research article modeling of a plasma antenna with

Research ArticleModeling of a Plasma Antenna with InhomogeneousDistribution of Electron Density

Zong-sheng Chen1 Li-fang Ma2 and Jia-chun Wang1

1State Key Laboratory of Pulsed Power Laser Technology Electronic Engineering Institute Hefei Anhui 230037 China2Institute of Information Ammunition Academy of Army Officers Hefei Anhui 230031 China

Correspondence should be addressed to Zong-sheng Chen chenzongsh12163com

Received 16 October 2014 Accepted 26 January 2015

Academic Editor Atsushi Mase

Copyright copy 2015 Zong-sheng Chen et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The distribution of the electron density along a plasma antenna can influence the antennarsquos performance But little has been done inthis regard in former studies In this paper a model of a practical plasma antenna with an inhomogeneous distribution of electrondensity is founded according to the transmission-line equivalent theory of a metal monopole from which the current distributionand the radiation pattern of a plasma antennawith appropriate parameters are calculatedThe results show that the electrical currentdistribution the maximum radiation direction and the beamwidth of a plasma antenna vary with electron density distributionsTo validate the model the plasma antenna with the same parameters is also simulated based on electromagnetic software HFSS Itis found that the results from the two ways are almost consistent

1 Introduction

Compared with the conventional metal antenna plasmaantennas use ionized gas as the conducting medium insteadof metal which have excellent potentials for applications andhave attracted intensive interest of researchers [1ndash3] Modelsof the plasma antenna and simulations of the radiationpattern by using different numerical methods have beenprovided [4ndash7] and some significative results have beenachieved A number of the models were founded on the dis-persion relation of surface wave along ideal plasma columnsin vacuum [1 4ndash6] But for practical plasma antennas theplasma is restricted in a tube So the outer and inner radiusof the tube the dielectric constant of the tube material andthe density distribution of the plasma should be also takeninto account in the computation Zhao et al [7] examinedinfluences of the dielectric constant and the radius of thetube on the far-field radiation pattern of the plasma antennaHowever the model assumed that the density distributionof the plasma in the tube is homogeneous other than thelinear distribution in the actual tube [3 8] In the presentpaper we developed a model of the plasma antenna withinhomogeneous distribution of the electron density From the

model electrical current distributions and radiation patternsof plasma antennas can be calculated Moreover anothermodel of the plasma antenna was constructed using elec-tromagnetic software HFSS which is an interactive softwarepackage for calculating the electromagnetic behavior of astructure [9] Results from the software could attest thevalidity of the first model

2 Theoretical Model

The electrical current distribution of the plasma antennacan be expressed mathematically and analogously to that ofa monopole According to the transmission-line equivalenttheory of a metal monopole the current distribution alongthe antenna can be written as

119868 (119911) = 1198680times [119890minus119894 int119911

01198961199031198891199111015840

times 119890minusint119911

01198961198941198891199111015840

minus 119890minus119894(2 int

119871

01198961199031198891199111015840

minusint119911

01198961199031198891199111015840

)times 119890minus(2 int119871

01198961198941198891199111015840

minusint119911

01198961198941198891199111015840

)]

(1)

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2015 Article ID 736090 5 pageshttpdxdoiorg1011552015736090

2 International Journal of Antennas and Propagation

where 1198680is the magnitude of the current 119871 is the length of

the antenna 119911 is the axial distance from the bottom of theantenna 119896

119903is the real part of the wave vector 119896(119911) while 119896

119894is

the imaginary partFor a metal monopole the far-field radiation is well

known as

119865 (120579) =

100381610038161003816100381610038161003816100381610038161003816

sin (120579)119868max

int

119871

minus119871

119868 (1199111015840) exp (119895119896

01199111015840 cos (120579)) 1198891199111015840

100381610038161003816100381610038161003816100381610038161003816

(2)

where 119868max is themaximal value of the current on the antennaUsing (1) and (2) the normalized radiation pattern of the

plasma antenna can be calculated if the wave vector 119896(119911) isknown

For a practical plasma antenna the plasma column ofa radius 119877 is contained in a dielectric tube of a thickness119889 A communication signal with an angular frequency 120596 islaunched at one end of the antenna The electron plasmaangular frequency is 120596

