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ETASR - Engineering, Technology & Applied Science Research Vol. 3, �o. 5, 2013, 516-521 516

www.etasr.com Sadeghikia and Hodjat-Kashani: A Two Element Plasma Antenna Array

A Two Element Plasma Antenna Array

F. Sadeghikia

Aerospace Research Institute

Tehran, Iran

sadeghi_kia@ari.ac.ir

F. Hodjat-Kashani

Department of Electrical Engineering

Iran University of Science and Technology

kashani@iust.ac.ir

Abstract—This theoretical study presents the characteristics of

plasma monopole antennas in the VHF/UHF range using finite

difference time domain (FDTD) simulation. Results show that

more broadband characteristics can be obtained by increasing

the diameter of the plasma tube and that the minor lobes

diminish in intensity as diameter increases. Furthermore, the

nulls are replaced by low level radiation. Since the collision

frequency, which is a function of gas pressure, represents the loss

mechanism of plasma, decreasing its value increases the gain and

radar cross section (RCS) of the antenna. Theoretical modeling

shows that at higher plasma frequencies with respect to the signal

frequency, the gain and radar cross section of the plasma antenna

are high enough and that the impedance curves are altered as the

plasma frequency varies. Using these preliminary studies, mutual

impedance and gain of a broadside array of two parallel side-by-

side plasma elements is presented.

Keywords-plasma antenna; radiation pattern; gain; input

impedance; surface wave

I. INTRODUCTION

Plasma antennas represent a completely new class of
antennas which employ ionized gas enclosed in a tube as the
conducting element of the antenna. Operating plasma antennas
can transmit and receive through a surface wave driven (SWD)
plasma column [1-3]. Therefore it could be possible for large
stacked antennas with improved range precision to replace
numerous small antennas, thus decreasing clutter, weight and
interface. Since plasma antennas have properties quite different
from those of metallic conductors, the key plasma parameters
should be determined and optimized with respect to the
characteristics of antennas. However, there are limited
numerical simulations in this regard [4-8]. Numerical
simulation is a powerful tool to evaluate, with maximum
flexibility and minimal cost, the performance of these novel
antennas. Numerical analysis of a broadside array of two
parallel side-by-side, equal in phase, current plasma elements is
the subject of this theoretical study. In the first part of this
paper, the radiation characteristics of a SWD plasma monopole
antenna are examined, considering the effects of variations of
plasma frequency, collision frequency and radius of the tube on
the gain, efficiency, input impedance and radar cross section
(RCS) of the antenna, because few studies are reported in this
regard [4-5]. Further, the primary goals are to investigate
efficiently the effects of gas pressure and the excitation power
on the performance of a SWD plasma antenna and to provide a

better understanding of a linear array of plasma elements.
These results should provide more insight to construct an
effective array of plasma antennas.

II. SIMULATION SETUP

The geometry of the simulated plasma column antenna is
illustrated in Figure 1. The plasma column is inserted in a
metallic box as a ground plane and a copper ring placed around
the tube as a coupling sleeve for launching the signal. The
length and radius of the column were chosen to be 600 mm and
12 mm respectively and the thickness and height of the
coupling sleeve were 3 mm and 30 mm. The surface wave is
launched applying an intense field between the coupling sleeve
and the metallic box, and the results are reported in [8]. The
dimensions of the metallic box were chosen to be

130 250 55 .mm× × The gap between the coupling sleeve and
the metallic box is 5 mm. The FDTD problem space is

60 80 200× × cells and the waveform of the source is a
modulated Gaussian pulse.

Fig. 1. Simulated plasma column antenna.

The power flux of the wave in a SWD plasma column
decreases axially as power is gradually transferred to the
discharge [1, 8-10] and the electron density steadily decreases
from the launcher which has been shown previously
experimentally [1] and theoretically [9]. Consequently, the
plasma column is axially non uniform and it will result in a non
uniform conductivity along the column. This non uniformity of
the SWD plasma column is considered as a shortcoming and
some remedies have been proposed to overcome it [11]. In this

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investigation, we have considered that the plasma density in the
discharge tube remains uniform, which is an ideal condition.

There are many different ways to simulate the
electromagnetic interaction in plasma. In this case, the direct
integration method (DI) was used to simulate the isotropic cold
plasma with a fixed uniform electron density [12]. In this
method, the temporal evolution of plasma state is not taken into
account and a weak electromagnetic wave propagates in a
previously created plasma [6]. In DI method, Maxwell's
equations are coupled to an auxiliary ordinary differential
equation modeling the response of the current density, J, to the
field, E as shown in (1)-(3).

