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Theoretical and experimental investigation of plasma antenna characteristics on the basis of

gaseous collisionality and electron density

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2015 Jpn. J. Appl. Phys. 54 016001

(http://iopscience.iop.org/1347-4065/54/1/016001)

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Theoretical and experimental investigation of plasma antenna characteristics

on the basis of gaseous collisionality and electron density

Teruki Naito1*, Shingo Yamaura2, Kazuo Yamamoto1, Tai Tanaka2, Hidetoshi Chiba2,Hayato Ogino3, Kazuhiro Takahagi4, Shinya Kitagawa4, and Daiki Taniguchi4

1Advanced Technology R&D Center, Mitsubishi Electric Corporation, Amagasaki, Hyogo 661-8661, Japan2Information Technology R&D Center, Mitsubishi Electric Corporation, Kamakura, Kanagawa 247-8501, Japan3Communication System Center, Mitsubishi Electric Corporation, Amagasaki, Hyogo 661-8661, Japan4Electronic Systems Research Center, Ministry of Defense, Setagaya, Tokyo 154-8511, JapanE-mail: naito.teruki@bc.mitsubishielectric.co.jp

Received July 16, 2014; revised October 28, 2014; accepted November 4, 2014; published online December 17, 2014

This paper reports plasma antenna characteristics investigated theoretically and experimentally, on the basis of the plasma parameters: gaseouscollisionality and electron density. The antenna structure is a basic quarter-wavelength monopole antenna in the UHF band. The dependence ofthe antenna gain on the plasma parameters is obtained by analytical equations from plasma and antenna theory, and by numerical simulations. Inthe plasma antenna, the ratio of the electron elastic collision frequency to the total number of electrons at the plasma cross section determines theantenna’s internal loss and the electrical equivalent antenna length, whereas the ratio of the radio wave frequency to the total number of electronsat the plasma cross section determines the antenna’s resonant frequency. These results are confirmed by experimental results of the antenna’simpedance and radiation patterns. © 2015 The Japan Society of Applied Physics

1. Introduction

A plasma antenna is a RF antenna partially composed ofplasma instead of metals or dielectrics. There are several typesof antenna structures such as pole,1–3) loop,4–7) reflection,8) andplane.9) In most cases, the plasma antenna is composed of adielectric tube filled with low-pressure gases, and plasmais generated by electric power fed at the end of the tube.The concept of wireless communication using plasma is notnew,10,11) but it had not been investigated intensively for a longtime because of its technical difficulties and few social needs.

Recently, the plasma antenna has been attracting moreattention as a new type antenna because of the followingunique characteristics, which conventional metallic antennasdo not have. First, interference between the antenna andambient radio waves can be significantly reduced by simplyswitching off the electric power applied to the plasma,because the ionized gas returns to its neutral state, which istransparent to radio waves. It is possible to install severalantennas closely without considering interference betweenthe antennas. Second, the antenna’s geometric reconfigura-tion can be easily realized by changing power feedingpatterns to plasma antenna arrays.12) The radio wave beam iselectrically steered simply by changing the discharge patternsof the plasma antenna arrays. These characteristics of plasmaantennas are not only useful in themselves, but also havehigh affinity with future intelligent radio systems, such ascognitive radio and smart antennas.13,14)

The characteristics of plasma antennas have been reportedtheoretically and experimentally by several groups.1–8,11,12)

Practical wireless communication using plasma antenna hasbeen demonstrated. However, the focus of those studies wasprimarily the antenna characteristics of plasma antennas,and plasma tended to be treated merely as a perfect or lossyconductive material.

As is well known, plasma is a dispersive medium.15,16) Thecomplex dielectric function of plasma strongly depends on aradio wave frequency ½ and plasma parameters such as theelectron density ne and the electron elastic collision frequency¯m. For collisionless plasma, the plasma acts as a metal if ½ is

lower than the electron plasma frequency ½pe, which isdetermined by ne, whereas the plasma acts as a dielectric if ½is higher than ½pe.

Therefore, it is likely that the antenna characteristics alsodepend on the plasma parameters, and it is important tocomprehend the relationship between the antenna character-istics and the plasma parameters for practical antenna designand application.

In this work, the dependence of antenna characteristics onthe plasma parameters is investigated theoretically and experi-mentally. The antenna structure is a basic quarter-wavelengthcylindrical monopole in the UHF band. The antenna gain isobtained by analytical equations and numerical simulations.The antenna impedance and the radiation patterns were meas-ured in experiments, and compared with the theoretical results.