119901 If 120596

119901gt 120596 the communica-

tion signal propagates as a surface wave There have beenmany researches on the surface wave both theoreticallyand experimentally [8] IVAN and EVGHENIA investigatedits characteristics detailedly when they examined plasmaresources produced and sustained by a travelling electromag-netic surface wave [10] From their study provided that theplasma density is radially constant the dispersion relation ofthe surface wave along a plasma column can be written as

120576119901

119886119901

1198681(119886119901)

1198680(119886119901)

+120576119889

119886119889

[1198861+ 11988621198861198891198701(120574119886V) 120576119889119886V1198700 (120574119886V)]

[1198863+ 11988641198861198891198701(120574119886V) 120576119889119886V1198700 (120574119886V)]

= 0 (3)

where

1198861= 1198691(119886119889)119867(1)

1(120574119886119889) minus 119867

(1)

1(119886119889) 1198691(120574119886119889)

1198862= 1198691(119886119889)119867(1)

0(120574119886119889) minus 119867

(1)

1(119886119889) 1198690(120574119886119889)

1198863= 119867(1)

0(119886119889) 1198691(120574119886119889) minus 1198690(119886119889)119867(1)

1(120574119886119889)

1198864= 119867(1)

0(119886119889) 1198690(120574119886119889) minus 1198690(119886119889)119867(1)

0(120574119886119889)

120576119901= 1 minus

1205962

119901

120596 (120596 + 119894V)

(4)

and 119886119901= radic119909

2 minus 1205902120576119901 119886119889= radic1205902120576

119889minus 1199092 119886V = radic1199092 minus 1205902

119909 = 119896119877 120590 = 120596119877119888 120574 = 1 + 119889119877 V is the collision frequencyof plasma 119869

0and 1198691are the Bessel functions 119868

0 1198681 1198700 and

1198701are the modified Bessel functions 119867(1)

0and 119867(1)

1are the

Hankel functions and 120576119889is the dielectric constant of the tube

materialIf we assume 119889 = 0 (3) becomes

12057611990111987901198681(119879119901119877)

1198701(1198790119877)

+

1198791199011198680(119879119901119877)

1198700(1198790119877)

= 0 (5)

where 1198792119901= 1198962minus 1205761199011198962

0 11987920= 1198962minus 1198962

0 1198960= 120596119888 Equation (5)

is just the dispersion relation of surface wave along plasmacolumn in vacuum as shown in former studies [4ndash6]

02

04

06

08

1

30

90

120

150

180 0

Metalnemax sim nemin = 4 times 1017 mminus3 sim 2 times 1016 mminus3

nemax sim nemin = 7 times 1017 mminus3 sim 4 times 1016 mminus3

Figure 1 Normalized radiation pattern of the plasma antenna

The electron density along the plasma antenna decreasesalmost linearly and can be expressed approximately as [3 811]

119899119890(119911) = 119899

119890max +119911

119871(119899119890min minus 119899119890max) (6)

where 119899119890max is the density at the bottomof the plasma antenna

while 119899119890min is that at the top

3 Numerical Results and Discussion

Using (1) to (3) and (6) the normalized radiation patternof the plasma antenna and its electrical current distributionwere calculated with119877 = 125mm 2times1016mminus3 le 119899

