The Propagation of Electromagnetic The Propagation of Electromagnetic Wave in Wave in AAtmospheric tmospheric PPressure ressure PPlasmalasma
Zhonghe Jiang XiWei Hu Shu Zhang Minghai LiuZhonghe Jiang XiWei Hu Shu Zhang Minghai Liu
HHuazhong uazhong UUniversity of niversity of SScience &cience & TTechnologyechnology
Workshop on ITER SimulationWorkshop on ITER Simulation May2006, PKU, Beijing, ChinaMay2006, PKU, Beijing, China
Section oneSection one
II Introduction and promotion
IIII Numerical results results
IIIIII Comparisons between Comparisons between analytic analytic
and numerical solutionsand numerical solutions
I IntroductionI Introduction
When the EM wave propagates in When the EM wave propagates in atmospheric pressure plasma layer, its atmospheric pressure plasma layer, its electric field will disturbs the electrons of electric field will disturbs the electrons of plasma, and the electrons will dissipate plasma, and the electrons will dissipate their energy by colliding with neutrals of their energy by colliding with neutrals of plasma. So the energy of EM wave will be plasma. So the energy of EM wave will be absorbed by the atmospheric plasma, and absorbed by the atmospheric plasma, and the level of dissipated energy strongly the level of dissipated energy strongly depends on the collision frequency depends on the collision frequency between the electrons and neutrals. between the electrons and neutrals.
The characteristics of EM wave in The characteristics of EM wave in APPAPP
Amplitude attenuated Amplitude attenuated strongly through strongly through electron-neutrals collision frequency (electron-neutrals collision frequency (ννee
00)), the characteristic time or length of wa, the characteristic time or length of wave attenuation are less than one period ve attenuation are less than one period or one wave length. or one wave length.
Phase shiftedPhase shifted both by electron density both by electron density ((nnee) and collision frequency) and collision frequency..
ReflectivityReflectivity of incident EM Wave depends both on electron density gradient (nnee
’’
), and collision frequencycollision frequency
CombineCombine wave and electron motion equations, we have got an integral-differential equation:
Obtain Obtain numericallynumerically full solutionsfull solutions of EM of EM
wave field in space and time domainwave field in space and time domain
),()(),(1),(
2
2
2
2
22
2
txEc
xw
t
txE
cx
txE pe
0),()(
0
)(2
2
dssxEevc
xw t tsvc
pe eo
IIII Numerical resultsNumerical results
Phase shift Phase shift ΔφΔφ Transmissivity Transmissivity TT Reflectivity Reflectivity RR Absorptivity Absorptivity AA
Thickness of plasma Thickness of plasma dd Electron density Electron density nnee
Collision frequency Collision frequency ννe0e0
Effects of profilesEffects of profiles
Electron density is Bell-like Electron density is Bell-like profileprofile
22
0 12
1)(
d
xnxn e
,0 dx
DeterminationDetermination
EE00—incident electric field of EM wave,—incident electric field of EM wave,
EE11—transmitted electric field,—transmitted electric field,
EE22—reflected electric field—reflected electric field TransmissivityTransmissivity: :
T=ET=E11 /E /E00 , T , Tdbdb =-20 =-20 lglg (T). (T). ReflectivityReflectivity: :
R=ER=E22 /E /E00 , R , Rdbdb =-20 =-20 lglg (R). (R). AbsorptivityAbsorptivity: A=1 - T: A=1 - T2 2 - R- R22
The transmitted plane wave The transmitted plane wave EE11
The reflected plane wave EThe reflected plane wave E22
The phase shift | The phase shift | ΔφΔφ | |
The transmissivity TThe transmissivity Tdbdb
The reflectivity RThe reflectivity Rdbdb
The absorptivity AThe absorptivity A
Briefly summaryBriefly summary All four quantities All four quantities ΔφΔφ, , TT, , RR, , AA
depend on depend on
--the electron density --the electron density nnee(x)(x), ,
--the collision frequency --the collision frequency ννe0 e0 , ,
--the thickness of plasma layer --the thickness of plasma layer dd. .
But, the But, the dd is well known in the is well known in the experiments.experiments.