2. Theoretical analysis

2.1 MethodThe dependence of the antenna gain on the plasma parame-ters is investigated analytically and numerically. In this work,the following approximations for plasma are accepted. First,the thermal motion of ions can be ignored (cold plasmaapproximation). Next, plasma can be treated as fluids (a fluidmodel). Third, the electron density and the spatial distribu-tion are temporally constant. Finally, the amplitude of theelectron oscillation is negligible compared with the spatialcell step of the numerical calculation.

The cold plasma approximation and the fluid model areaccepted widely in analyses of weakly ionized plasma suchas the glow discharge in a fluorescent lamp or vacuumchamber. The third approximation means that the electrondensity and the spatial distribution are not disturbed by theradio wave. This approximation is accepted if the electricfield intensity of the radio wave is small enough that it doesnot ionize neutral molecules and that the ponderomotiveforce can be ignored. In this study, it might be enough that theelectric field intensity is smaller than 103V/m because theponderomotive force is sufficiently smaller than the plasmapressure gradient force,17) and the ionization coefficient isquite low at the low reduced electric field.18) The final

Japanese Journal of Applied Physics 54, 016001 (2015)

http://dx.doi.org/10.7567/JJAP.54.016001

REGULAR PAPER

016001-1 © 2015 The Japan Society of Applied Physics

approximation is requested from the validity of the numericalcalculation. The amplitude of the electron oscillation is on theorder of a few microns with the electric field intensity in theUHF band. Thus, the numerical spatial cell step should belarger than the amplitude.

First, the equation of the antenna gain is developedanalytically according to basic equations of plasma andantenna theory. The plasma conductivity ·p is expressed by15)

�pðrÞ ¼ e2neðrÞmeð�m þ j!Þ ; ð1Þ

where e is the electron charge, me is the electron mass, andj is the imaginary unit. ne is a function of the plasma radius r.Then, the impedance of a cylindrical plasma antenna Zp(= Rp + jXp) can be written as

Zp ¼ Rp þ jXp ¼ l

� Z R

0

2�r�pðrÞ dr ¼ lme

e2Neð�m þ j!Þ;

ð2Þwhere l is the plasma length, R is the radius of the plasma,and Ne is the total number of electrons at the plasma crosssection,

Ne ¼Z R

0

2�rneðrÞ dr: ð3Þ

Assuming that the plasma antenna is matched externally tothe radio wave feed line, the antenna gain G is written in thefollowing analytical form,

G ¼ D0

Rr

Rr þ Rp¼ D0 1þ lme

e2Rr

�mNe

� ��1

; ð4Þ

where D0 and Rr are the directivity and the radiationresistance of the plasma antenna, respectively.19) As is clearfrom the above equation, the antenna gain depends not on ½,but only on ¯m/Ne.

Next, the numerical method is explained. The antenna gainand the radiation pattern of the plasma antenna are calculatedusing a Finite difference time domain (FDTD) method.20) Theplasma is embedded in the FDTD simulation by Young’sdirect integration (DI) method in which the electron motionequation is calculated in the similar manner as Maxwell’sequations.21)

The simulation model is shown in Fig. 1. Because of theazimuthal symmetry of the monopole structure, Maxwell’sequations are calculated in the half area of the antenna crosssection. The simulation model is discretized according to Yee’salgorithm for cylindrical coordinates.22) There is a singularityat r = 0 in the evolution of Ez arising from the cylindricalcoordinates. The singularity is avoided using the integral formof Ampere’s circuital law.23) In order to analyze open structuresand to account for radiation, two absorbing boundary condi-tions are used to truncate the mesh at its boundary: Mur’ssecondary absorbing boundary condition and the modified dis-persive boundary condition.24,25) The far-field radiation patternis obtained by the near-zone to far-zone transformation.26) Theantenna gain is calculated from the ratio of the far-fieldradiation intensity at a given direction to the input real power.

The simulation model was composed of a ground plate anda dielectric tube filled with plasma. The length and the outerdiameter of the dielectric tube were 275 and 26mm, res-pectively. The dielectric thickness was 2mm. The relative

permittivity of the dielectric was 3.77, assuming a quartzdielectric. The diameter of the ground plate was 500mm, andthe thickness was 2mm. There was a 2mm gap betweenthe dielectric tube and the ground plate, and a 300MHzsinusoidal voltage with an amplitude of 1V was applied tothe gap by delta-gap feeding. There was a 25-mm-long probeat the bottom of the dielectric tube in order to guide theradio wave into the plasma. According to the courant stabilitycondition and the stability criteria of Young’s DI method, thetemporal and spatial cell steps were determined as follows:¦r = 1mm, ¦z = 2mm, and ¦t = 2 ps.