119890min le 4times

1016mminus3 4times 1017mminus3 le 119899

119890max le 7times 1017mminus3 120576

119889= 378 119871 =

1m V = 4times108Hz 119889 = 09mm and a communication signal

frequency 119891 = 200MHz These parameters are consistentwith the cases of our experiments which have been provenreasonable for the practical plasma antenna With otherappropriate values the model founded in our paper can bealso applicable Figure 1 is the normalized radiation patternof the plasma antenna with different distributions of electrondensity Comparatively the normalized radiation pattern ofa metallic antenna with the same length is also presentedThe calculating results show that the normalized radiationpattern of the plasma antenna is markedly influenced by theelectron density distribution and has great difference fromthat of a metallic antenna with the same length In spite of thesame collision frequency and length the maximum radiationdirection and beamwidth of the plasma antenna vary dueto different density distributions The main reason for thisphenomenon is that the plasma density and its collisionfrequency determine the wave vector 119896 which impacts theelectrical current distribution along the plasma antennaFigure 2 gives the real part and the imaginary part of the wavevector 119896 along the plasma antenna

From Figure 2 we can find that Re(119896) and Im(119896) havegreat changes axially which result from electron densitydistributions On the contrary if we assume that the plasmadensity is uniform then the value of the wave vector 119896 is afixed value which deviates from the fact From the bottom to

International Journal of Antennas and Propagation 3

0 01 02 03 04 05 06 07 08 09 14

5

6

7

8

9

10

11

12

13

14

z (cm)

Re(k

)



(a)

0 02 04 06 08 1z (cm)

0

05

1

15

2

25

3

Im(k

)



(b)

Figure 2 Real part and imaginary part of the wave vector 119896 alongthe plasma antenna

the top of the plasma antenna Im(119896) increases with declineof the plasma density This indicates that attenuation ofthe signal augments so the plasma antenna can be viewedas a type of antenna with a continuously varying resistiveloading Additionally under the condition of an invariablecollision frequency Re(119896) and Im(119896) both decrease alongwiththe increase of the plasma density Figure 3 is the currentdistribution along the plasma antenna which shows thatthe density distribution along the plasma antenna influencesthe electrical current distribution Actually it is becausedifferent electrical current distributions lead to variations ofthe maximum radiation direction and the beamwidth

0 01 02 03 04 05 06 07 08 09 10

02

04

06

08

1

12

|I|

z (cm)



Figure 3 Current distribution along the plasma antenna

z

yx

Figure 4 HFSS model of the plasma antenna with 13 segments

Moreover we found anothermodel of the plasma antennabased on HFSS which is a useful tool in the field of antennadesign When setting up the model we should pay attentionto the dielectric constant and the conductivity of the plasmabecause they are both involved with the electron density thecollision frequency and the communication signal frequencyFor the plasma antenna with the liner distribution of electrondensity its dielectric constant and conductivity vary axiallyevenwith the same communication signal frequencyHere tobe convenient for simulation the plasma antenna is dividedinto sufficient segments in which the electron density isassumed uniform As a result the dielectric constants andconductivities of adjacent segments will have a little discrep-ancyThese settings will benefit the veracity of the simulationFigure 4 is the HFSS model of the plasma antenna which isput on an infinite metallic plane The air volume object isdefined as a radiation boundary at which waves are absorbedcompletely essentially ballooning the boundary infinitely far


0

30

60

90

120

150

minus180

minus150

minus120

minus90

minus60

minus30

400

300

200

100

40 4000

Figure 5 Radiation pattern of the plasma antenna from HFSSmodel

away from the antenna At the end of the antenna a lumpedport is assigned

To compare with the first model and its calculatingresults the same parameters are set in the HFSS model Theplasma antenna is divided into 13 segments The length ofthe first 12 segments from the bottom is 8 cm each while thatof the last is 4 cm We find that results acquired from themodel with 13 segments are almost the same as those fromthe model with 20 segments so 13 segments are enough forour simulation Figure 5 gives the radiation pattern of theplasma antenna simulated with 119899

119890min = 2 times 1016mminus3 and

119899119890max = 4 times 10

17mminus3 Its electrical current distribution isshown in Figure 6 From Figures 1 3 5 and 6 we can getthat the results of the twomodels are almost consistent whichindicates that both models are valid

