Research Article Research on Radiation Characteristic of Plasma Antenna …downloads.hindawi.com/journals/tswj/2014/290148.pdf · 2019-07-31 · Research Article Research on Radiation

Research ArticleResearch on Radiation Characteristic of PlasmaAntenna through FDTD Method

Jianming Zhou Jingjing Fang Qiuyuan Lu and Fan Liu

School of Information and Electronics Beijing Institute of Technology Beijing 100081 China

Correspondence should be addressed to Jianming Zhou zhoujmbiteducn

Received 2 May 2014 Revised 16 June 2014 Accepted 16 June 2014 Published 9 July 2014

Academic Editor Rui C Marques

Copyright copy 2014 Jianming Zhou et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The radiation characteristic of plasma antenna is investigated by using the finite-difference time-domain (FDTD) approach in thispaper Through using FDTD method we study the propagation of electromagnetic wave in free space in stretched coordinateAnd the iterative equations of Maxwell equation are derived In order to validate the correctness of this method we simulatethe process of electromagnetic wave propagating in free space Results show that electromagnetic wave spreads out around thesignal source and can be absorbed by the perfectly matched layer (PML) Otherwise we study the propagation of electromagneticwave in plasma by using the Boltzmann-Maxwell theory In order to verify this theory the whole process of electromagnetic wavepropagating in plasma under one-dimension case is simulated Results show that Boltzmann-Maxwell theory can be used to explainthe phenomenon of electromagnetic wave propagating in plasma Finally the two-dimensional simulationmodel of plasma antennais established under the cylindrical coordinate And the near-field and far-field radiation pattern of plasma antenna are obtainedThe experiments show that the variation of electron density can introduce the change of radiation characteristic

1 Introduction

Plasma antenna usually adopts the partially or fully ion-ized gas as conducting medium instead of metallic materi-als Compared with conventional metallic antenna plasmaantenna has many peculiar properties For instance it canbe rapidly switched on or off this characteristic makesplasma antenna suitable for stealth applications for militarycommunication fields Also if this kind of antenna is usedas the antenna array the coupling between the elements ofantenna array is small In particular radiation pattern ofplasma antenna can be reconfigured through changing thefrequency and intensity of pump signal gas pressure vesseldimensions and so on Because of the advantages abovemany researchers and scientific utilities show great interestsin it

At present studies concerning plasma antenna may havethree aspects experimental investigation theory derivationand numerical calculation Theodore Anderson togetherwith Igor Alexeff [1] designed a smart plasma antenna andimplemented a wide range of plasma antenna experiments

Their studies had proved that plasma antenna has reconfig-urable characteristics Kumar and Bora [2] designed a 30 cmplasma antenna and proved that the frequency and radiationpattern can be altered with the frequency and power ofthe pump signal Yang et al [3] and Zhao [4] obtained thedispersion relationships of the surface wave along the plasmacolumn by using theoretical derivation approach Wu et al[5] and Xia and Yin [6] studied the radiation characteristic ofplasma antenna through theoretical derivation Dai et al [7]calculated the coefficients of reflection and transmission ofelectromagnetic wave in plasma by using FDTD numericalmethod Liang [8] simulated the radiation characteristic ofcylindrical monopolar antenna by using FDTD methodRusso et al [9ndash13] established one-dimensional and two-dimensional self-consistent model of plasma antenna andvalidated the correctness of the model through using FDTDmethod

From the investigations and research mentioned abovewe can draw a conclusion that plasma is so complicatedthat one cannot find the real issues of the problem onlythrough experimental approach It is necessary to establish

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 290148 7 pageshttpdxdoiorg1011552014290148

2 The Scientific World Journal

a rigorous mathematical model to investigate the radiationcharacteristic of plasma antenna The numerical calculationapproach applied in this paper is to study the radiationcharacteristic of plasma antenna

2 Propagation of Electromagnetic Wave inFree Space and Plasma

There are two key issues to deal with in this research oneis the propagation of electromagnetic wave in free space andthe other one is the propagation of electromagnetic wave inthe plasma Only these two problems are solved then theinvestigation of radiation characteristic of plasma antennacan be further conducted

21 Propagation of Electromagnetic Wave in Free Space Inorder to apply FDTD method to simulate the propagation ofelectromagnetic wave in free space in cylindrical coordinatethe stretched coordinate is selected So themodifiedMaxwellequations can be expressed as below

nabla119904timesH = 119895120596120576E (1)

nabla119904times E = minus119895120596120583H (2)

where E represents electric field strength vector in volts permeterH representsmagnetic field strength vector in amperesper meter 120576 denotes the permittivity in farad per meter 120583denotes the permeability in henry per meter120596 represents theangular frequency of incidence signal in radian per second

In stretched coordinate [14] we define

119904119903= 1 +

120590119903

1198951205961205760

119904119911= 1 +

120590119911

1198951205961205760

(3)

where 119904119903and 119904119911are coordinate stretched factor

119877 997888rarr int

119903

0

119904119903(1199031015840

) 1198891199031015840

=

119903 1199031015840

lt 1199030

119903 +1

1198951205961205760

int

119903

1199030

120590119903(1199031015840

) 1198891199031015840

1199031015840

lt 1199030

(4)

119885 997888rarr int

119911

0

119904119911(1199111015840

) 1198891199111015840

=

119911 1199111015840

lt 1199110

119911 +1

1198951205961205760

int

119911

1199110

120590119911(1199111015840

) 1198891199111015840

1199111015840

lt 1199110

(5)

where 1199030and 119911

0represent the distance between the signal

source and inner boundary of PML along 119903 direction and 119911direction respectively

Maxwell curl equation (1) then can be represented bythese three scale equations in cylindrical coordinate systemas (6a)ndash(6c)

1198951205961205760119864119903=1

119877

120597119867119911

120597120593minus

120597119867120593

120597119885 (6a)

1198951205961205760119864120593=120597119867119903

120597119885minus120597119867119911

120597119877 (6b)

1198951205961205760119864119911=1

119877

120597 (119877119867120593)

120597119877minus1

119877

120597119867119903

120597120593 (6c)

From (4) and (5) (7) can be obtained as follows

120597

120597119877=1

119904119903

120597

120597119903

120597

120597119885=1

119904119911

120597

120597119911 (7)

Substituting (7) into (6a)ndash(6c) yields

1198951205961205760119864119903=1

119877

120597119867119911

120597120593minus1

119904119911

120597119867120593

120597119911 (8a)