2.2 Results and discussion2.2.1 Dependence on the plasma parameters The an-tenna gain was calculated for each ne and ¯m. In this calcu-lation, the electron radial distribution was assumed to be afunction of the usual zero-order Bessel function J0, which isthe typical electron distribution in a positive column.27) Theequation of the electron distribution is

neðrÞ ¼ ne0J0ð2:4r=RÞ; ð5Þwhere ne0 is the electron density at r = 0.

Figure 2 shows the antenna maximum gain as a function ofne0 at r = 0, where the plasma DC conductivity ·dc was fixed.

500 mm

275

mm

2.5

mm

Dielectric tube(Quartz)

Ground plate

Delta gap source

Plasma

r

zAnalyzed area

500 mm

1000

mm

Fig. 1. (Color online) Schematic diagram of the plasma antenna modelused in the FDTD simulation.

An

ten

na

max

imu

m g

ain

(d

Bi)

Electron density (cm-3)

A

BC

1012 10141010 1011 1013 1015109108

0

-10

-20

-30

-40

-50

dc = 45 S/mdc = 4.5 S/mdc = 0.45 S/m

Eq. (4) FDTDσσσ

Fig. 2. (Color online) Dependence of the antenna maximum gain on theelectron density ne.

Jpn. J. Appl. Phys. 54, 016001 (2015) T. Naito et al.

016001-2 © 2015 The Japan Society of Applied Physics

The antenna maximum gain was defined as the antenna gainin the direction of maximum radiation, and it did not takeinto account reflection losses at the antenna input terminal.The plasma DC conductivity ·dc is equal to Eq. (1) at r = 0and ½ = 0. When ne0 = 1.0 © 1012 cm¹3 and ¯m/2³ =

1GHz, ·dc = 4.5 S/m. In Fig. 2, each dashed line shows ananalytical antenna gain obtained by Eq. (4), and each solidline with markers shows a numerical antenna gain obtainedby the FDTD simulation. The dot-dash lines are equi-¯mcontours, which might be obtained in experiments underconstant gas pressure. In the calculations of the analyticalantenna gain, the following values of D0 and Rr wereassigned: D0 = 1.681 dB and Rr = 80.8³. These values wereobtained by the FDTD simulation for a metallic antenna withthe same shape as the plasma antenna in Fig. 1.

As expected from Eq. (4), the analytical antenna gain wasconstant if ·dc was constant, regardless of ne0. On the otherhand, the numerical antenna gain depended on ne0, and thereappeared two different tendencies of the dependence on ne0according to the value. When ne0 was more than 1012 cm¹3,the numerical antenna gain depended not on ne0, but only on·dc. The difference between the analytical and the numericalantenna gain increased with decreasing ·dc. On the otherhand, the numerical antenna gain depended mainly on ne0when ne0 was lower than 1012 cm¹3. The numerical antennagain decreased in proportion to ne0, regardless of ·dc.

Figure 3 shows the axial electric field Ez near the plasmaantenna under the conditions A, B, and C marked in Fig. 2.The plasma parameters of each condition are shown inTable I. ne is the same in conditions A and B, whereas ·dc isthe same in conditions A and C.

In condition A, where the numerical antenna gain almostcoincided with the analytical antenna gain, the uniform elec-tric field was distributed across the plasma antenna similarlyto a quarter-wave metallic monopole antenna. Conversely,the electric field was inhomogeneous across the plasmaantenna in conditions B and C. In condition B, the electricfield did not spread over the whole plasma antenna andremained around the antenna input terminal. The wavelengthof the radio wave was electrically shortened on the plasmaantenna in condition C.

