research article research on radiation characteristic of
TRANSCRIPT
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
4 The Scientific World Journal
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
The Scientific World Journal 5
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
Number of grids in z direction
Figure 5 Near-field of plasma antenna with iterative number 1000
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
Number of grids in z direction
Figure 6 Near-field of plasma antenna with iterative number 1500
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
6 The Scientific World Journal
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
The Scientific World Journal 7
[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
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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
4 The Scientific World Journal
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
The Scientific World Journal 5
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
Number of grids in z direction
Figure 5 Near-field of plasma antenna with iterative number 1000
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
Number of grids in z direction
Figure 6 Near-field of plasma antenna with iterative number 1500
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
6 The Scientific World Journal
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
The Scientific World Journal 7
[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
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
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
4 The Scientific World Journal
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
The Scientific World Journal 5
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
Number of grids in z direction
Figure 5 Near-field of plasma antenna with iterative number 1000
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
Number of grids in z direction
Figure 6 Near-field of plasma antenna with iterative number 1500
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
6 The Scientific World Journal
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
The Scientific World Journal 7
[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
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
4 The Scientific World Journal
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
The Scientific World Journal 5
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
Number of grids in z direction
Figure 5 Near-field of plasma antenna with iterative number 1000
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
Number of grids in z direction
Figure 6 Near-field of plasma antenna with iterative number 1500
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
6 The Scientific World Journal
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
The Scientific World Journal 7
[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
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
The Scientific World Journal 5
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
Number of grids in z direction
Figure 5 Near-field of plasma antenna with iterative number 1000
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
Number of grids in z direction
Figure 6 Near-field of plasma antenna with iterative number 1500
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
6 The Scientific World Journal
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
The Scientific World Journal 7
[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
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
6 The Scientific World Journal
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
The Scientific World Journal 7
[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
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
The Scientific World Journal 7
[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
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of