Briefly summary (cont.)Briefly summary (cont.) So, all four quantities So, all four quantities ΔφΔφ, , TT, , RR, , AA can be can be
used to diagnose both andused to diagnose both andννe0e0 of APP of APP (Atmospheric Pressure Plasma):(Atmospheric Pressure Plasma):
--linear average electron density --linear average electron density ννe0e0 --electron-neutrals collision frequency, --electron-neutrals collision frequency,
hence thehence the linear average neutral linear average neutral density .density . But, the best quantities for diagnostics But, the best quantities for diagnostics
are are Δφ Δφ and and TT
en
en
0n
The method of electron The method of electron density density diagnosticsdiagnostics in in APPAPP
IIIIII Comparisons between Comparisons between analytic and numerical analytic and numerical
solutionssolutions
The Appleton formula The Appleton formula
.))((
,))((
0 0
0 0
dxxkkA
dxxkk
d
ii
d
rr
.112
2
22
22
22
2
22
2
2
22
c
pec
c
pe
c
per ck
.112
2
22
22
22
2
22
2
2
22
c
pec
c
pe
c
pei ck
( ) ( ) ( )r ik x k x k x
},)(exp{],,[),](,,[0x
yyy dsskitiJuEtxJuE
The conclusionThe conclusion When the reflected wave is weak, the phasWhen the reflected wave is weak, the phas
e shift e shift Δφ Δφ and transmissivity transmissivity TT obtained fr obtained from analytic and numerical solutions are agom analytic and numerical solutions are agreed well.reed well.
when the wave reflected strongly, we have when the wave reflected strongly, we have to take the numerical full solutions of micrto take the numerical full solutions of microwave passed through the APP to diagnose owave passed through the APP to diagnose thethe
--linear average electron density --linear average electron density --electron-neutrals collision frequency --electron-neutrals collision frequency ννe0e0
then the linear average neutral density then the linear average neutral density
en
0n
Section Two:Section Two:
Two-dimensional Two-dimensional
numerical simulation in numerical simulation in
APPAPP
II Introduction
s-polarized s-polarized p-p-polarizedpolarized
z e zJ en u
yzHE
x t
xz HE
y t
y x zz
H H EJ
x y t
0z
z e ze
u eE u
t m
yzy
EHJ
x t
y x zE E H
x y t
xzx
EHJ
y t
i e iJ en u
0i
i e i
u eE u
t m
Combine Maxwell’sCombine Maxwell’s and electron motion equations, we have got a set
of integral-differential equations: S-polarized S-polarized integral-differential
equations:equations:
P-polarized P-polarized integral-differential equations:equations:
0
0
yzHE
x t
0
0
xz HE
y t
( )0 0
00 0
( , )eoty v s tx ez
zc
H H nEe E x s ds
x y t n
( )0 0
00 0
( , )eot v s tx ez
xc
E nHe E x s ds
y t n
0
0
y x zE E E
x y t
( )0 0
00 0
( , )eoty v s tez
yc
E nHe E x s ds
x t n
.Z
Y
X
Plasma LayerAbsorbing Boundary
Connecting Boundary
Incident Wave
Reflected Wave
Outputting Bundary
Finite-difference-time-Finite-difference-time-domaindomain(FDTD)(FDTD)
II ComparisonsII Comparisons between one dimensional and two dimensional solutions
The electron density of two-The electron density of two-dimensional simulation is Bell-like dimensional simulation is Bell-like