H
E

∂

∂
−=×∇

�

0µ (1)

J
t

E
H

�

+
∂

∂
=×∇ 0ε

(2)

EJ
t

J
p

��

�

2
0ωευ =+

∂

∂ (3)

Where E
�

and H
�

are the electric (V/m) and magnetic

(A/m) fields, respectively,
0

µ is the magnetic permeability

(H/m) of free space,
0

ε is the free space permittivity (F/m), υ

is the average collision frequency (Hz) and J
�

is the plasma

current density (A/m
2
). For details of the FDTD methodology,

the reader is referred to [8, 13-14].

To calculate the RCS of a plasma antenna, we assume an
arbitrary incidence and polarization plane wave as:

rikj
i erE

.
)ˆsinˆ(cos)( ϕαθα += (4)

where α is the polarization angle,
i

k is the propagation

vector given by:

)ˆcosˆsinsinˆcos(sin0 zyxkk iiiiii θϕθϕθ ++= (5)

and θ̂ and φ̂ are the unit vectors in the spherical coordinate

system and ( , )
i i

θ φ defines the angle of arrival of the plane
wave. In the three dimensional case, the RCS is defined as
[15]:

2
),,(),,(

(4lim),(

r E

rErE
rRCS

ϕθϕθ
πϕθ

ϕθ
+

=
∞→

(6)

To validate our FDTD program, RCS of a plasma
monopole antenna with fp=70 GHz and collision frequency of
10 GHz is compared with those of CGFFT numerical results
which were simulated in [7], as shown in Figure 2. In this
comparison we considered the radius of the plasma column r=5

mm, dielectric constant of plasma tube 3.4
r

ε = and thickness

of the column as 2 mm. Comparison between our FDTD

simulation and CGFFT result shows close agreement between
the two different codes.

1 2 3 4 5 6 7
-40

-30

-20

-10

Frequency (GHz)

R
C

S
(
d
B
)

CG-FFT method [7]

FDTD numerical simulation

Fig. 2. Comparison between RCS of a plasma column antenna with FDTD

numerical simulation and CG-FFT method results.

III. NUMERICAL RESULTS AND DISCUSSION

A. The effects of the radius of the plasma column

Numerical simulation of a plasma antenna, as shown in
Figure 3, reveals that in a SWD plasma monopole antenna,
similar to a conventional metallic radiator, one method to
widen the acceptable operational bandwidth will be to decrease

the rL / ratio [16], where L is the length of the plasma
antenna and r is the radius of the tube. It has been observed
that for a given length of a plasma column, its impedance
variations becomes less sensitive as a function of frequency as

rL / decreases. Thus, more broadband characteristics can be
obtained by increasing the diameter of the plasma tube, similar
to metallic conventional antennas. To demonstrate this, in
Figure 3a, we have plotted, as a function of frequency, the

input impedance of plasma monopole antenna with 70/ =rL ,
34 and 23. When the plasma frequency is large enough with
respect to the excitation frequency, the imaginary part of the
input impedance of plasma antenna can be eliminated by

making the total length L of the antenna less than 4λ , where

λ is the wavelength. This value is approximately

0.18 ,Fλ ′ when the plasma frequency is 7500 MHz and

rL
F

+
=′ . However, its value increases by increasing the

plasma frequency and consequently conductivity of the plasma
while for the maximum conductivity this value becomes

0.24 Fλ ′ [16]. In Figure 3a it is observed that increasing the
radius of the column decreases the resistance at the first
resonance. The radiation pattern is essentially unaffected by the
thickness of the plasma tube in the regions of intense radiation.
However, as the radius of the tube increases, the minor lobes
diminish in intensity and the nulls are replaced by low level
radiation as shown in Figure 3b.

B. The effects of the collision frequency

The collision frequency is a function of pressure and
represents the loss mechanism of plasma. It depends on the
type of gas and the average number of the particles. There are

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various kinds of collisions in plasma whereas their evaluation
is complicated and is not reported here. Readers interested in
this subject can refer to [17]. The complex plasma conductivity
is stated as:

υω

ωε
ωσ

+
=

p
2

0
)( (7)

Where,
2

0
2 /p pf $e mω π ε= = in which pf is the

plasma resonant frequency (Hz), $ is the electron density

(m
-3
), υ is the average collision frequency (Hz), 0ε is the

free space permittivity (F/m), e and m are the electron
charge (c) and mass (Kg), respectively.

(a)

50 100 150 200 250
-150

-100

-50

100

150

Frequency (MHz)

In
p
u
t
I
m

p
e
d
a
n
c
e
(
O

h
m

s
)

L / r = 70

L / r = 34

L / r = 23

(b)

-40 -20 0 20

90
270

300

330

L / r = 70

L / r = 34

L / r = 23

Fig. 3. The effects of the variations of the diameter of plasma tube, in the

plasma frequency of 7500 MHz and collision frequency of 400 MHz, on (a)

input impedance, (b) radiation pattern when the length of antenna is 3 / 2λ .