As shown in Fig. 3(b), the apparent antenna length becameshorter in condition B than that in condition A. The apparentantenna length was roughly 165mm, with which the appliedvoltage to the antenna input terminal dropped by 97%.The radiation resistance and the directivity of a metallicantenna with an antenna length of 165mm were 5.8³,and 1.58 dBi, respectively. With these antenna parametersapplied to Eq. (4), the analytical antenna gain was calculatedto be ¹25.7 dBi in condition B. This analytical antennagain coincides well with the numerical antenna gain incondition B, so that the numerical antenna gain decreasedbecause of the decrease in the apparent or electrical equiv-alent antenna length. The decrease in the electrical equivalentantenna length might be caused by the increase of the plasmaresistance Rp because the current distribution length de-creases with the internal resistance of the antenna.28)

According to Fig. 3(c), the electrical resonant frequency ofthe plasma antenna became lower in condition C. In general,the antenna’s resonant frequency drops by inserting a loadingcoil in series between the antenna and its feed line.29) Theplasma reactance Xp increases with decreasing ne fromEq. (2). Accordingly, it is probable that the plasma mightact as a loading coil and cause the electrical shortening ofthe plasma antenna. Figure 4 shows the axial electric field Ez

and the radiation pattern of the plasma antenna at ½/2³ =

60MHz with the same plasma parameters as those incondition C. The wavelength of the radio wave coincidedwith the antenna length, and the plasma antenna was resonantat 60MHz. The antenna gain was still lower than the ana-lytical gain because the antenna’s effective length was muchshorter than the wavelength of the radio wave in free space.

Ez (V/m)10.09.08.07.06.05.04.03.02.01.00.0-1.0-2.0-3.0-4.0-5.0-6.0-7.0-8.0-9.0-10.0

Z a

xis

(cm

)r axis (cm)

(b)

84 6 1020

95

85

90

100

80

75

105

Z a

xis

(cm

)

r axis (cm)

(a)

Plasmaantenna

84 6 1020

95

85

90

100

80

75

105

Groundplate

Z a

xis

(cm

)

r axis (cm)

(c)

84 6 1020

95

85

90

100

80

75

105

Fig. 3. (Color online) Axial electric field Ez near the plasma antenna. (a), (b), and (c) correspond to conditions A, B, and C shown in Fig. 2 and Table I.

Table I. Plasma parameters in conditions A, B, and C shown in Fig. 2.

ne(cm¹3)

¯m(GHz)

·dc(S/m)

A 1 © 1013 1 45

B 1 © 1013 100 0.45

C 1 © 1010 0.001 45

Jpn. J. Appl. Phys. 54, 016001 (2015) T. Naito et al.

016001-3 © 2015 The Japan Society of Applied Physics

2.2.2 Dependence on the electron spatial distributionThe dependence of the antenna gain on the electron spatialdistribution ne(r) was investigated. In addition to the electrondistribution expressed by Eq. (5), the following three types ofelectron distributions were considered:30)

neðrÞ ¼ ne0ð1:0þ 0:0122r=R� 2:214ðr=RÞ2 þ 1:208ðr=RÞ3Þ;ð6Þ

neðrÞ ¼ ne0e�ðr=0:3RÞ2 ; ð7Þ

neðrÞ ¼ ne0ð1:0� ðr=RÞ10Þ; ð8ÞThese electron distributions are typical for a mercury-noble-gas discharge, high-pressure discharge, and electronegativeplasma, respectively.

Figure 5 shows each electron distribution. Accordingto Eq. (4), the antenna gain depends on the total number ofelectrons at the plasma cross section Ne. For this reason, thevalue of ne0 in each electron distribution was determined sothat Ne might be same in all cases. For example, ne0 was set at1.0 © 1012 cm¹3 for Eq. (5). ¯m/2³ was fixed at 1.0GHz.

The radiation pattern for each electron distribution isshown in Fig. 6. The radiation pattern shows little de-pendence on the electron distribution. This might be becausethe plasma skin depth of the radio wave and the wavelengthof the radio wave are larger than the antenna radius. In theplasma antenna, all electrons across the cross-sectional area

of the plasma are subject to a uniform electric field as shownin Fig. 3. Consequently, if Ne is constant, the same electriccurrent is induced in the plasma antenna, and the radiationpattern becomes independent of the electron distribution orthe antenna’s outer shape. This result is different from thecase of a metallic antenna where the skin depth of the radiowave is a few microns and only electrons at the antennasurface contribute to the radiation. It should be noted that theelectron distribution must be taken into consideration whenthe plasma radius is not negligible with respect to the plasmaskin depth or the wavelength of the radio wave.

3. Experimental verification

3.1 Experimental setupThe experimental setup is shown in Fig. 7. Two plasmaantennas were prepared. The plasma antennas were ³-shapedquartz tubes filled with argon and small amount of mercury.The argon pressure was 267 Pa in one tube and 1333 Pa inthe other. The pressure of the mercury was a few Pa asdetermined by the temperature of the tube walls, whichwas around 20 °C. There was a pair of cylindrical nickelelectrodes at each end of the tubes. The diameter and thelength of the electrodes were 15 and 25mm, respectively. Thelength between the edge and the folded point of the tubes was275mm. The outer diameter of the tubes was 19mm with a1mm thickness.

