PLASMA WAVES & DIFFUSION

PLASMA WAVES& DIFFUSION

Ch.4Review (Single ptl Motions)

y

BvqBqvF

qB

Bmv

z

BF

qEuBE

tkzBy

tkzEx

v

v

qB

Bvmv

Bqvmv

VV

qB

m

qB

m

B

BVEqmdt

d

Bt•

bebee.I.

magneticdiadirection

va

m

qB

tytxat

czxy

zz

mc

xtzyx

y

x

cE

pEei

pc

pE

pepi

polariz

E

c

ccc

ccc

q

2

32

21

2

)0(

)1(

2

)0()1()1(

)0()1()0()1(

22

2

)0()0()0(

2

2

rfquadratic

)cos(ˆ

)cos(ˆ

Waveplane .m.e Large

)(

ˆDriftorder st 1

0)(

Driforder th 0

)ˆˆ()ˆˆ(ˆ132

:

Gyromotion

)cos(ˆ)sin(ˆ)(

of . vari.freqlow

B

V

B)(v

B

E

EBVV :•

BEV

v

BEV :

)(

,

r

B

E

E

00E

E(t)

F

+ -

•B

+-

•B

E

EV

- +

peV

•B

EV

piV

(反 )

E

Ex

By

kz

μ ,

•

• SUMMARY OF PLASMA WAVES

(1) BO = 0

uncoupled

11210~

10~

1~

ccn

KeVT

TB

plasmasizedfinitetodue

ificwaves

longeiklawFor

.mod,

),.(

(2) BO = 0 : coupled

IA : hot electron –shield ion - wave

22peceu

cicePICIL ~22

22

2

2

)1( cepe

ce

pe

(3) Bo = 0

LH

UH

cs~vi

IA

EC

IC

RL

C

IAW

tev

tiv

pepe

pipi cs

pi

)( onlyonlyk //

k0.1

44

200

wLH=210wL

ceci

RP

vA

W

SAMS

vA

(4) Bo = 0 Almost )0(

~

C

Av

CsICW

smT

C

~n

B.~V

s

A

/10~10~

10221022

64

69

//

,

:2222

kneeds

IAWIC

Ck

ICW

sci

MS

2.

22

2

222

2

2

22

22

2

2

2

2

2

2

2.

222

2.

22

2

222

2

2

2

2

2

222

2

0

002

1110

1

.

)(1

)(

:

1

.

1

)(

/

1

.5.2

the

pe

s

iei

s

ss

ss

epebpb

ss

thepe

the

ee

s

ss

pee

es

s

s

ss

s

ss

e

vk

k

v

k

dispersiainstpb

kvkv

GrossBohmvk

vkvk

dispLangmuir

vkvk

w

i

k

wave)icoldshieldede(hotWI.A.

freq.Low

10 e.g, beam

10 e.g, warm

10 e.g, cold

K tensor Response

χIε const. dielectric

ε

litySusceptibi

s

0 k

wpi

Cs

e

i

s

sss

c

ss

R

R

iv

2π

θforLH

2π

θforUHe.g.coscos

magnetized

)(

lcollisiona

222

22

2

2

2

2

Plasma ApplicationModeling, POSTECH

Bohm velocity of

bi-Maxwellian electron distribution

2006. 2.27 .

G.J. Kim


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


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

d


012

222

22

21

22

21

222

2

eth

pe

eth

pe

ith

pi

vkvkvk

M

m

T

T

v

vkvKw

e

e

eth

eth

pe

eth

pe

,

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


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

)edunmagnetiz(

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

B

nDnEn

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

PLASMA WAVES & DIFFUSION

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