1198951205961205760119864120593=1

119904119911

120597119867119903

120597119911minus1

119904119903

120597119867119911

120597119903 (8b)

1198951205961205760119864119911=1

119877

1

119904119903

120597 (119877119867120593)

120597119903minus1

119877

120597119867119903

120597120593 (8c)

After multiplying 119904119911sdot 119877119903 119904

119911sdot 119904119903 119904119903sdot 119877119903 respectively (8a)

(8b) and (8c) can be expressed as below

1198951205961205760119904119911

119877

119903119864119903=1

119903

120597 (119904119911119867119911)

120597120593minus119877

119903

120597119867120593

120597119911 (9a)

1198951205961205760119904119911119904119903119864120593=120597 (119904119903119867119903)

120597119911minus120597 (119904119911119867119911)

120597119903 (9b)

1198951205961205760119904119903

119877

119903119864119911=1

119903

120597 (119877119867120593)

120597119903minus1

119903

120597 (119904119903119867119903)

120597120593 (9c)

Substituting 119904119911119867119911= 1198671015840

119911 119904119903119867119903= 1198671015840

119903 119877119867120593119903 = 119867

1015840

120593 119877119864120593119903 =

1198641015840

120593 119904119911119864119911= 1198641015840

119911 and 119904

119903119864119903= 1198641015840

119903into (9a)ndash(9c) (9a)ndash(9c) can be

written as

1198951205961205760

119904119911

119904119903

119877

1199031198641015840

119903=1

119903

1205971198671015840

119911

120597120593minus

1205971198671015840

120593

120597119911 (10a)

1198951205961205760119904119911119904119903

119903

1198771198641015840

120593=

120597 (1198671015840

119903)

120597119911minus

120597 (1198671015840

119911)

120597119903 (10b)

1198951205961205760

119904119903119877

1199041199111199031198641015840

119911=1

119903

120597 (1199031198671015840

120593)

120597119903minus1

119903

120597 (1198671015840

119903)

120597120593 (10c)

The Scientific World Journal 3

Namely

[[[[[[[[[[

[

1

119903

1205971198671015840

119911

120597120593minus

1205971198671015840

120593

120597119911

120597 (1198671015840

119903)

120597119911minus

120597 (1198671015840

119911)

120597119903

1

119903

120597 (1199031198671015840

120593)

120597119903minus1

119903

120597 (1198671015840

119903)

120597120593

]]]]]]]]]]

]

= 1198951205961205760120576119903120576

[[[[

[

1198641015840

119903

1198641015840

120593

1198641015840

119911

]]]]

]

(11)

Equation (11) can be shortly expressed as

nabla timesH = 1198951205961205760120576119903120576E (12)

According to the duality theorem Maxwell curl equation(2) can be represented by equation

[[[[[[[[[[

[

1

119903

1205971198641015840

119911

120597120593minus

1205971198641015840

120593

120597119911

120597 (1198641015840

119903)

120597119911minus

120597 (1198641015840

119911)

120597119903

1

119903

120597 (1199031198641015840

120593)

120597119903minus1

119903

120597 (1198641015840

119903)

120597120593

]]]]]]]]]]

]

= minus1198951205961205830120583119903120583

[[[[

[

1198671015840

119903

1198671015840

120593

1198671015840

119911

]]]]

]

(13)

Equation (13) can be expressed as

nabla times E = minus1198951205961205830120583119903120583H (14)

where

120576 = 120583 =

[[[[[[

[

119904119911119877

119904119903119903

0 0

0119904119911119904119903119903

1198770

0 0119904119903119877

119904119911119903

]]]]]]

]

(15)

AS the plasma antenna is rotationally symmetric Thusit is suitable to study this problem in cylindrical coordinateThe TM modes are excited Maxwell equations involve threecomponents 119864

119903 119864119911 and 119867

120593 Thus the Maxwell equation

of electromagnetic wave propagating in free space will bereduced as

minus1198951205961205830119904119911119904119903

119903

1198771198671015840

120593=

120597 (1198641015840

119903)

120597119911minus

120597 (1198641015840

119911)

120597119903 (16a)

1198951205961205760

119904119911

119904119903

119877

1199031198641015840

119903= minus

1205971198671015840

120593

120597119911 (16b)

1198951205961205760

119904119903119877

1199041199111199031198641015840

119911=1

119903

120597 (1199031198671015840

120593)

120597119903 (16c)

Applying the auxiliary differential equation method(ADE) [15] the iterative equations [16] of (16a)ndash(16c) arederived as follows

119861119899+1

120593|119894119895= (

21205760minus 119889119905120590119903

21205760+ 119889119905120590119903

)119861119899

120593|119894119895

+ (21205760119889119905

21205760+ 119889119905120590119903

)

[[[[

[

119864119899+12

119911|119894+12119895minus 119864119899+12

119911|119894minus12119895

119889119903

minus

119864119899+12

119903|119894119895+12minus 119864119899+12

119903|119894119895minus12

119889119911

]]]]

]

(17a)

119867119899+1

120593|119894119895= (

21205760minus 120590119911119889119905

21205760+ 120590119911119889119905)119867119899+1

120593|119894119895

+21205760119877

(21205760+ 120590119911119889119905) 1205830120583119903119903(119861119899+1

120593|119894119895minus 119861119899

120593|119894119895)

(17b)

119863119899+1

119903|119894+12119895119896= (

21205760minus 120590119911119889119905

21205760+ 120590119911119889119905)119863119899

119903|119894+12119895119896+ (

21205760119889119905

21205760+ 120590119911119889119905)

times

1

119903119894+12

119867119899+12

119911|119894+12119895+12119896minus 119867119899+12

119911|119894+12119895minus12119896

119889120593

minus

119867119899+12

120593|119894+12119895119896+12minus 119867119899+12

120593|119894+12119895sdot119896minus12

119889119911

(18a)

119864119899+1

119903|119894+12119895119896= 119864119899

119903|119894+12119895119896

+119903

1205760120576119903119877(

21205760+ 119889119905120590119903

21205760

119863119899+1

119903|119894+12119895119896

minus21205760minus 119889119905120590119903

21205760

119863119899

119903|119894+12119895119896

)

(18b)

