of the plasma column, is the wave number is free space. and denote modified Bessel function of the first and second kind respectively. is the plasma dielectric constant, and is the electron-neutral collision frequency. The quantity is the electron plasma frequency, where is the plasma density.The wave vector propagating along the plasma column is a complex quantity, and it can be expressed as
. (4)
For the plasma antenna 2, when the plasma density is very high enough to be used as a radiator , the plasma antenna surface current distributionmay be assumed to be sinusoidal and given by[11][12]
(5)
where are the attenuation coefficient and the phase coefficient of the surface wave, respectively.I0is the maximum current of antenna 2.If we consider the plasma density of antenna 1 is uniform and high enough to work as a metallic antenna, the expression for the parallel component of electric fieldin the vicinity of a radiating element 1, is given as[13]
(6)
then the impedance of plasma antennas is
(7)
where
- The mutual impedance for uniformdistribution of plasma density in antenna 2
(a)
(b)
Fig 2. Curves of (a) mutual resistance R21and (b) mutual reactance X21of two parallel side-by-side antennas as function of distance between them
A basic dimension of antenna 2 is selected as follows: the radius of plasma column a2= a1 =0.0125m, the plasma columnlengthl2=l1=0.5m, the plasma density nz=51017/m3, the frequency of propagation signal is 150 MHz，and the electron-neutral collision frequency. Fromthe equation (7), we can get the mutual impedance between the two plasma column antennas,and compare with that between two metallic antennas,both of which have the same configure and size,as shown in figure 2.Simulation results indicatethatthe variation character of plasma antennas’ mutual resistance, with the variationof distancesbetween two plasma antennas, is similar to Bessel’s function distribution.The mutual reactance of plasma antennas displaysa sinusoidal distribution and its amplitude decreases gradually. And the amplitudes of plasma antennas’ mutual resistance and reactanceare smaller than that of metallic antennas. The lower mutual coupling of plasma antennas is beneficial to built antenna array.
When the plasma column length l2= l1=0.5m, the antenna 1 keepsthe postulation ahead and the antenna 2 keepsbasic parameters to be unchanged, then we can get the mutual impedance between the two plasma column antennas which vary with the plasma density of plasma 2 and the distance between two antennas, as shown in Fig3.
(a)
(b)
Fig 3. Curves of (a) mutual resistance R21and (b) mutual reactance X21 of two parallel side-by-side plasma antennas with different plasma density in antenna 2
It is the collision frequency that is relevant toplasma’s conductive and dielectric properties, which impact antennas’ characteristics with using plasma as a radiator. When the plasma column length l2= l1=1m, the antenna 1 keepsthe postulation ahead and the antenna 2 keeps basic parameters to be unchangedexcept the plasma collision frequency inside antenna 2, then we can get the mutual impedance between the two plasma column antennas which vary with the plasma collision frequency inside antenna 2 and the distance between two antennas, as shown in Fig 4.
(a)
(b)
Fig 4. Curves of (a) mutual resistance R21and (b) mutual reactance X21 of two parallel side-by-side plasma antennas with differentcollision frequency in antenna 2
From Fig.3 and Fig.4, we find that the mutual resistance of plasma antennas exhibits a vibrating character similar to Bessel’s function distribution and the mutual reactance shows a sinusoidal distribution with the variation of distance between two plasma antennas, and amplitudes of mutual resistance and reactancedecrease evidently with the plasma’s density descending.This may be explained from the physical character of plasma. With the increasement of concentration for plasma, the imaginary part of wave vector for surface wave would become small and even may be neglected, and the real part approximates to the wave number in vacuum.So the mutual coupling of high density plasma antennas is more intensive than that of lower density antennas.While the collision frequencyhas less influence on the wave number than on thedamping rate, collision frequency increasing will also lead to the damping rate of surface wave become bigger, then cause amplitude of mutual impedance decreasing,
- The mutual impedance for nonuniformdistributionof plasma density in antenna 2
At present, the plasma antenna is always driven from one end of the column by excitation of the plasma surface wave.So the plasma density in the column is non-uniform, and decreases in an approximately linear fashion along plasma column [8]. Letthe plasma column length l2= l1=0.5m, the antenna 1 keepsthe postulation ahead, and the plasma density of antenna 2 is described as,where n0=21018/m3isthe plasma density excited at the base of the column 2, nr=51017/m3is the minimum plasma density required to keep surface wave propagating. The other basic parameters of antenna 2 keep same as before. Then we can get the mutual impedance between the two plasma column antennas which vary with the plasma density of plasma 2 and the distance between two antennas.As shown in Fig 5,with the variation of distance between two plasma antennas, the mutual resistance of plasma antennas exhibits a vibrating character similar to Bessel’s function distribution and the mutual reactance shows a sinusoidal distribution. Due to the non-uniform distribution ofplasma in antenna 2, the curves ofmutual resistance and reactanceare not smooth and vibrate tempestuously at the extreme value.
(a)
(b)
Fig 5. Curves of(a) mutual resistance R21and (b) mutual reactance X21 of two parallel side-by-side plasma antennas with uniform and nonuniform plasma distribution in antenna 2
III. Conclusion
As for plasma antennas, the curve of mutual impedanceis similar to that of mental antennas with the increasing of distance between two plasma antennas, and the amplitudes of plasma antennas’mutual resistance and reactanceare less than that of metallic antennas’. Due to physical characteristics of plasma, the density and collision frequency of plasma in antenna 2 impact the mutual impedance of plasma antenna array, and the nonuniform distribution of density inside plasma column 2 inducesunsmoothed variation curves of mutual impedance. The low mutual coupling of plasma antennas is convenient for the construction of antenna array. Furthermore, it is helpful to realize the beam forming and antennas reconfiguration through the change of plasma characters.
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