-50

-40

-30

-20

-10

0

10

0 15 30 45 60 75 90

An

ten

na

gai

n (

dB

i)

Azimuth angle (deg)

ω/2π = 60 MHzω/2π = 300 MHz

84 6 1020

95

85

90

100

80

75

10510

8

6

4

2

0

-2

-4

-6

-8

-10r (mm)

z (m

m)

Ez (V/m)

Plasma

Groundplate

Fig. 4. (Color online) Radiation patterns at ½/2³ = 60 and 300MHzwhen the plasma parameters were same as in condition C shown in Table I.The inset figure shows the axial electric field Ez near the plasma antenna at½/2³ = 60MHz.

0E+00

5E+17

1E+18

2E+18

2E+18

3E+18

3E+18

4E+18

4E+18

5E+18

0 2 4 6 8 10 12

Ele

ctro

n d

ensi

ty (

cm-3

)

r axis (mm)

eq. (5)eq. (6)eq. (7)eq. (8)

Fig. 5. (Color online) Electron spatial distribution used in the simulations.

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10

0 15 30 45 60 75 90

An

ten

na

gai

n (

dB

i)

Elevation angle (deg)

Analytical gaineq. (5)eq. (6)eq. (7)eq. (8)

Fig. 6. (Color online) Dependence of the antenna radiation patterns on theelectron spatial distribution.

Ground plate

Discharge tube

Matching elements

High-pass filter

RF signal source

DC power supply

Low-pass filter

Plasma antenna

Plasma

Fig. 7. (Color online) Schematic diagram of the experimental setup.

Jpn. J. Appl. Phys. 54, 016001 (2015) T. Naito et al.

016001-4 © 2015 The Japan Society of Applied Physics

The discharge tubes were set on a 500-mm-diameteraluminum plate, which served as a ground plate. Theelectrodes were connected to a DC/RF power feed circuitattached to the back side of the ground plate. The feed circuitcomprised a high-pass filter connected to an RF supply forthe radio wave and a low-pass filter connected to a DC supplyfor the discharge. The high-pass filter prevented the DCpower from flowing into the RF feed line, and the-low passfilter prevented the RF power from flowing into the DC feedline. The impedance of the RF feed line was 50³.

The plasma DC conductivity ·dc was measured with thefollowing two methods: A search coil method and estimationfrom current–voltage (I–V ) characteristics. In the search coilmethod, ·dc is estimated by the impedance change of thesearch coil wound around a discharge tube.30) The search coilused in the measurement was a three-turn coil with an innerdiameter of 19mm. The coil was composed of copper wirewith a diameter of 1mm, and wound at the center betweenthe edge and the folded point of the tubes. The impedancewas measured by a network analyzer (Agilent E8364B) in thefrequency range 16 to 17MHz. The electron distribution ofEq. (6) was assumed in the calculations of ·dc.

In the estimation from the I–V characteristics, ·dc iscalculated by the following analytical relation obtained byintegrating the relational equation of the current density andthe electric field (Ohm’s law) in a positive column:

�dc ¼ ne0lp

� Z R

0

2�rneðrÞ dr� �

IpVp

; ð9Þ

where lp is the length of the positive column, Ip is the electriccurrent flowing through the positive column, and Vp is thevoltage applied to the positive column. In Eq. (9), the elec-tron distribution of Eq. (6) was assumed. Ip was measuredwith a shunt resistor of 100³. Vp was obtained by subtractingthe cathode fall voltage from the applied voltage betweenelectrodes.

The cathode fall voltage was measured by a method usinga capacitive-type probe.31) The capacitive-type probe wasa copper ring with a length of 10mm, and wound aroundthe tube 10mm away from the top of the electrode. Twoseries ceramic capacitors of 10 pF were connected betweenthe copper ring and the ground terminal of the DC powersupply. The voltage at the midpoint of the capacitors wasmeasured by an oscilloscope (Tektronix DPO4104). Whenthe DC power supply was turned off, a voltage proportionalto the plasma potential was induced at the midpoint. Thecathode fall voltage was obtained by comparing the ampli-tude of the induced voltages at a cathode and an anode.

The antenna impedance was measured by the networkanalyzer. The antenna radiation patterns were measuredinside an anechoic chamber.