119863119899+1

119911|119894119895119896+12= (

21205760minus 120590119903119889119905

21205760+ 120590119903119889119905)119863119899

119911|119894119895119896+12+ (

21205760119889119905

21205760+ 120590119903119889119905)

times

(1

2119903+1

119889119903)119867119899+12

120593|119894+12119895119896+12

+(1

2119903minus1

119889119903)119867119899+12

120593|119894minus12119895119896+12

(19a)

119864119899+1

119911|119894119895119896+12= 119864119899

119911|119894119895119896+12

+119903

1205760120576119903119877(

21205760+ 119889119905120590119911

21205760

119863119899+1

119911|119894119895119896+12

minus21205760minus 119889119905120590119911

21205760

119863119899

119911|119894119895119896+12

)

(19b)

By using these six iterative equations we can calculate thevalue of electromagnetic field in PML Also we can use theseiterative equations to calculate the value of electromagneticfield in free space by setting the electric conductivity at120590

119911= 0

120590119903= 0 and 120576

119903= 1

In order to validate the correctness of the theory abovewe apply this approach in the propagation of electromagnetic


r

z

FDTDregion

PML

r

z

InterfacePEC

Signal source

E1

M1

H1

Er

Ez H120593

Δr

Δz

Figure 1 Two-dimensional FDTD computational space

0 20 40 60 80 0

20

40

0

50

2

4

minus2

minus4

minus6

minus8

minus10

minus5

minus10

minus15

times10minus7

times10minus7

Figure 2 Propagating the electric field 119864119903in free space

field in free space The two-dimensional FDTD computa-tional space is shown as in Figure 1

Figure 1 shows that half of the free space is simulatedThe computational space is composed of 50 times 100 Yee sellsThe signal source is sinusoidal signal with the frequency of20GHz The spatial step is Δ119903 = Δ119911 = 0003mThe temporalstep is Δ119905 = 2123 times 10minus12 s The total number of time steps is500 The number of PML cells is 9 The propagating processof electric field 119864

119903in free space is shown as in Figure 2

In Figure 2 it is shown that the electric field 119864119903spreads

out around the signal sourceWhen the electric field arrives atthe interface between PML and free space it can be absorbedby the PML So the theory put forward above is correct

3 Radiation Characteristic of Plasma Antenna

In this part the radiation characteristic of plasma antennaunder two-dimensional case is investigated The geometry[17 18] of plasma antenna is shown in Figure 3

As Figure 3 illustrated 119881 represents free space aroundthe plasma antenna The plasma antenna is fed by coaxial

ab

O

zSe

PEC

Coaxial cable

Grid

R

V

Plasma antenna

l

lA

A-A998400

Figure 3 Two-dimension geometry of plasma antenna

cable The parameters 119886 and 119887 are inner and outer radius ofcoaxial cable with the ratio of 119887119886 = 23 to ensure that thecharacteristic impedance is 50Ω 119897 represents the length ofplasma antenna tube By using the FDTD approach togetherwith the theory in Section 2 we study the near-field and far-field radiation pattern of plasma antenna

31 Near-Field Radiation Pattern If we want to obtain theunique solution to Maxwell equation within 119881 we mustinitialize the electromagnetic fields E andH within 119881 at time119905 = 0 Furthermore the values n times E and n times H must beinitialized also on the boundary surface for all time 0 lt 119905 lt 119905

0

The gauss pulse voltage source is imposed on the cross section119860-1198601015840 as shown in Figure 3 The expression of 119864

119903is as follows

119864119894

119903(119905) =

119881119894

(119905)

ln (119887119886) 119903119903 (20)

This is the only electric field at the cross section if wechoose 2119897

119860gt 1198881199050 because the field reflected from the end of

the linewill not reach the cross section during the observationtime The outer conductor of coaxial cable connects withground The inner conductor outer conductor and groundare considered as perfect electric conductor (PEC) So thevalue of n times E is zero on the surface of the coaxial cable andground during the observation process

The gauss pulse voltage source is initialized with theparameters 120591

119886= ℎ119888 120591

119901120591119886= 8 times 10

minus2 The parametersdescribing the plasma antenna are as follows the length


100 200 300 400 500

20

40

60

80

100

120

140

160

Near field of Er

Num

ber o

f grid

s inr

dire

ctio

n

Number of grids in z direction

Figure 4 Near-field of plasma antenna with iterative number 500

100 200 300 400 500 600 700

50

100

150

200

250

300

Near field of Er

Num

ber o

f grid

s inr

dire

ctio

n



119897 = 50 cm and the radius of the conductors of the coaxialline 119886 = 1 cm and 119887 = 23 cm The spatial step is Δ119903 = Δ119911 =(119887minus119886)4The temporal step can be calculated according to theexpression Δ119905 = 1119888 lowastradic11198891199032 + 11198891199112 Usually the time stepis chosen to be 20 smaller than the courant stability limitThe parameters of plasma are initialized electron density is119899119890= 1times10

17mminus3 and collision frequency is ]119888= 15times10

8HzFrom the equation 120596

119901= radic1198902119899

1198901198981205760 the angular frequency

of plasma can be obtained as 120596119901= 17815 times 10

10 radsThrough FDTD method the near-field of plasma antennacorresponding to the iterative numbers is 500 1000 and 1500The corresponding results are shown in Figures 4 5 and 6

Figure 4 sim Figure 4 are the near-field of plasma antennawith different iterative number Figure 6 shows the part ofthe power radiated to the free space and part of powerreflected back to the coaxial cable when electromagnetic wavepropagates from the bottom to the joint of coaxial cable

100 200 300 400 500 600 700 800

50

100

150

200

250

300

350

400

450

Near field of Er

Num

ber o

f grid

s inr

dire

ctio

n



Observation point

120579

o

r

r

z

r998400

r minus r998400

Figure 7 Schematic map of NF-FF transformation

and plasma antenna Figure 5 shows that when the iterativenumber is 1000 the electromagneticwave continues to spreadout and has not reached the top of the plasma antenna Atthe same time the reverse electric field in coaxial cable willcontinue to propagate in signal source direction When theiterative number comes to 1500 the electromagneticwavewillarrive at the top of the plasma antenna Figure 6 shows thatreflection has happened and the second radiation is formed

32 Far-Field Radiation Pattern The finite-difference time-domain (FDTD) method [19 20] is used to compute electricand magnetic field within a finite space around an electro-magnetic object Namely only the value of near magneticfield can be obtained Otherwise we also care about thefar-zone electromagnetic field of plasma antenna The far-zone electromagnetic field can be computed from the near-field FDTD data through a near-field to far-field (NF-FF)transformation technique

