Keiji Sawada and Shinichi Hidaka Shinshu University, Japan

Motoshi Goto NIFS, Japan

2016.3 IAEA

Collisional-Radiative Model of

Molecular Hydrogen

Neutral-Transport Code

Introduction : Our models

・Hydrogen atom

・Hydrogen molecule

(H2 and D2 )

・Helium atom (M. Goto) elastic collision

Collisional–Radiative Models

H2 and D2 Collisional-Radiative Model (EvJ model)

Electronic, vibrational, and rotational states are included.

15

10

5

0

En

erg

y (

eV)

E

B

H

C

B'D G J 3 3

3 3 33

22

2

1g

+

ns np np nd nd nd

1u

+ 1u

1g

+ 1g

1g

ns np np nd nd nd

3

3

3 3 3 3

2 2a c

he

d g i j

Singlet TripletX

1

b2

3g

+ 3u

+ 3u

3g

+ 3g

3g

O B'' D' P R S fk p r s4

4 4 4 4 4 44 4 4 4

I

H2+

repulsive

metastable(v=0) Hund’s case (b)

n < 7

H2 4133 , D2 7817

levels are included.

Spectroscopic diagnostic ne, Te , Tvib , Trot , nH2

H2 and D2 Collisional-Radiative Model (EvJ model)

Electronic, vibrational, and rotational states are included.

H2 Collisional-Radiative Model

Electronic, vibrational, and rotational

states are included.

J. Horacek et al., NIFS-DATA-73 (Feb. 2003)

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

MA

R

RA

TE

CO

EF

FIC

IEN

T

(cm

3/s

)

14121086420

v

H2(v) + e -> H- + H

H- + H

+ -> H + H

*

H*-> H

H2(v) + H+ -> H2

+ + H

H2+ + e -> H + H

*

H*-> H

Te 2eV

ne 1014

cm-3

CX

DAEffective rate coefficients

for neutral transport code

Table of Contents

2. Test for the spectroscopic diagnostic using RF plasmas

1. Introduction of CR model : H CR model

: H2 (D2 ) CR model

3. Calculation of effective rate coefficients

Collisional-Radiative Model of

Atomic Hydrogen

H Collisional-Radiative Model

ieie

pq pq

ee nnpnnpqnpqAnpqFqnnpqCdt

pdn)()()()},(),({)(),(

)(2

pq

e

pq pq

pnqpAnpSqpCqpF )()],(})(),(),([{

)(),( qnnpqF e

)(),( pnnqpC e

q

i

p

de-excitation spontaneous transition

Ionization

3-body rec. radiative rec.

ie nnp2)(

)(),( qnpqA

)()( pnnpS e

iennp)(

excitation

inflow

outflow

PLASMA

e H+ H

eei

e

e

nn

C

Cnn

n

n

n

n

n

ndt

d)1(

)2,1(

)3,1(

.

.

).2()2(

)3()3(

.

.

)2(

)3(

.

.

....

....

....

....

)2(

)3(

.

.

ieie

pq pq

ee nn)p(nn)p()q(n)}p,q(An)p,q(F{)q(nn)p,q(Cdt

)p(dn

2

pq

e

pq pq

pnqpAnpSqpCqpF )()],(})(),(),([{

eei nnpRnnpRpn )1()()()( 10

ee nnnnSdt

dnH

CRCR

)1()1(

Solving Rate equations

0

p>=2

quasi-steady-

state

approximation

(QSS)

p=1

Recombining

component

unknown

SCR effective ionization rate coefficient

αCR effective recombination rate coefficient

Ionizing

component

Effective Ionization and Recombination Rate coefficients

10-16

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

SC

R an

d

CR

(

cm

3/s

)

0.1 1 10 100 1000

electron temperature (eV)

SCR

CR

ne=108cm

-3

ne=1015

cm-3

ne=108cm

-3

1012

cm-3

1011

cm-3

1010

cm-3

109cm

-3

1013

cm-3

1014

cm-3

1015

cm-3

ee nnnnSdt

dnH

CRCR

)1()1(

SCR Effective Ionization Rate Coefficient

αCR Effective Recombination Rate Coefficient

Ionizing component Te=10eV ne=1010cm-3

n(1)=1cm-3

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

n(p

)/g

(p)

(

cm

-3)

2 3 4 5 6 7 8 9

102

principal quantum number

Ionizing plasma

Te=10eV

ne=108cm

-3

1010

cm-3

1012

cm-3

1014

cm-3

ex. “1.27E2” denotes 1.27x102 [1/(cm3・s)]

Griem’s

boundary

S(1)n(1)ne=6.92E1 [1/(cm3・s)]

blue : electron impact

red : spontaneous transition

10-14

10-12

10-10

10-8

10-6

10-4

n(p

)/g

(p)

(

cm

-3)