In a certain plasma frequency the conductivity of the
plasma column decreases as the collision frequency increases
and it affects all characteristics of a plasma antenna. Increasing
the collision frequency from 200 MHz to 1000 MHz, in a fixed
plasma frequency, decreases the gain of the plasma antenna, as
illustrated in Figure 4a, which is due to the increased loss in the
plasma column. The gain of a plasma monopole antenna, in our
case, is less than that of a conventional metallic antenna and
their difference increases as frequency increases. This means
that at lower lengths plasma antenna operates more effectively
than at higher lengths.

Stealth application of a plasma antenna has high priority
over its different applications. Numerical investigation of the
impact of collision frequency on the RCS of a plasma antenna,
as shown in figure 4.b, reveals that RCS reduces with
increasing the collision frequency which is due to the reduced
conductivity of the antenna. Therefore, a larger collision
frequency is preferable for the purpose of RCS reduction. It is

conceivable to optimize the plasma RCS by controlling the
plasma collision frequency for practical applications. In our
simulations, the incident plane wave is with

180 ,
o

i
θ = 0 ,

i
φ = 0

o
α = .

(a)

0.5 1 1.5
-2

Antenna length (wavelength)

G
a
in

(
d
B

)

Collision = 200 MHz

Collision = 600MHz

Collision = 1000MHz

Metallic antenna

(b)

100 200 300 400 500 600 700 800
-15

-10

-5

Frequency (MHz)

R
C

S
(
d
B

)

Collision = 200MHz

Collision = 600MHz

Collision = 1000MHz

Metallic antenna

(c)

100 200 300 400 500 600 700 800
0

Frequency (MHz)

E
ff
ic

ie
n
c
y
(
%

)

Collision = 200 MHz

Collision = 400 MHz

Collision = 1000MHz

(d)

50 100 150 200 250 300 350

-100

100

200

Frequency (MHz)

I
n
p
u
t
I
m

p
e
d
a
n
c
e
(
O

h
m

s
)

Collision = 200 MHz

Collision = 600 MHz

Collision = 1000MHz

Fig. 4. Characteristics of a plasma antenna when the plasma frequency is

7500
p

f GHz= and at different collision frequencies (a) gain, (b) RCS,

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The efficiency of the plasma antennas is a key parameter to
evaluate the possibility of using a plasma element instead of a
metallic one. The efficiency takes into account the losses at the
input terminal and the structure of the antenna and is directly
related to plasma conductivity. Due to the much lower
conductivity of the plasma, at higher collision frequencies the
efficiency of the antenna decreases, as shown in Figure 4c.

It is noted that the radiation pattern of a plasma antenna is
essentially unaffected by the variation of the collision
frequency. However, as the collision frequency increases, the
minor lobes diminish in intensity and the nulls are replaced by
low level radiation. When the plasma frequency is small, at low
collision frequencies, the input impedance of the antenna has a
lot of oscillations which decrease when collision frequency
increases. The collision loss of plasma increases the loss of the
antenna, resulting in a reduced radiated power and damping the
impedance variations. Therefore, increasing the collision
frequency increases the bandwidth of the plasma antenna.
However, the collision frequency does not influence the period
of resonance as shown in Figure 4d. This may be considered as
one of the useful methods which can be used for a dynamic
control of an antenna bandwidth by varying the Q-factor of the
antenna.

C. The effects of the plasma frequency

Measurements of plasma electron number density using
Langmuir probes have proved that the increase of input RF
power at a fixed filling gas pressure increases the plasma
density in the column [18, 19] and plasma frequency is a
function of plasma density. Increasing the plasma frequency in
the column increases the conductivity and consequently it
causes considerable increment in the values of the gain, RCS
and efficiency of a plasma antenna. At higher plasma
frequencies with respect to the excitation frequency, the gain
and the RCS of a plasma antenna are as high as of a metallic
antenna. The variations of the gain, RCS and efficiency of a
plasma antenna versus the plasma frequency, in the collision
frequency of 400 MHz, are shown in Figures 5a-5c.

Comparison between the radiation patterns of a plasma

antenna with 23λ=L at different plasma frequencies with a

metallic antenna (Figure 5d) shows that in the plasma antenna,
the numbers of lobes are increased up to those of a
conventional metallic antenna when the plasma frequency
increases and also that the radiation pattern finds deeper nulls.
At higher plasma frequencies, the radiation pattern becomes
more similar to that of a metallic one. Furthermore, an

interesting phenomenon is observed when 2.5
p

f f < .