The far-field value is calculated in cylindrical coordinateThe schematic map of NF-FF is shown as in Figure 7

The vector r denotes the position of the observation point(119903 120579) the vector r1015840 denotes the position of source The valueof the source can be calculated through FDTD method


Through using the Green function under two-dimensionconditions the expressions of far-zone electromagnetic fieldin cylindrical coordinate are

119864119911=exp (minus119895119896119903)2radic2119895120587119896119903

(119895119896) (minus119885119891119911+ 119891119898120593)

119867119911=exp (minus119895119896119903)2radic2119895120587119896119903

(minus119895119896) (119891120593+1

119885119891119898119911)

(21)

where 119891120577(120593) 119891

119898120577(120593) (120577 = 119911 120593) are current moment and

magnetic moment respectively

f120577(120593) = int

119897

J (r1015840) exp (jk sdot r1015840) 1198891198971015840

fm120577 (120593) = int119897

Jm (r1015840) exp (jk sdot r1015840) 1198891198971015840

(22)

Mapping from spherical coordinate to cylindrical coordinatewe have

k sdot r1015840 = 119896 sin (120579) sdot 1199031015840 + 119896 cos (120579) sdot 119911 (23)

Substituting (23) into (22) (22) can be rewritten as

119891120577(120593) = int

119897

119869120577(1199031015840

) exp (119895 (119896 sin (120579) sdot 1199031015840

+119896 cos (120579) sdot 119911)) 1198891198971015840

119891119898120577(120593) = int

119897

119869119898120577(1199031015840

) exp (119895 (119896 sin (120579) sdot 1199031015840

+119896 cos (120579) sdot 119911)) 1198891198971015840

(24)

Substituting (24) into (21) the far-field electromagnetic fieldcan be obtained

Through the NF-FF method the affection of electrondensity to the radiation characteristic of plasma antenna isstudied We initialize the typical parameters of plasma asbelow

Collision frequency is ]119888= 15 times 10

8Hz and the electrondensity is set as 119899

119890= 1times10

16mminus3 119899119890= 1times10

17mminus3 and 119899119890=

1times1018mminus3 respectively And the far-field of plasma antenna

under different electron density is shown as in Figure 8In Figure 8 it is shown that with the variation of

electron density of plasma antenna the profile of far-fieldradiation pattern will change The reason is that when theelectromagnetic wave arrives at the plasma region the inter-action between electromagnetic wave and plasma changes thesurface current distribution of plasma antenna as it is knownthat the radiation pattern is determined by the surface currentdistribution of antenna Thus the far-field radiation patternof plasma antenna will be changed

4 Conclusion

The radiation characteristic of plasma antenna is investi-gated in this paper Before studying this problem two key

02

04

06

08

1

60

300

90

ne = 1e17ne = 1e18ne = 1e16

minus30

minus60

minus90

Figure 8 Far-field of plasma antenna under different electrondensity

issues are investigated Firstly we study the propagation ofelectromagnetic wave in free space by using FDTD methodThe updating equations of Maxwell equation in stretchedcoordinate are derived In order to validate the correctnessof the theory the propagation of electromagnetic wave in freespace is calculated Results show that the theory is correct andcan be used in cylindrical coordinate Secondly the radiationcharacteristic of plasma antenna under two-dimension caseand the near-field radiation pattern are obtained Throughthe NF-FF transformation we obtain the far-field radiationpattern From the results we can conclude that the electrondensity can influence the radiation characteristic of plasmaantenna

Conflict of Interests

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

Acknowledgment

The work is supported by the Chinese Pre-Research FundGrant no 40404110203

References

[1] T Anderson Plasma Antenna Artech House 2011[2] R Kumar and D Bora ldquoA reconfigurable plasma antennardquo

Journal of Applied Physics vol 107 no 5 Article ID 053303 9pages 2010

[3] L L Yang Y Tu and B P Wang ldquoAxisymetric surface wavedispersionin plasma antennardquo Vacuum Science and Technologyvol 24 no 6 pp 424ndash426 2004

[4] G W Zhao Research of basic theory and nonlinear phenomenain plasma antennas [PhD thesis] Center for Space Science andApplied Research Beijing China 2007

[5] Z Wu Y Yang and J Wang ldquoStudy on current distributionand radiation characteristics of plasma antennasrdquo Acta PhysicaSinica vol 59 no 3 pp 1890ndash1894 2010

[6] X R Xia and C Y Yin ldquoNumerical calculation of radiationpattern of plasma channel antennardquoNuclear Fusion and PlasmaPhysics vol 30 no 1 pp 30ndash36 2010


[7] Z Dai S Liu Y Chen and N G Nanjing ldquoDevelopment andinvestigation of reconfigurable plasma antennasrdquo in Proceedingsof the International Conference on Microwave and MillimeterWave Technology (ICMMT 10) pp 1135ndash1137 Chengdu ChinaMay 2010

[8] Z W Liang Research on electronical function and noise mecha-nism of plasma-column antenna [PhD thesis] Center for SpaceScience and Applied Research Beijing China 2008

[9] P Russo G Cerri and E Vecchioni ldquoSelf-consistent model forthe characterisation of plasma ignition by propagation of anelectromagnetic wave to be used for plasma antennas designrdquoIET Microwaves Antennas amp Propagation vol 4 no 12 pp2256ndash2264 2010

[10] G Cerri F Moglie R Montesi and E Vecchioni ldquoFDTDsolution of the Maxwell-Boltzmann system for electromagneticwave propagation in a plasmardquo IEEE Transactions on Antennasand Propagation vol 56 no 8 part 2 pp 2584ndash2588 2008

[11] G Cerri P Russo and E Vecchioni ldquoA self-consistent FDTDmodel of plasma antennasrdquo in Proceedings of the 4th EuropeanConference on Antennas and Propagation (EuCAP rsquo10) pp 12ndash16 April 2010

[12] G Cerri P Russo and E Vecchioni ldquoElectromagnetic char-acterization of plasma antennasrdquo in Proceedings of the 3rdEuropean Conference on Antennas and Propagation (EuCAPrsquo09) pp 3143ndash3146 Berlin Germany March 2009

[13] G Cerri V M Primiani P Russo and E Vecchioni ldquoFDTDapproach for the characterization of electromagnetic wavepropagation in plasma for application to plasma antennasrdquo inProceedings of the 2nd European Conference on Antennas andPropagation Edinburgh UK November 2007