2 3 4 5 6 7 8 9

102

principal quantum number

Recombining plasma

Te=0.1eV

ne=108cm

-3

1010

cm-3

1012

cm-3

1014

cm-3

Byron’s

boundary

Griem’s

boundary

（ (1)ne+β(1))nzne=4.69E-1 [1/(cm3・s)]

Recombining component

Te=0.1eV ne=1012cm-3 ni=1cm-3

Recombining RF plasma at Hokkaido University

K. Sasaki and S. Nishiyama

40x103

30

20

10

0

Sign

al (

not c

alib

rate

d)

600550500450400350

Wavelength (nm)

Collisional-Radiative Model of

Molecular Hydrogen

Electronic states 18

17

16

15

14

13

12

11

Po

ten

tia

l e

ne

rgy

[e

V]

6543210

Internuclear distance [Å]

X1g

+ 1s

O1g

+ 4s

C1u 2p

D1u 3p

D'1u 4p

V1u 4f

GK1g

+ 3d

I1g 3d

R1g 4d

J1g 3d

P1g

+ 4d

B1u

+ 2p

B,1u

+ 3p

B''1u

+ 4p

EF1g

+ 2s

H2+

Singletb

3u

+ 2p

18

17

16

15

14

13

12

11

Po

ten

tial en

erg

y [

eV

]

6543210

Internuclear distance [Å]

b3u

+ 2p

c3u 2p

a3g

+2s

e3u

+ 3p

h3g

+ 3s

i3g 3d

r3g 4d

f3u

+ 4p

g3g

+ 3d

k3u 4p

j3g 3d

s3g 4d

d3u 3p

m3u

+ 4f

4s3g

+

H2+

X1g

+ 1s Triplet

35

30

25

20

15

10

5

0

Po

ten

tia

l E

ne

rgy

(e

V)

43210Internuclear Distance (Å)

H2

X1

g

+

b3

u

+

X2

g

+

H2+

n=3

n=4

E,F1

g

+

a3

g

+

B1

u

+C

1

u

c3

u

H++ H

H + H

Transition Probability

[1] S.A.Astashkevich et al. ,

J. Quant. Spectrosc. Radiat. Transfer 56,

725-751 (1996).

e->a, d->a, i->c, j->c, I->C, J->C

[2] S.A.Astashkevich and B.P.Lavrov,

Lifetimes of the electronic-vibro-rotational

states of hydrogen molecule (review),

Optics and Spectroscopy 92,

888-922, (2002).

[3] S.A.Astashkevich and B.P.Lavrov,

Tables of the lifetimes for excited

electronic-vibro-rotational

states of isotopomers of diatomic

hydrogen, (2008).

http://arxiv.org/html/0812.4573v1

15

10

5

0E

nerg

y (e

V)

E

B

H

C

B'D G J 3 3

3 3 33

22

2

1g

+

ns np np nd nd nd

1u

+ 1u

1g

+ 1g

1g

ns np np nd nd nd

3

3

3 3 3 3

2 2a c

he

d g i j

Singlet TripletX

1

b2

3g

+ 3u

+ 3u

3g

+ 3g

3g

O B'' D' P R S fk p r s4

4 4 4 4 4 44 4 4 4

I

H2+

repulsive

metastable(v=0)

H2 Transition Probability

Hönl-London

factor

Transition moment

25

20

15

10

5

0

Po

ten

tial en

erg

y (e

V)

6543210

Internuclear distance (Å)

B,1u

+ 3p

G1g

+ 3d

H1g

+ 3s

i3g 3d

I1g 3d

h3g

+ 3s

g3g

+ 3d

e3u

+ 3p

B1u

+ 2p

d3u 3p

X1g

+ 1s

E1g

+ 2s

c3u 2p

C1u 2p

a3g

+ 2s

b3u

+ 2p

D1u 3p

j3g 3d

J1g 3d

Re(R)

Kolos and Wolniewicz et al.

SJ’J’’

Annie Hansson and James

K.G. Watson, Journal of

Molecular Spectroscopy 233

(2005) 169-173

25

20

15

10

5

0

Po

ten

tial en

erg

y (e

V)

6543210

Internuclear distance (Å)

B,1u

+ 3p

G1g

+ 3d

H1g

+ 3s

i3g 3d

I1g 3d

h3g

+ 3s

g3g

+ 3d

e3u

+ 3p

B1u

+ 2p

d3u 3p

X1g

+ 1s

E1g

+ 2s

c3u 2p

C1u 2p

a3g

+ 2s

b3u

+ 2p

D1u 3p

j3g 3d

J1g 3d

H2 Transition Probability to Continuum states

H2(X) + e → H2* + e

W.T. Miles, R. Thompson, and A.E.S. Green,

J. Appl. Phys. 43, 678 (1972).

Born-Bethe approximation modified at low

energies by phenomenological techniques

All cross sections are given for n

H2(X1+g) + e → H2(d3u ) + e

W.T. Miles, R. Thompson, and A.E.S Green, J. Appl. Phys.43, 678 (1972).