Whereas the metallic monopole antenna does not radiate
energy along the monopole axis, the plasma antenna radiates
thus showing the characteristics of an end fire antenna, as was
introduced before in [4] and [20]. This occurs because the
radiating source is a surface wave along the column. The
plasma column does not carry a current, but a surface wave
propagates along the column and reaches its tip. Therefore, it
contributes the radiation towards the end fire direction, as
shown in Figure 5d and increasing the collision frequency,
increases this property. This narrow cone beam is associated

with the least antenna efficiency as was shown in Figure 5c

(the dotted line where 1500 MHz
p

f = ), so it is not of

practical interest. Numerical simulation reveals that the input
impedance curves of the antenna, as shown in Figure 5e, are
altered as the plasma frequency varies. This property can be
used to construct dynamically reconfigurable antennas.

D. A linear array of two plasma elements

Essential background for this section is covered in the
previous sections and the 'elements' are SWD plasma monopole
antennas with a radius of 12 mm and a length of 600 mm at the
plasma frequency of 7500 MHz and the collision frequency of
400 MHz. A broadside array of two parallel side-by-side, equal
in phase current elements has been analyzed numerically. Let d
be the separation of elements. Referring to the arrangement of

Figure 6a, the mutual resistance
12

R and reactance
12

X of the

first resonant frequency of the antenna are presented in Figure
6b as a function of the spacing d. Moreover, the quantity

11 12
R R+ , which is important in this array calculation is also

illustrated, where
11

R is the self impedance of the elements. It

is worthy to mention that at the spacing 0.45 0.52d< <

between the elements, the total resistance is in its minimum
value around 28.5; which is incorporated with the maximum
array gain as shown in Figure 6c.

IV. CONCLUSION

Numerical simulation of the characteristics of a plasma
column antenna, when the plasma density is uniform in the
column, has been established in this paper. Numerical
simulation was validated through comparisons with other
investigations. It has been shown that for a fixed excitation
power, the variation of gas pressure, which varies the collision
frequency, changes antenna characteristics. Increasing the
collision frequency decreases antenna gain, RCS, efficiency
and peak input impedance and it may be considered as one of
the useful methods which can be used for a dynamic control of
an antenna bandwidth. From the computed numerical results it
is clear that increasing the excitation power, which increases
the plasma frequency, increases the conductivity and
consequently it causes considerable increment in the values of
gain, RCS and efficiency of the antenna. Moreover, it can be
considered as a powerful tool to construct dynamically
reconfigurable antennas because the impedance curves are
altered as plasma frequency varies. Variations of the radii of
the plasma column have non negligible effects on the antenna
characteristics. Increasing the radius of the tube can be
considered as a method to widen the acceptable operational
bandwidth of the antenna and replacing the nulls in the
radiation pattern by low level radiation. Finally, we have
presented the mutual impedance and gain of a broadside array
of two parallel side-by-side, equal in phase current SWD
plasma monopole antenna and it was concluded that maximum
gain will be achieved when the spacing between elements is

around 2/λ .

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(a)

0.5 1 1.5
-40

-30

-20

-10

Antenna length (Wavelengths)

G
a
in

(
d
B
)

fp = 1500MHz

fp = 3500MHz

fp = 7500MHz

Metallic antenna

(b)

0.5 1 1.5
-25

-20

-15

-10

-5

Antenna length (Wavelengths)

R
C

S
(
d
B

)

fp = 1500MHz

fp = 3500MHz

fp = 7500MHz

Metallic antenna

(c)

100 200 300 400 500 600 700
0

Frequency (MHz)

E
ff

ic
ie

n
c
y
(
%

)

fp = 1500 MHz

fp = 3500 MHz

fp = 7500MHz

(d)

(e)

50 100 150 200 250 300 350
-200

-100

100

200

Frequency (MHz)

I
n
p
u
t
im

p
e
d
a
n
c
e
(
O

h
m

s
)

fp = 2500 MHz

fp = 6500 MHz

fp = 20500 MHz

metal antenna

Fig. 5. The effects of the plasma frequency on the characteristics of a plasma antenna at the collision frequency of 400 MHz: (a) gain, (b) RCS, (c) efficiency,

(d) radiation pattern and (e) input impedance.

0 0.2 0.4 0.6 0.8 1

-100

-50

Distance between elements, d/lambda

M
u
tu

a
l
im

p
e
d
a
n
c
e
(
O

h
m

s
)

R12

R11+R12

X12

0.2 0.4 0.6 0.8 1

1.5

2.5

3.5

Distance between elements, d/lambda

G
a
in

(
d
B
)

(a) (b) (c)

Fig. 6. (a) Arrangement of an array of two parallel side-by-side SWD plasma elements, (b) mutual impedance of the broadside array as a function of

separation between elements and (c) gain of the array.

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