[14] H X Zhang Y H Lu and J G Lu ldquoThe application ofPML-FDTD and boundary consistency conditions of total-scattered fields in three dimension cylindrical coordinatesrdquo inProceedings of the 6th International Symposium on AntennasPropagation and EM Theory pp 698ndash702 Beijing ChinaOctober 2003

[15] J X Li Research on algorithms for implementing perfectlymatched layers in the finite difference time domainmethod [PhDthesis] Tianjin Univesity Tianjin China 2007

[16] K S Yee ldquoNumerical solution of initial boundary value prob-lems involving Maxwellrsquos equations in isotropic mediardquo IEEETransactions on Antennas and Propagation vol 14 pp 302ndash3071966

[17] J G Maloney G S Smith and W R Scott Jr ldquoAccuratecomputation of the radiation from simple antennas using thefinite-difference time-domain methodrdquo IEEE Transactions onAntennas and Propagation vol 38 no 7 pp 1059ndash1068 1990

[18] J G Maloney K J Shlager and G S Smith ldquoSimple DFDTDmodel for transient excitation of antennas by transmissionlinesrdquo IEEE Transactions on Antennas and Propagation vol 42no 2 pp 289ndash292 1994

[19] A Taflove and S C Hagness Computational ElectrodynamicsThe Finite-Difference Time-Domian Method Artech House2000

[20] ldquoPlasma antennasrdquo in Frontiers i n Antennas F Gross Edchapter 10 pp 411ndash441 Artech House Norwood Mass USA2011

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



a rigorous mathematical model to investigate the radiationcharacteristic of plasma antenna The numerical calculationapproach applied in this paper is to study the radiationcharacteristic of plasma antenna

2 Propagation of Electromagnetic Wave inFree Space and Plasma

There are two key issues to deal with in this research oneis the propagation of electromagnetic wave in free space andthe other one is the propagation of electromagnetic wave inthe plasma Only these two problems are solved then theinvestigation of radiation characteristic of plasma antennacan be further conducted

21 Propagation of Electromagnetic Wave in Free Space Inorder to apply FDTD method to simulate the propagation ofelectromagnetic wave in free space in cylindrical coordinatethe stretched coordinate is selected So themodifiedMaxwellequations can be expressed as below

nabla119904timesH = 119895120596120576E (1)

nabla119904times E = minus119895120596120583H (2)

where E represents electric field strength vector in volts permeterH representsmagnetic field strength vector in amperesper meter 120576 denotes the permittivity in farad per meter 120583denotes the permeability in henry per meter120596 represents theangular frequency of incidence signal in radian per second

In stretched coordinate [14] we define

119904119903= 1 +

120590119903

1198951205961205760

119904119911= 1 +

120590119911

1198951205961205760

(3)

where 119904119903and 119904119911are coordinate stretched factor

119877 997888rarr int

119903

0

119904119903(1199031015840

) 1198891199031015840

=

119903 1199031015840

lt 1199030

119903 +1

1198951205961205760

int

119903

1199030

120590119903(1199031015840

) 1198891199031015840

1199031015840

lt 1199030

(4)

119885 997888rarr int

119911

0

119904119911(1199111015840

) 1198891199111015840

=

119911 1199111015840

lt 1199110

119911 +1

1198951205961205760

int

119911

1199110

120590119911(1199111015840

) 1198891199111015840

1199111015840

lt 1199110

(5)

where 1199030and 119911

0represent the distance between the signal

source and inner boundary of PML along 119903 direction and 119911direction respectively

Maxwell curl equation (1) then can be represented bythese three scale equations in cylindrical coordinate systemas (6a)ndash(6c)

1198951205961205760119864119903=1

119877

120597119867119911

120597120593minus

120597119867120593

120597119885 (6a)

1198951205961205760119864120593=120597119867119903

120597119885minus120597119867119911

120597119877 (6b)

1198951205961205760119864119911=1

119877

120597 (119877119867120593)

120597119877minus1

119877

120597119867119903

120597120593 (6c)

From (4) and (5) (7) can be obtained as follows

120597

120597119877=1

119904119903

120597

120597119903

120597

120597119885=1

119904119911

120597

120597119911 (7)

Substituting (7) into (6a)ndash(6c) yields

1198951205961205760119864119903=1

119877

120597119867119911

120597120593minus1

119904119911

120597119867120593

120597119911 (8a)

1198951205961205760119864120593=1

119904119911

120597119867119903

120597119911minus1

119904119903

120597119867119911

120597119903 (8b)

1198951205961205760119864119911=1

119877

1

119904119903

120597 (119877119867120593)

120597119903minus1

119877

120597119867119903

120597120593 (8c)

After multiplying 119904119911sdot 119877119903 119904

119911sdot 119904119903 119904119903sdot 119877119903 respectively (8a)

(8b) and (8c) can be expressed as below

1198951205961205760119904119911

119877

119903119864119903=1

119903

120597 (119904119911119867119911)

120597120593minus119877

119903

120597119867120593

120597119911 (9a)

1198951205961205760119904119911119904119903119864120593=120597 (119904119903119867119903)

120597119911minus120597 (119904119911119867119911)

120597119903 (9b)

1198951205961205760119904119903

119877

119903119864119911=1

119903

120597 (119877119867120593)

120597119903minus1

119903

120597 (119904119903119867119903)

120597120593 (9c)

Substituting 119904119911119867119911= 1198671015840

119911 119904119903119867119903= 1198671015840

119903 119877119867120593119903 = 119867

1015840

120593 119877119864120593119903 =

1198641015840

120593 119904119911119864119911= 1198641015840

119911 and 119904

119903119864119903= 1198641015840

119903into (9a)ndash(9c) (9a)ndash(9c) can be

written as

1198951205961205760

119904119911

119904119903

119877

1199031198641015840

119903=1

119903

1205971198671015840

119911

120597120593minus

1205971198671015840

120593

120597119911 (10a)

1198951205961205760119904119911119904119903

119903

1198771198641015840

120593=

120597 (1198671015840

119903)

120597119911minus

120597 (1198671015840

119911)

120597119903 (10b)

1198951205961205760

119904119903119877

1199041199111199031198641015840

119911=1

119903

120597 (1199031198671015840

120593)

120597119903minus1

119903

120597 (1198671015840

119903)