profile along profile along the the YY axis, and is uniform along axis, and is uniform along XX axis axis
22
0 12
1)(
d
xnxn e
,0 dx
0.1 1 10 100
0
5
10
15
20
e0
/f
one-dimension two-dimension
Tra
ns
mit
ivit
y (
dB
)
0.1 1 10 100
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
5,00, 0.5nc
Re
fle
cti
vit
y
e0
/f
one-dimension two-dimension
0.1 1 10 1000.0
0.2
0.4
0.6
0.8
1.0
e0/f
one-dimension two-dimension
Ab
so
rbti
vit
y
0.1 1 10 100
0
50
100
150
200
250
300
5,00, 0.5nc
e0
/f
Ph
as
es
hif
t (0
) one-dimension two-dimension
III III Numerical results Phase shift Phase shift ΔφΔφ Transmissivity Transmissivity TT Reflectivity Reflectivity RR Absorptivity Absorptivity AA
Thickness of plasma Thickness of plasma dd Electron density Electron density nnee
Incident angle Incident angle θθ Polarization Polarization s, ps, p Collision frequency Collision frequency ννe0e0
The phaseshift The phaseshift | | ΔφΔφ | |
0.1 1 10 100
0
50
100
150
200
250
300
Ph
as
es
hif
t (0
)
e0
/f
S,1nc,
S,3nc,
S,5nc,
P,1nc,
P,3nc,
P,5nc,
0.1 1 10 100-50
0
50
100
150
200
250
300
350
Ph
as
es
hif
t(0
)
e0
/f
S,2nc,
S,2nc,
S,2nc,
P,2nc,
P,2nc,
P,2nc,
0.1 1 10 100
0
20
40
60
80
Ph
as
es
hif
t (0 )
e0
/f
S,1nc,
S,1nc,
S,1nc,
P,1nc,
P,1nc,
P,1nc,
The transmissivity The transmissivity TTdbdb
0.1 1 10 100
0
5
10
15
20
25
S,1nc,
S,3nc,
S,5nc,
P,1nc,
P,3nc,
P,5nc,
Tra
ns
mis
siv
ity(d
B)
e0
/f
0.1 1 10 100
0
5
10
15
20
Tra
ns
mis
siv
ity
(d
B)
S,2nc,
S,2nc,
S,2nc,
P,2nc,
P,2nc,
P,2nc,
e0
/f
0.1 1 10 100
0
1
2
3
4
5
6
Tra
ns
mis
siv
ity(
dB
)
e0
/f
S,1nc,
S,1nc,
S,1nc,
P,1nc,
P,1nc,
P,1nc,
The reflectivity RThe reflectivity Rdbdb
0.1 1 10 100
0
10
20
30
40
50
Re
fle
cti
vit
y(d
B)
S,2nc,
S,2nc,
S,2nc,
P,2nc,
P,2nc,
P,2nc,
e0
/f
0.1 1 10 1000
10
20
30
40
50
Ref
lect
ivity
(dB
)
e0
/f
S,1nc,
S,1nc,
S,1nc,
P,1nc,
P,1nc,
P,1nc,
0.1 1 10 10010
15
20
25
30
35
40
45
50
55
60
R
efl
ec
tiv
ity
(dB
)
e0
/f
S,1nc,
S,3nc,
S,5nc,
P,1nc,
P,3nc,
P,5nc,
The absorptivityThe absorptivity A A
0.1 1 10 100
0.2
0.4
0.6
0.8
1.0
Ab
so
rbti
vit
y
e0
/f
S,1nc,
S,3nc,
S,5nc,
P,1nc,
P,3nc,
P,5nc,
0.1 1 10 1000.0
0.2
0.4
0.6
0.8
Ab
so
rbti
vit
y
e0
/f
S,1nc,
S,1nc,
S,1nc,
P,1nc,
P,1nc,
P,1nc,
0.1 1 10 100
0.0
0.2
0.4
0.6
0.8
1.0
Ab
so
rbti
vit
y
e0
/f
S,2nc,
S,2nc,
S,2nc,
P,2nc,
P,2nc,
P,2nc,
The conclusionThe conclusion
Like one-dimensional results, all four quaLike one-dimensional results, all four quantities ntities ΔφΔφ, , TT, , RR, , AA are are be sensitive to be sensitive to nnee, , ννe0 e0 , d, d..
For the two-dimensional case, the all four For the two-dimensional case, the all four quantities quantities ΔφΔφ, , TT, , RR, , AA also depend on also depend on the the incident angle.incident angle.
The polarized mode of EM wave can take The polarized mode of EM wave can take effect on the above parameters when the effect on the above parameters when the electron density electron density gradient nnee
’’ and incident and incident angle are high enough.angle are high enough.
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