4 Conclusions

Taking the electron density distribution of plasma intoaccount a model of the practical plasma antenna is foundedfrom which we can calculate electrical current distributionsand radiation patterns of plasma antennas The results cal-culated with appropriate parameters show that the electricalcurrent distribution the maximum radiation direction andthe beamwidth of the plasma antenna vary due to differentdensity distributions As for the plasma antenna the electrondensity distribution is vitally important to its performanceDifferent from the case of the uniform electron density signalattenuation augments due to the linear decline of the plasmadensity from the bottom to the top so the plasma antenna canbe viewed as a type of antenna with a continuously varyingresistive loading Because themodel only needs the condition

21008e + 001

19715e + 001

18421e + 001

17128e + 001

15835e + 001

13249e + 001

11956e + 001

10662e + 001

14542e + 001

93692e + 000

80760e + 000

67829e + 000

54897e + 000

41965e + 000

29033e + 000

16102e + 000

31698e minus 001

J vol

(Am

2)

z

yx

Figure 6 Electrical current distribution along the plasma antennafrom HFSS model

that a communication signal must propagate as a surfacewave along the plasma antenna the results from the modelcan be extended to other communication signal frequenciesif the electron plasma angular frequency is higher than thecommunication signal angular frequency The results fromthe model we set up in this paper are in close agreementwith those from the HFSS model This model seems usefulin studying the plasma antenna

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work is supported by the Fund of National Defense Pre-Research (Grant no 07048)

References

[1] G G Borg J H Harris D G Miljak and N M MartinldquoApplication of plasma columns to radio frequency antennasrdquoApplied Physics Letters vol 74 no 22 pp 3272ndash3274 1999

[2] I Alexeff T Anderson S Parameswaran E P Pradeep JHulloli and P Hulloli ldquoExperimental and theoretical resultswith plasma antennasrdquo IEEE Transactions on Plasma Sciencevol 34 no 2 pp 166ndash172 2006

[3] S Wang N Sun J Li Q Xiang and C Wei ldquoEssentialcharacteristics of plasma antennas driven by one-ended surfacewaverdquo Plasma Science and Technology vol 12 no 2 pp 230ndash234 2010

[4] Y Lee and S Ganguly ldquoAnalysis of a plasma-column antennausing FDTD methodrdquo Microwave and Optical Technology Let-ters vol 46 no 3 pp 252ndash259 2005


[5] J P Rayner A P Whichello and D Cheetham ldquoPhysical char-acteristics of plasma antennasrdquo IEEE Transactions on PlasmaScience vol 32 no 1 pp 269ndash281 2004

[6] Z H Qian R S Chen H W Yang K W Leung and E K NYung ldquoFDTD analysis of a plasma WHIP antennardquoMicrowaveand Optical Technology Letters vol 47 no 2 pp 147ndash150 2005

[7] G W Zhao Y-M Xu and C Chen ldquoCalculation of dispersionrelation and radiation pattern of plasma antennardquo Acta PhysicaSinica vol 56 no 9 pp 5298ndash5303 2007 (Chinese)

[8] M Moisan and Z Zakrzewski ldquoPlasma sources based onthe propagation of electromagnetic surface wavesrdquo Journal ofPhysics D Applied Physics vol 24 no 7 pp 1025ndash1048 1991

[9] Ansoft HFSS Online Help httpansoftcom[10] I Zhelyazkov and E Benova ldquoModeling of a plasma column

produced and sustained by a traveling electromagnetic surfacewaverdquo Journal of Applied Physics vol 66 no 4 pp 1641ndash16501989

[11] A Sola J Cotrino A Gamero and V Colomer ldquoStudy ofsurface-wave-produced plasma column lengthsrdquo Journal ofPhysics D Applied Physics vol 20 no 10 pp 1250ndash1258 1987