120597120593 (10c)


Namely

[[[[[[[[[[

[

1

119903

1205971198671015840

119911

120597120593minus

1205971198671015840

120593

120597119911

120597 (1198671015840

119903)

120597119911minus

120597 (1198671015840

119911)

120597119903

1

119903

120597 (1199031198671015840

120593)

120597119903minus1

119903

120597 (1198671015840

119903)

120597120593

]]]]]]]]]]

]

= 1198951205961205760120576119903120576

[[[[

[

1198641015840

119903

1198641015840

120593

1198641015840

119911

]]]]

]

(11)


nabla timesH = 1198951205961205760120576119903120576E (12)


[[[[[[[[[[

[

1

119903

1205971198641015840

119911

120597120593minus

1205971198641015840

120593

120597119911

120597 (1198641015840

119903)

120597119911minus

120597 (1198641015840

119911)

120597119903

1

119903

120597 (1199031198641015840

120593)

120597119903minus1

119903

120597 (1198641015840

119903)

120597120593

]]]]]]]]]]

]

= minus1198951205961205830120583119903120583

[[[[

[

1198671015840

119903

1198671015840

120593

1198671015840

119911

]]]]

]

(13)



where

120576 = 120583 =

[[[[[[

[

119904119911119877

119904119903119903

0 0

0119904119911119904119903119903

1198770

0 0119904119903119877

119904119911119903

]]]]]]

]

(15)


119903 119864119911 and 119867



minus1198951205961205830119904119911119904119903

119903

1198771198671015840

120593=

120597 (1198641015840

119903)

120597119911minus

120597 (1198641015840

119911)

120597119903 (16a)

1198951205961205760

119904119911

119904119903

119877

1199031198641015840

119903= minus

1205971198671015840

120593

120597119911 (16b)

1198951205961205760

119904119903119877

1199041199111199031198641015840

119911=1

119903

120597 (1199031198671015840

120593)

120597119903 (16c)


119861119899+1

120593|119894119895= (

21205760minus 119889119905120590119903

21205760+ 119889119905120590119903

)119861119899

120593|119894119895

+ (21205760119889119905

21205760+ 119889119905120590119903

)

[[[[

[

119864119899+12

119911|119894+12119895minus 119864119899+12

119911|119894minus12119895

119889119903

minus

119864119899+12

119903|119894119895+12minus 119864119899+12

119903|119894119895minus12

119889119911

]]]]

]

(17a)

119867119899+1

120593|119894119895= (

21205760minus 120590119911119889119905

21205760+ 120590119911119889119905)119867119899+1

120593|119894119895

+21205760119877

(21205760+ 120590119911119889119905) 1205830120583119903119903(119861119899+1

120593|119894119895minus 119861119899

120593|119894119895)

(17b)

119863119899+1

119903|119894+12119895119896= (

21205760minus 120590119911119889119905

21205760+ 120590119911119889119905)119863119899

119903|119894+12119895119896+ (

21205760119889119905

21205760+ 120590119911119889119905)

times

1

119903119894+12

119867119899+12

119911|119894+12119895+12119896minus 119867119899+12

119911|119894+12119895minus12119896

119889120593

minus

119867119899+12

120593|119894+12119895119896+12minus 119867119899+12

120593|119894+12119895sdot119896minus12

119889119911

(18a)

119864119899+1

119903|119894+12119895119896= 119864119899

119903|119894+12119895119896

+119903

1205760120576119903119877(

21205760+ 119889119905120590119903

21205760

119863119899+1

119903|119894+12119895119896

minus21205760minus 119889119905120590119903

21205760

119863119899

119903|119894+12119895119896

)

(18b)

119863119899+1

119911|119894119895119896+12= (

21205760minus 120590119903119889119905

21205760+ 120590119903119889119905)119863119899

119911|119894119895119896+12+ (

21205760119889119905

21205760+ 120590119903119889119905)

times

(1

2119903+1

119889119903)119867119899+12

120593|119894+12119895119896+12

+(1

2119903minus1

119889119903)119867119899+12

120593|119894minus12119895119896+12

(19a)

119864119899+1

119911|119894119895119896+12= 119864119899

119911|119894119895119896+12

+119903

1205760120576119903119877(

21205760+ 119889119905120590119911

21205760

119863119899+1

119911|119894119895119896+12

minus21205760minus 119889119905120590119911

21205760

119863119899

119911|119894119895119896+12

)

(19b)


119911= 0

120590119903= 0 and 120576

119903= 1



r

z

FDTDregion

PML

r

z

InterfacePEC

Signal source

E1

M1

H1

Er

Ez H120593

Δr

Δz


0 20 40 60 80 0

20

40

0

50

2

4

minus2

minus4

minus6

minus8

minus10

minus5

minus10

minus15

times10minus7

times10minus7










ab

O

zSe

PEC

Coaxial cable

Grid

R

V

Plasma antenna

l

lA

A-A998400




0


119903is as follows

119864119894

119903(119905) =

119881119894

(119905)

ln (119887119886) 119903119903 (20)





119886= ℎ119888 120591

119901120591119886= 8 times 10



100 200 300 400 500

20

40

60

80

100

120

140

160

Near field of Er

Num

ber o

f grid

s inr

dire

ctio

n



100 200 300 400 500 600 700

50

100

150

200

250

300

Near field of Er

Num

ber o

f grid

s inr

dire

ctio

n






119901= radic1198902119899





100 200 300 400 500 600 700 800

50

100

150

200

250

300

350

400

450

Near field of Er

Num

ber o

f grid

s inr

dire

ctio

n



Observation point

120579

o

r

r

z

r998400

r minus r998400








119864119911=exp (minus119895119896119903)2radic2119895120587119896119903

(119895119896) (minus119885119891119911+ 119891119898120593)

119867119911=exp (minus119895119896119903)2radic2119895120587119896119903

(minus119895119896) (119891120593+1

119885119891119898119911)

(21)

where 119891120577(120593) 119891



f120577(120593) = int

119897

J (r1015840) exp (jk sdot r1015840) 1198891198971015840

fm120577 (120593) = int119897

Jm (r1015840) exp (jk sdot r1015840) 1198891198971015840

(22)