3.2 Results and discussionFigure 8 shows the relationship between Ip and ·dc. Thecathode fall region was less than a few mm,32) and most partsof the discharge tubes became a positive column. In everycase, ·dc was proportional to Ip. For the 1333 Pa tube, ·dcincreased rapidly at Ip = 200mA because of the rapidincrease of the cathode fall voltage. This is likely becausethe discharge mode was changed from normal discharge toabnormal discharge. ·dc could not be measured at Ip = 50mA

in the 1333 Pa tube because striation caused Ip to oscillate.33)

For the 266 Pa tube, the values of ·dc obtained by the searchcoil method were within the range of the twice values of ·dcobtained by the estimation from I–V characteristics. Thisdifference seems reasonable compared with other measure-ment methods.34)

Figure 9 shows the impedance of the plasma antennaplotted on the Smith chart. The impedance was measuredfrom 200 to 400MHz. The black dashed circle indicates anarea where the voltage standing wave ratio (VSWR) is lessthan 2.0. The impedance at 300MHz is also expressed as anopen triangle. The impedance described a circular trajectoryaround the center of the Smith chart, and the input terminal ofthe plasma antenna acted as an open end when the plasmaantenna was turned off (Ip = 0mA). With increasing Ip, thetrajectory came closer to the center of the Smith chart. As forthe impedance at 300MHz, the antenna resistance decreasedwhile the antenna reactance increased with increasing Ip.Figure 10 shows the resonant frequency of the plasmaantenna, at which the reflection loss became a minimum. Theerror bar shows the area where the VSWR was less than 2.0.The resonant frequency increased from 269 to 287MHz inproportion to Ip. The fractional bandwidth was approximately15% on average at VSWR = 2.0.

0

2

4

6

8

10

0 50 100 150 200 250

Pla

sma

dc

con

du

ctiv

ity

(S/m

)

Electric current (mA)

266 Pa (Search coil)266 Pa (I-V char.)1333 Pa (I-V char.)

Fig. 8. (Color online) Plasma DC conductivity ·dc as a function of theelectric current Ip.

0 mA (OFF)50 mA100 mA150 mA200 mA300 MHz

VSWR = 2.0

Ω 0 ∞

j10

j25

j50

j100

-j100

-j50

-j25

-j10

50

200 MHz

400 MHz

Fig. 9. (Color online) Impedance of the plasma antenna as a function ofthe electric current Ip.

Jpn. J. Appl. Phys. 54, 016001 (2015) T. Naito et al.

016001-5 © 2015 The Japan Society of Applied Physics

The radiation patterns of the plasma antenna at 300MHzare shown in Figs. 11 and 12. The inset figures show thedefinition of the elevation angle ª and the polarization of theelectric field Eª in each figure. The plasma antenna radiatedvertically polarized waves because the gains of the cross-polarized wave were no more than ¹20 dBi, regardless of Ip.The antenna gain increased with Ip. The plasma antennashad symmetric radiation patterns like a slice of a torus. Theradiation patterns did not depend on the polarity of Ip in spiteof the asymmetric plasma structure such as the cathode fallregion on one side where ne was lower than that of thepositive column region. This might be because the cathodefall region was electrically negligible because of the lowcapacitance between the electrode and the plasma. The radia-tion patterns were slightly asymmetric around 0 degrees evenwithout plasma because of the asymmetric configuration ofthe feed circuit.

Figure 13 shows the antenna maximum gain as a functionof ·dc. The maximums of the analytical and numericalantenna gains are also shown in the figure although the modelused in the calculation was a single monopole as shown inFig. 1. According to the numerical results of the electronspatial distribution dependence, the plasma radius in themodel was modified so that the total number of electrons atthe plasma cross section Ne might be same as in the experi-

ment. The electron distribution of Eq. (6) was assumed,and ¯m/2³ was fixed at 1.69GHz corresponding to 266 Paof Ar. The antenna gain increased with increasing ·dc. Theantenna gain was lower than the analytical antenna gain andcoincided well with the numerical antenna gain.

4. Discussion

The experimental results coincide with the numericalcalculation results investigated in the previous section.

The antenna reactance increased with increasing Ip and ·dc.This result corresponds to the numerical result that the elec-trical equivalent antenna length was increased and the plasmaantenna became inductive with increasing ·dc as shown by thetransition from condition B to condition A in Fig. 2.

The antenna resonant frequency increased with increasingIp and ne0. This result corresponds to the numerical result thatthe plasma reactance Xp decreased and the electrical short-ening was suppressed with increasing ne0 as shown by thetransition from condition C to condition A in Fig. 2.