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where 1198680is the magnitude of the current 119871 is the length of

the antenna 119911 is the axial distance from the bottom of theantenna 119896

119903is the real part of the wave vector 119896(119911) while 119896

119894is

the imaginary partFor a metal monopole the far-field radiation is well

known as

119865 (120579) =

100381610038161003816100381610038161003816100381610038161003816

sin (120579)119868max

int

119871

minus119871

119868 (1199111015840) exp (119895119896

01199111015840 cos (120579)) 1198891199111015840

100381610038161003816100381610038161003816100381610038161003816

(2)

where 119868max is themaximal value of the current on the antennaUsing (1) and (2) the normalized radiation pattern of the

plasma antenna can be calculated if the wave vector 119896(119911) isknown

For a practical plasma antenna the plasma column ofa radius 119877 is contained in a dielectric tube of a thickness119889 A communication signal with an angular frequency 120596 islaunched at one end of the antenna The electron plasmaangular frequency is 120596

119901 If 120596

119901gt 120596 the communica-

tion signal propagates as a surface wave There have beenmany researches on the surface wave both theoreticallyand experimentally [8] IVAN and EVGHENIA investigatedits characteristics detailedly when they examined plasmaresources produced and sustained by a travelling electromag-netic surface wave [10] From their study provided that theplasma density is radially constant the dispersion relation ofthe surface wave along a plasma column can be written as

120576119901

119886119901

1198681(119886119901)

1198680(119886119901)

+120576119889

119886119889

[1198861+ 11988621198861198891198701(120574119886V) 120576119889119886V1198700 (120574119886V)]

[1198863+ 11988641198861198891198701(120574119886V) 120576119889119886V1198700 (120574119886V)]

= 0 (3)

where

1198861= 1198691(119886119889)119867(1)

1(120574119886119889) minus 119867

(1)

1(119886119889) 1198691(120574119886119889)

1198862= 1198691(119886119889)119867(1)

0(120574119886119889) minus 119867

(1)

1(119886119889) 1198690(120574119886119889)

1198863= 119867(1)

0(119886119889) 1198691(120574119886119889) minus 1198690(119886119889)119867(1)

1(120574119886119889)

1198864= 119867(1)

0(119886119889) 1198690(120574119886119889) minus 1198690(119886119889)119867(1)

0(120574119886119889)

120576119901= 1 minus

1205962

119901

120596 (120596 + 119894V)

(4)

and 119886119901= radic119909

2 minus 1205902120576119901 119886119889= radic1205902120576

119889minus 1199092 119886V = radic1199092 minus 1205902

119909 = 119896119877 120590 = 120596119877119888 120574 = 1 + 119889119877 V is the collision frequencyof plasma 119869

0and 1198691are the Bessel functions 119868

0 1198681 1198700 and

1198701are the modified Bessel functions 119867(1)

0and 119867(1)

1are the

Hankel functions and 120576119889is the dielectric constant of the tube

materialIf we assume 119889 = 0 (3) becomes

12057611990111987901198681(119879119901119877)

1198701(1198790119877)

+

1198791199011198680(119879119901119877)

1198700(1198790119877)

= 0 (5)

where 1198792119901= 1198962minus 1205761199011198962

0 11987920= 1198962minus 1198962

0 1198960= 120596119888 Equation (5)

is just the dispersion relation of surface wave along plasmacolumn in vacuum as shown in former studies [4ndash6]

02

04

06

08

1

30

90

120

150

180 0

Metalnemax sim nemin = 4 times 1017 mminus3 sim 2 times 1016 mminus3


Figure 1 Normalized radiation pattern of the plasma antenna

The electron density along the plasma antenna decreasesalmost linearly and can be expressed approximately as [3 811]

119899119890(119911) = 119899

119890max +119911

119871(119899119890min minus 119899119890max) (6)

where 119899119890max is the density at the bottomof the plasma antenna

while 119899119890min is that at the top

3 Numerical Results and Discussion

Using (1) to (3) and (6) the normalized radiation patternof the plasma antenna and its electrical current distributionwere calculated with119877 = 125mm 2times1016mminus3 le 119899

