plasma waves & diffusion
DESCRIPTION
PLASMA WAVES & DIFFUSION. •. μ ,. • SUMMARY OF PLASMA WAVES. (1). B O = 0. uncoupled. c s. IAW. (2) B O = 0 : coupled. c s ~v i. IA. IA : hot electron –shield ion - wave. (3) B o = 0. v A. UH. w LH =210. R. v A. w L. 200. L. C. EC. LH. 4. 4. W. - PowerPoint PPT PresentationTRANSCRIPT
PLASMA WAVES& DIFFUSION
Ch.4Review (Single ptl Motions)
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•
• SUMMARY OF PLASMA WAVES
(1) BO = 0
uncoupled
11210~
10~
1~
ccn
KeVT
TB
plasmasizedfinitetodue
ificwaves
longeiklawFor
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(2) BO = 0 : coupled
IA : hot electron –shield ion - wave
22peceu
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22
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2
)1( cepe
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(3) Bo = 0
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pi
)( onlyonlyk //
k0.1
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10 e.g, beam
10 e.g, warm
10 e.g, cold
K tensor Response
χIε const. dielectric
ε
litySusceptibi
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Plasma ApplicationModeling, POSTECH
Bohm velocity of
bi-Maxwellian electron distribution
2006. 2.27 .
G.J. Kim
Plasma ApplicationModeling, POSTECH
20 0
2( ) 1 1 2
1x
1
( )( )
eV xx
kT
2
1 2
N
N N
1
2
T
T
1 21 2
( ) exp expef N NkT kT
0.0 0.5 1.0 1.5 2.0 2.5
-15
-10
-5
0
5
10
15
Vel
ocity
[103 m
/sec
]
x [cm]
0.0 0.5 1.0 1.5 2.0 2.50
10
20
30
40
50
60
70
pote
ntia
l [V
]
x [cm]
0.0 0.5 1.0 1.5 2.0 2.50.0
0.5
1.0
1.5
2.0
Ne
NAr+
Ne/N
Ar+
x [cm]
Den
sity
[1015
m-3]
0.0
0.2
0.4
0.6
0.8
1.0
ratio [Ne /N
Ar + ]
Godyak, IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 23, NO. 4, 728
Plasma ApplicationModeling, POSTECH
0 5 10 15 20 25 301E10
1E11
1E12
1E13
1E14
1E15
1E16
T2=6.06eV, N
2= 9.4x1012m-3
T1=0.74eV, N
1= 2.92x1015m-3
EE
PF
[eV
-1.5m
-3]
energy [eV]0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Ar+ Density electron Density Potential
x [cm]
Den
sity
[1015
m-3]
61.0
61.1
61.2
61.3
61.4
61.5
61.6
61.7
Phi [V
]
0.0 0.5 1.0 1.5 2.0 2.5-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
-1250 [m/sec]
1290 [m/sec]
U_i Phi
x [cm]
Vel
ocity
[103 m
/sec
]
0
10
20
30
40
50
60
Phi [V
]
Ion velocity at the bulk-sheath boundary is correspond to the low energy electron group in case of bi-Maxwellian EEPF.
1 20.74 6.06 1.21effT T T
3 3 31 21.3 10 3.8 10 1.7 10effU U U
5mTorr, 0.2A, 40.12MHz 0.97i
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Plasma ApplicationModeling, POSTECH
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22
21
22
21
222
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eth
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eth
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ith
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,
1,,
1
22
1
22
1
1
1
0)1/(1)1/(
1 22
222
k
wKww
)/exp()/exp( 2211 eee TnTnn 0
2
21
2
n
n
nn
n
Dispersion relation
Plasma ApplicationModeling, POSTECH
Dispersion relation
Ch.5 Diffusion(Transport) of Ptls, Heat, Momentum
Classification
-without or with plasma instabilities
anomalous diffusion(defends on source type)
our subject this ch.
-weakly Ionized plasma vs Fully Ionized plasma
collision of charged (high-Temp.)
ptls e,I with abundant -no neutral
neutral gas particles just collision of e,I (e-e,
e-i,i-i)
important!
)()diffusionambipolar(
E
0
agnetized)W.I.P.(unm-
0
ieie nnif
nmv
T
mv
qnvn
B
ie vv
PECVD
R.I.E.
I.C.P.
H.S. Lee
D
10~
ln)4(
1
)(
yresistivitSpitzer
)nofindep.(
,
)(/y,resistivit
ondistributivelocityvv
freq.collision
)v(1
,
ParametersBasic
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11
)1()1(
netized)W.I.P.(mag-
20
2/3
2
e
20
2
0
//
22
22//
22//
/
e
eee
p
e
e
c
cc
kT
em
nTT
vnem
n
nmfp
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Γ
ΓΓ
Γ
ΓΓ
vvvΓ
//i
i//
DEMERIE
E.C.R.
Helicon
H.S. Lee
(小 )
(大 ) (大 )(小 )
•Mobility Diffusion Coeff () (D)
vEvvv mnvpqnt
mn
)(
vvvv
N.L.no
S.S
n
D
mv
T
μ
mv
qnn
EvΓ
•Ambipolar Diffusion-Definition:
μn
nDD
nDnnD
n
ei
eia
iie
e
E
EE
nDnDt
n
nDD
nD
nE
nDD
aa
iTeTiDaD
ei
ieeii
a
ei
eii
2
)(2~
)(
Γ
•MHD Eqs(conservation Forms)
v
v
vBBvBvB
IBBvvv
)1
v2
1[()
)(
2
..
1.
v(
)(
][)(
)]2
(1
[)(
2
0
2
.
2
0
2
pp
energywavefield
B
EP
p
EKt
t
t
Bp
t e
A single fluid
Eq.for ⓔ & ⓘ
Under E&B ]1
0 BE
i
iiii
iii
n
nD
nt
n
Ev
v
0)(
DT
q
relEinstein
from
Drift-Diffusion
Approx.(PDP)
ΓΓΓ ie
S.E. Park
Transports(L&L)
5.1 uEu mmnvpqnt
mn
)1(
E
u
n
n
mv
kTn
mv
nqn
D
m
n
m
EuΓ
(2) Other fluid eq0
eievnt
nΓ
E nnDField-free=Free Diffusion (p130)nD 2
Const. For hi-pressure(pN)e
ii
T
T
l
e
kTD
(3) Third fluid eqinpceie PvneTkTnkT
t
ΓEKΓ )
2
5()
2
3(
relFranzWiedemanenkTK :/2
3/
5.2 steady solutions (1-D slab)Three cases
const:)(pHigh)1( N DT
T
l e
ii
nvnD iz
dx
d2
2
2Γ
:1.5.
cos0
Fig
xl
nn
D
vizField free 5.3
(2)Low-pN(but finit collisions) nvn izi )( u Solution (5.3.7)&Fig 5.2(b)
n
n
e
kT
uM
e
Mv
e
i
i
mi
EE
(3)Collision-less Case(very-Low pN;Free-Fall solutions)nv
n
n
M
eTn
M
enn iz
ei
0
ln22
)( u
(1.1)(1.2)
no source
(1.9) Einstein rel
(1.7)
(p136)
(2.19)(2.20)
(3.10)&Fig(5.3)Langmuir soln
S.E. Park