The antenna gain for the 1333 Pa tube was slightly higherthan that of the 266 Pa tube for ·dc < 4 S/m. Ne is roughlyproportional to the gas pressure when ·dc is fixed. Thus, it isprobable that the Ne at 1333 Pa was larger than that at 266 Pa,and that the antenna gain was increased by the suppressionof Xp.

200

220

240

260

280

300

320

340

0 50 100 150 200 250

Rea

son

ant

freq

uen

cy (

MH

z)

Electric current (mA)

VSWR 2.0

Fig. 10. Resonant frequency of the plasma antenna as a function of theelectric current Ip. The error bars indicate the frequency where VSWR is lessthan 2.0.

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An

ten

na

gai

n (

dB

i, E

θθ)

Elevation angle θ (deg)

0 mA (OFF)50 mA100 mA150 mA200 mA x y

z

Eθ

θ = 0°

θ = -90 °

θ = 90°

Fig. 11. (Color online) Radiation patterns of the plasma antenna filledwith Ar at 266Pa (2 Torr).

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An

ten

na

gai

n (

dB

i, E

θθ)

Elevation angle θ (deg)

0 mA (OFF)100 mA150 mA200 mA x y

z

Eθ

θ = 0°

θ = -90°

θ = 90°

Fig. 12. (Color online) Radiation patterns of the plasma antenna filledwith Ar at 1333Pa (10Torr).

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-5

0

0 1 2 3 4 5 6 7 8 9 10

An

ten

na

max

imu

m g

ain

(d

Bi)

Plasma dc conductivity (S/m)

Analytical gainNumerical gain266 Pa (Search coil)266 Pa (I-V char.)1333 Pa (I-V char.)

Fig. 13. (Color online) Antenna maximum gain as a function of plasmaDC conductivity ·dc.

Jpn. J. Appl. Phys. 54, 016001 (2015) T. Naito et al.

016001-6 © 2015 The Japan Society of Applied Physics

The experimental and numerical antenna gains matchedwell although the antenna structure and the electron spatialdistribution were different. The plasma antenna was a doublecolumn structure in the experiment, whereas it was a singlemonopole in the simulation. This result corresponds to thenumerical calculation result that the antenna gain depends noton the electron spatial distribution, but on Ne.

According to these results, the following two parametersare important in addition to the ordinary antenna parameterswhen a plasma antenna is designed. The first is the ratio ofthe electron elastic collision frequency to the total number ofelectrons at the plasma cross section, ¯m/Ne, which deter-mines the antenna internal loss and the electrical equivalentantenna length. The second is the ratio of the radio wavefrequency to the total number of electrons at the plasmacross section, ½/Ne, which determines the antenna resonantfrequency.

Finally, the influences of the antenna dimensions suchas l and R are not investigated in this work because theantenna dimensions are usually determined by the targetantenna characteristics such as the wave frequency, direc-tivity, and bandwidth. Once the antenna type is determined,further discussion is possible. In the case of a quarter-wave-length monopole antenna, l is about ³c0/2½. Ne is expressedapproximately as S0ne0/½2 because R is inversely propor-tional to ½. Here, c0 is the speed of light in vacuum, and S0 isa proportional constant that depends on the electron spatialdistribution. Then, Eq. (2) can be rewritten as

Zp ¼ Rp þ jXp ¼ �cme

2e2S0

!�mne0

þ j!2

ne0

� �: ð10Þ

Rp is proportional to ½, whereas Xp is proportional to ½2.The influence of Xp becomes more prominent at higher ½.

5. Conclusions

In this study, the plasma antenna characteristics were inves-tigated theoretically and experimentally, focusing on theplasma parameters. In a plasma antenna, the ratio of theelectron elastic collision frequency and the total number ofelectrons at the plasma cross section determine the antennainternal loss and the electrical equivalent antenna length,whereas the ratio of the radio wave frequency to the totalnumber of electrons at the plasma cross section determinesthe antenna resonant frequency. The antenna gain is deter-mined from the balance of these two parameters. It ismeaningless to consider only the electron density or theelectron plasma frequency, which are usually used as criteriafor deciding whether plasma is metallic or dielectric.

The plasma parameters available for antenna operation arein the range of values observed in common plasmas such as a

glow discharge in fluorescent lamps. The plasma antenna hasmany advantages over the conventional metallic antennas,and the potential for wide application in future wirelesscommunication systems.

1) J. P. Rayner, A. P. Whichello, and A. D. Cheetham, IEEE Trans. Plasma Sci.32, 269 (2004).