119891120577(120593) = int

119897

119869120577(1199031015840

) exp (119895 (119896 sin (120579) sdot 1199031015840

+119896 cos (120579) sdot 119911)) 1198891198971015840

119891119898120577(120593) = int

119897

119869119898120577(1199031015840

) exp (119895 (119896 sin (120579) sdot 1199031015840

+119896 cos (120579) sdot 119911)) 1198891198971015840

(24)





119890= 1times10

16mminus3 119899119890= 1times10

17mminus3 and 119899119890=




4 Conclusion


02

04

06

08

1

60

300

90

ne = 1e17ne = 1e18ne = 1e16

minus30

minus60

minus90





Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Namely

[[[[[[[[[[

[

1

119903

1205971198671015840

119911

120597120593minus

1205971198671015840

120593

120597119911

120597 (1198671015840

119903)

120597119911minus

120597 (1198671015840

119911)

120597119903

1

119903

120597 (1199031198671015840

120593)

120597119903minus1

119903

120597 (1198671015840

119903)

120597120593

]]]]]]]]]]

]

= 1198951205961205760120576119903120576

[[[[

[

1198641015840

119903

1198641015840

120593

1198641015840

119911

]]]]

]

(11)


nabla timesH = 1198951205961205760120576119903120576E (12)


[[[[[[[[[[

[

1

119903

1205971198641015840

119911

120597120593minus

1205971198641015840

120593

120597119911

120597 (1198641015840

119903)

120597119911minus

120597 (1198641015840

119911)

120597119903

1

119903

120597 (1199031198641015840

120593)

120597119903minus1

119903

120597 (1198641015840

119903)

120597120593

]]]]]]]]]]

]

= minus1198951205961205830120583119903120583

[[[[

[

1198671015840

119903

1198671015840

120593

1198671015840

119911

]]]]

]

(13)



where

120576 = 120583 =

[[[[[[

[

119904119911119877

119904119903119903

0 0

0119904119911119904119903119903

1198770

0 0119904119903119877

119904119911119903

]]]]]]

]

(15)


119903 119864119911 and 119867



minus1198951205961205830119904119911119904119903

119903

1198771198671015840

120593=

120597 (1198641015840

119903)

120597119911minus

120597 (1198641015840

119911)

120597119903 (16a)

1198951205961205760

119904119911

119904119903

119877

1199031198641015840

119903= minus

1205971198671015840

120593

120597119911 (16b)

1198951205961205760

119904119903119877

1199041199111199031198641015840

119911=1

119903

120597 (1199031198671015840

120593)

120597119903 (16c)


119861119899+1

120593|119894119895= (

21205760minus 119889119905120590119903

21205760+ 119889119905120590119903

)119861119899

120593|119894119895

+ (21205760119889119905

21205760+ 119889119905120590119903

)

[[[[

[

119864119899+12

119911|119894+12119895minus 119864119899+12

119911|119894minus12119895

119889119903

minus

119864119899+12

119903|119894119895+12minus 119864119899+12

119903|119894119895minus12

119889119911

]]]]

]

(17a)

119867119899+1

120593|119894119895= (

21205760minus 120590119911119889119905

21205760+ 120590119911119889119905)119867119899+1

120593|119894119895

+21205760119877

(21205760+ 120590119911119889119905) 1205830120583119903119903(119861119899+1

120593|119894119895minus 119861119899

120593|119894119895)

(17b)

119863119899+1

119903|119894+12119895119896= (

21205760minus 120590119911119889119905

21205760+ 120590119911119889119905)119863119899

119903|119894+12119895119896+ (

21205760119889119905

21205760+ 120590119911119889119905)

times

1

119903119894+12

119867119899+12

119911|119894+12119895+12119896minus 119867119899+12

119911|119894+12119895minus12119896

119889120593

minus

119867119899+12

120593|119894+12119895119896+12minus 119867119899+12

120593|119894+12119895sdot119896minus12

119889119911

(18a)

119864119899+1

119903|119894+12119895119896= 119864119899

119903|119894+12119895119896

+119903

1205760120576119903119877(

21205760+ 119889119905120590119903

21205760

119863119899+1

119903|119894+12119895119896

minus21205760minus 119889119905120590119903

21205760

119863119899

119903|119894+12119895119896

)

(18b)

119863119899+1

119911|119894119895119896+12= (

21205760minus 120590119903119889119905

21205760+ 120590119903119889119905)119863119899

119911|119894119895119896+12+ (

21205760119889119905

21205760+ 120590119903119889119905)

times

(1

2119903+1

119889119903)119867119899+12

120593|119894+12119895119896+12

+(1

2119903minus1

119889119903)119867119899+12

120593|119894minus12119895119896+12

(19a)

119864119899+1

119911|119894119895119896+12= 119864119899

119911|119894119895119896+12

+119903

1205760120576119903119877(

21205760+ 119889119905120590119911

21205760

119863119899+1

119911|119894119895119896+12

minus21205760minus 119889119905120590119911

21205760

119863119899

119911|119894119895119896+12

)

(19b)


119911= 0

120590119903= 0 and 120576

119903= 1



r

z

FDTDregion

PML

r

z

InterfacePEC

Signal source

E1

M1

H1

Er

Ez H120593

Δr

Δz


0 20 40 60 80 0

20

40

0

50

2

4

minus2

minus4

minus6

minus8

minus10

minus5

minus10

minus15

times10minus7

times10minus7










ab

O

zSe

PEC

Coaxial cable

Grid

R

V

Plasma antenna

l

lA

A-A998400




0


119903is as follows

119864119894

119903(119905) =

119881119894

(119905)

ln (119887119886) 119903119903 (20)





119886= ℎ119888 120591

119901120591119886= 8 times 10



100 200 300 400 500

20

40

60

80

100

120

140

160

Near field of Er

Num

ber o

f grid

s inr

dire

ctio

n



100 200 300 400 500 600 700

50

100

150

200

250

300

Near field of Er

Num

ber o

f grid

s inr

dire

ctio

n






119901= radic1198902119899





100 200 300 400 500 600 700 800

50

100

150

200

250

300

350

400

450

Near field of Er

Num

ber o

f grid

s inr

dire

ctio

n



Observation point

120579

o

r

r

z

r998400

r minus r998400








119864119911=exp (minus119895119896119903)2radic2119895120587119896119903

(119895119896) (minus119885119891119911+ 119891119898120593)

119867119911=exp (minus119895119896119903)2radic2119895120587119896119903

(minus119895119896) (119891120593+1

119885119891119898119911)