119890min le 4times

1016mminus3 4times 1017mminus3 le 119899

119890max le 7times 1017mminus3 120576

119889= 378 119871 =

1m V = 4times108Hz 119889 = 09mm and a communication signal

frequency 119891 = 200MHz These parameters are consistentwith the cases of our experiments which have been provenreasonable for the practical plasma antenna With otherappropriate values the model founded in our paper can bealso applicable Figure 1 is the normalized radiation patternof the plasma antenna with different distributions of electrondensity Comparatively the normalized radiation pattern ofa metallic antenna with the same length is also presentedThe calculating results show that the normalized radiationpattern of the plasma antenna is markedly influenced by theelectron density distribution and has great difference fromthat of a metallic antenna with the same length In spite of thesame collision frequency and length the maximum radiationdirection and beamwidth of the plasma antenna vary dueto different density distributions The main reason for thisphenomenon is that the plasma density and its collisionfrequency determine the wave vector 119896 which impacts theelectrical current distribution along the plasma antennaFigure 2 gives the real part and the imaginary part of the wavevector 119896 along the plasma antenna

From Figure 2 we can find that Re(119896) and Im(119896) havegreat changes axially which result from electron densitydistributions On the contrary if we assume that the plasmadensity is uniform then the value of the wave vector 119896 is afixed value which deviates from the fact From the bottom to


0 01 02 03 04 05 06 07 08 09 14

5

6

7

8

9

10

11

12

13

14

z (cm)

Re(k

)



(a)

0 02 04 06 08 1z (cm)

0

05

1

15

2

25

3

Im(k

)



(b)



0 01 02 03 04 05 06 07 08 09 10

02

04

06

08

1

12

|I|

z (cm)




z

yx




0

30

60

90

120

150

minus180

minus150

minus120

minus90

minus60

minus30

400

300

200

100

40 4000





119899119890max = 4 times 10


4 Conclusions


21008e + 001

19715e + 001

18421e + 001

17128e + 001

15835e + 001

13249e + 001

11956e + 001

10662e + 001

14542e + 001

93692e + 000

80760e + 000

67829e + 000

54897e + 000

41965e + 000

29033e + 000

16102e + 000

31698e minus 001

J vol

(Am

2)

z

yx





Acknowledgment


References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 01 02 03 04 05 06 07 08 09 14

5

6

7

8

9

10

11

12

13

14

z (cm)

Re(k

)



(a)

0 02 04 06 08 1z (cm)

0

05

1

15

2

25

3

Im(k

)



(b)



0 01 02 03 04 05 06 07 08 09 10

02

04

06

08

1

12

|I|

z (cm)




z

yx




0

30

60

90

120

150

minus180

minus150

minus120

minus90

minus60

minus30

400

300

200

100

40 4000





119899119890max = 4 times 10


4 Conclusions


21008e + 001

19715e + 001

18421e + 001

17128e + 001

15835e + 001

13249e + 001

11956e + 001

10662e + 001

14542e + 001

93692e + 000

80760e + 000

67829e + 000

54897e + 000

41965e + 000

29033e + 000

16102e + 000

31698e minus 001

J vol

(Am

2)

z

yx





Acknowledgment


References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

30

60

90

120

150

minus180

minus150

minus120

minus90

minus60

minus30

400

300

200

100

40 4000





119899119890max = 4 times 10


4 Conclusions


21008e + 001

19715e + 001

18421e + 001

17128e + 001

15835e + 001

13249e + 001

11956e + 001

10662e + 001

14542e + 001

93692e + 000

80760e + 000

67829e + 000

54897e + 000

41965e + 000

29033e + 000

16102e + 000

31698e minus 001

J vol

(Am

2)

z

yx





Acknowledgment


References















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article modeling of a plasma antenna with

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