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.