(21)

where 119891120577(120593) 119891



f120577(120593) = int

119897

J (r1015840) exp (jk sdot r1015840) 1198891198971015840

fm120577 (120593) = int119897

Jm (r1015840) exp (jk sdot r1015840) 1198891198971015840

(22)




119891120577(120593) = int

119897

119869120577(1199031015840

) exp (119895 (119896 sin (120579) sdot 1199031015840

+119896 cos (120579) sdot 119911)) 1198891198971015840

119891119898120577(120593) = int

119897

119869119898120577(1199031015840

) exp (119895 (119896 sin (120579) sdot 1199031015840

+119896 cos (120579) sdot 119911)) 1198891198971015840

(24)





119890= 1times10

16mminus3 119899119890= 1times10

17mminus3 and 119899119890=




4 Conclusion


02

04

06

08

1

60

300

90

ne = 1e17ne = 1e18ne = 1e16

minus30

minus60

minus90





Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










r

z

FDTDregion

PML

r

z

InterfacePEC

Signal source

E1

M1

H1

Er

Ez H120593

Δr

Δz


0 20 40 60 80 0

20

40

0

50

2

4

minus2

minus4

minus6

minus8

minus10

minus5

minus10

minus15

times10minus7

times10minus7










ab

O

zSe

PEC

Coaxial cable

Grid

R

V

Plasma antenna

l

lA

A-A998400




0


119903is as follows

119864119894

119903(119905) =

119881119894

(119905)

ln (119887119886) 119903119903 (20)





119886= ℎ119888 120591

119901120591119886= 8 times 10



100 200 300 400 500

20

40

60

80

100

120

140

160

Near field of Er

Num

ber o

f grid

s inr

dire

ctio

n



100 200 300 400 500 600 700

50

100

150

200

250

300

Near field of Er

Num

ber o

f grid

s inr

dire

ctio

n






119901= radic1198902119899





100 200 300 400 500 600 700 800

50

100

150

200

250

300

350

400

450

Near field of Er

Num

ber o

f grid

s inr

dire

ctio

n



Observation point

120579

o

r

r

z

r998400

r minus r998400








119864119911=exp (minus119895119896119903)2radic2119895120587119896119903

(119895119896) (minus119885119891119911+ 119891119898120593)

119867119911=exp (minus119895119896119903)2radic2119895120587119896119903

(minus119895119896) (119891120593+1

119885119891119898119911)

(21)

where 119891120577(120593) 119891



f120577(120593) = int

119897

J (r1015840) exp (jk sdot r1015840) 1198891198971015840

fm120577 (120593) = int119897

Jm (r1015840) exp (jk sdot r1015840) 1198891198971015840

(22)




119891120577(120593) = int

119897

119869120577(1199031015840

) exp (119895 (119896 sin (120579) sdot 1199031015840

+119896 cos (120579) sdot 119911)) 1198891198971015840

119891119898120577(120593) = int

119897

119869119898120577(1199031015840

) exp (119895 (119896 sin (120579) sdot 1199031015840

+119896 cos (120579) sdot 119911)) 1198891198971015840

(24)





119890= 1times10

16mminus3 119899119890= 1times10

17mminus3 and 119899119890=




4 Conclusion


02

04

06

08

1

60

300

90

ne = 1e17ne = 1e18ne = 1e16

minus30

minus60

minus90





Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










100 200 300 400 500

20

40

60

80

100

120

140

160

Near field of Er

Num

ber o

f grid

s inr

dire

ctio

n



100 200 300 400 500 600 700

50

100

150

200

250

300

Near field of Er

Num

ber o

f grid

s inr

dire

ctio

n






119901= radic1198902119899





100 200 300 400 500 600 700 800

50

100

150

200

250

300

350

400

450

Near field of Er

Num

ber o

f grid

s inr

dire

ctio

n



Observation point

120579

o

r

r

z

r998400

r minus r998400








119864119911=exp (minus119895119896119903)2radic2119895120587119896119903

(119895119896) (minus119885119891119911+ 119891119898120593)

119867119911=exp (minus119895119896119903)2radic2119895120587119896119903

(minus119895119896) (119891120593+1

119885119891119898119911)

(21)

where 119891120577(120593) 119891



f120577(120593) = int

119897

J (r1015840) exp (jk sdot r1015840) 1198891198971015840

fm120577 (120593) = int119897

Jm (r1015840) exp (jk sdot r1015840) 1198891198971015840

(22)




119891120577(120593) = int

119897

119869120577(1199031015840

) exp (119895 (119896 sin (120579) sdot 1199031015840

+119896 cos (120579) sdot 119911)) 1198891198971015840

119891119898120577(120593) = int

119897

119869119898120577(1199031015840

) exp (119895 (119896 sin (120579) sdot 1199031015840

+119896 cos (120579) sdot 119911)) 1198891198971015840

(24)





119890= 1times10

16mminus3 119899119890= 1times10

17mminus3 and 119899119890=




4 Conclusion


02

04

06

08

1

60

300

90

ne = 1e17ne = 1e18ne = 1e16

minus30

minus60

minus90





Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119864119911=exp (minus119895119896119903)2radic2119895120587119896119903

(119895119896) (minus119885119891119911+ 119891119898120593)

119867119911=exp (minus119895119896119903)2radic2119895120587119896119903

(minus119895119896) (119891120593+1

119885119891119898119911)

(21)

where 119891120577(120593) 119891



f120577(120593) = int

119897

J (r1015840) exp (jk sdot r1015840) 1198891198971015840

fm120577 (120593) = int119897

Jm (r1015840) exp (jk sdot r1015840) 1198891198971015840

(22)




119891120577(120593) = int

119897

119869120577(1199031015840

) exp (119895 (119896 sin (120579) sdot 1199031015840

+119896 cos (120579) sdot 119911)) 1198891198971015840

119891119898120577(120593) = int

119897

119869119898120577(1199031015840

) exp (119895 (119896 sin (120579) sdot 1199031015840

+119896 cos (120579) sdot 119911)) 1198891198971015840

(24)





119890= 1times10

16mminus3 119899119890= 1times10

17mminus3 and 119899119890=




4 Conclusion


02

04

06

08

1

60

300

90

ne = 1e17ne = 1e18ne = 1e16

minus30

minus60

minus90





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











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Research on Radiation Characteristic of Plasma Antenna …downloads.hindawi.com/journals/tswj/2014/290148.pdf · 2019-07-31 · Research Article Research on Radiation