2) R. Kumar and D. Bora, J. Appl. Phys. 109, 063303 (2011).3) P. R. Russo, V. M. Primiani, G. Cerri, R. D. Leo, and E. Vecchioni, IEEE

Trans. Antennas Propag. 59, 425 (2011).4) I. Alexeff, T. Anderson, and E. Farshi, Phys. Plasmas 15, 057104 (2008).5) V. V. Ovsyanikov, I. A. Reznichenko, A. L. Ol’shevs’kiy, V. M. Popel’,

K. V. Rodin, and Y. D. Romanenko, Proc. 4th Int. Conf. UWBUSIS, 2008,p. 77.

6) L. Zheng, L. Cao, and Z. Zhang, Proc. Int. Symp. Antennas, Propagationand EM Theory, 2008, p. 222.

7) T. Fukawasa, H. Chiba, H. Miyashita, Y. Konishi, T. Naito, K. Yamamoto,and M. Hayama, IEICE Tech. Rep. 113, SANE2013-13, 25 (2013)[in Japanese].

8) I. Alexeff, T. Anderson, S. Parameswaran, E. P. Pradeep, J. Hulloi, and P.Hulloi, IEEE Trans. Plasma Sci. 34, 166 (2006).

9) C. Metz, U.S. Patent 7145512 (2006).10) J. Hettinger, U.S. Patent 1309031 (1919).11) R. Ghose, IEEE Trans. Antennas Propag. 15, 713 (1967).12) T. Anderson and I. Alexeff, Ext. Abstr. IEEE Int. Conf. Plasma Sci., 2004,

p. 328.13) J. Mitola and G. Q. Maguire, Jr., IEEE Personal Commun. 6, 13 (1999).14) J. H. Winters, IEEE Personal Commun. 5, 23 (1998).15) M. A. Lieberman and A. J. Lichtenberg, Principles of Plasma Discharges

and Materials Processing (Wiley, Hoboken, NJ, 2005) 2nd ed., p. 96.16) T. Naito, O. Sakai, and K. Tachibana, Appl. Phys. Express 1, 066003

(2008).17) H. K. Malik and A. K. Aria, J. Appl. Phys. 108, 013109 (2010).18) Y. P. Raizer, Gas Discharge Physics (Springer, Berlin, 1991) 1st ed., p. 55.19) C. A. Balanis, Antenna Theory (Wiley, Hoboken, NJ, 2005) 3rd ed.,

Chap. 2.20) A. Taflove, IEEE Trans. Electromagn. Compat. EMC-22, 191 (1980).21) S. A. Cummer, IEEE Trans. Antennas Propag. 45, 392 (1997).22) Y. Chen, R. Mittra, and P. Harms, IEEE Trans. Microwave Theory Tech. 44,

832 (1996).23) N. Dib, T. Weller, M. Scardelletti, and M. Imparato, IEEE Trans.

Microwave Theory Tech. 47, 509 (1999).24) G. Mur, IEEE Trans. Electromagn. Compat. EMC-23, 377 (1981).25) Q. Chen and V. F. Fusco, Proc. Int. Conf. Computations in Electromag.,

1994, p. 323.26) R. Luebbers, K. S. Kunz, M. Schneider, and F. Hunsberger, IEEE Trans.

Antennas Propag. 39, 429 (1991).27) M. A. Lieberman and A. J. Lichtenberg, Principles of Plasma Discharges

and Materials Processing (Wiley, Hoboken, NJ, 2005) 2nd ed., p. 540.28) J. Lally and D. Rouch, IEEE Trans. Antennas Propag. 18, 764 (1970).29) R. C. Hansen, IEEE Trans. Commun. 23, 430 (1975).30) K. Misono and M. Kando, Rep. Grad. School Electron. Sci. Technol.

Shizuoka Univ. 20, 49 (1999) [in Japanese].31) Y. Takeda, R. Kitamoto, T. Uetsuki, and O. Fukumasa, Shomei Gakkaishi

91, 700 (2007) [in Japanese].32) A. V. Engel, Ionized Gases (AIP Press, New York, 1994) 1st ed., p. 230.33) T. Donahue and G. H. Dieke, Phys. Rev. 81, 248 (1951).34) S. Knappmiller, S. Robertson, and Z. Sternovsky, IEEE Trans. Plasma Sci.

34, 786 (2006).

Jpn. J. Appl. Phys. 54, 016001 (2015) T. Naito et al.

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