R.K.Janev, D.Reiter, U. Samm, http:/www.Eirene.de/report_4105.pdf G.R.Möhlmann and F.J.De Heer, Chem.Phys.Letters 43,240 (1976).

18

17

16

15

14

13

12

11

Po

ten

tial en

erg

y [

eV

]

6543210

Internuclear distance [Å]

b3u

+ 2p

c3u 2p

a3g

+2s

e3u

+ 3p

h3g

+ 3s

i3g 3d

r3g 4d

f3u

+ 4p

g3g

+ 3d

k3u 4p

j3g 3d

s3g 4d

d3u 3p

m3u

+ 4f

4s3g

+

H2+

X1g

+ 1s Triplet

d3u − a

3

+g

a – c : C. S. Sartori et al., Phys. Rev A. 58, 2857-2863 (1998).

a - d, c - g, c – h : R. Celiberto et al., J. Plasma Fusion Res. SERIES, Vol.7, 207-209 (2006).

B – I : R. Celiberto et al., Atomic Data and Nuclear Data Tables 77, 161-213 (2001).

H2 electron impact excitation among excited levels

He He

T.E Sharp, Atomic Data and Nuclear Data Tables 2, 119-169 (1970) H2 electron impact

excitation among

excited levels

He data are used.

Energy difference is

taken into account.

Vibrationally and rotationally resolved rate coefficient X -> B, C, d

Proceedings of the Lebedev Physics Institute

Academy of Sciences of the USSR Series,

Editor N.G.Basov, Volume 179 Supplemental

Volume 2,

ELECTRON-EXCITED MOLECULES IN

NONEQUILIBRIUM PLASMA

Edited by N.N.Sobolev

15

10

5

0

Po

ten

tia

l e

ne

rg

y (

eV

)

3.02.52.01.51.00.50.0

Internuclear distance (A)

X1g

+

d3u

+

a3g

+

v=0

v=13

v '=0

v '=3

v ''=0

v ''=5

H2

“Adiabatic Approximation”

Vibrationally and rotationally resolved rate coefficient

15

10

5

0

En

erg

y (e

V)

E

B

H

C

B'D G J 3 3

3 3 33

22

2

1g

+

ns np np nd nd nd

1u

+ 1u

1g

+ 1g

1g

ns np np nd nd nd

3

3

3 3 3 3

2 2a c

he

d g i j

Singlet TripletX

1

b2

3g

+ 3u

+ 3u

3g

+ 3g

3g

O B'' D' P R S fk p r s4

4 4 4 4 4 44 4 4 4

I

H2+

repulsive

metastable(v=0)

Rate coefficient ∝ Franck-Condon factor

ΔN = 0 or ΔN = ±1

“a” and “s” symmetry does not change

H2(X,v,J) + H+ → H + H2

+

H2(X,v,J) + e → H + H-

H2(X,v=0,J) + H2 → H2(X,v=0,J’) + H2

H2 (X,v,J) → cross sections

J. Horacek et al.,

Rate Coefficients for Low-Energy Electron

Dissociative Attachment to Molecular

Hydrogen, NIFS-DATA-73 (Feb. 2003).

A.Ichihara et al.,

J. Phys. B 33 4747-4758 (2000).

H2(X,v,J) + e → H2(X,v’,J’) + e

T.-G.LEE et al., The Astrophysical Journal ,

689:1105-1111 (2008).

J. Horacek et al., Nukleonika 48, 109-112 (2003).

M.A.Morrison and B.C.Saha, Phys. Rev. A 34, 2786-2797 (1986).

Table of Contents

2. Test for the spectroscopic diagnostic using RF plasmas

1. Introduction of CR model : H CR model

: H2 (D2 ) CR model

3. Calculation of effective rate coefficients

D2 + He RF plasma (He 0.064 torr，D2 0.008 torr )

RF power 500 W

4

3

2

1

0

Te (

eV

)

2.52.01.51.00.50.0

R (cm)

109

2

4

1010

2

4

1011

2

4

1012

ne (c

m-3)

ne

Te

He Collisional-Radiative Model

Determination of Te , ne , n(21S) , n(23S) , I31p , I41P

25

20

15

10

5

0

En

erg

y (

eV

)

1S

3S

1P

3P

1D

3D

1F

3F

1

2

2

43 3

3 33

22

3

4 4 4 4 4 44

Singlet Triplet

4Photon absorption is considerd

4

3

2

1

0

Te (

eV

)

2.52.01.51.00.50.0

R (cm)

109

2

4

1010

2

4

1011

2

4

1012

ne (c

m-3)

ne

Te

d3u − a

3

+g → Tvib = 3000 K , Trot = 500 K

Experiment and Calculation

Experiment and Calculation

Blue : calculation (Te, ne, Tvib, Trot are used) Red : experiment

Experiment and Calculation ( 458.5 nm - 469.6 nm )

Experiment and Calculation ( 599.1 nm – 617.9 nm )

Experiment and Calculation ( 762.9 nm – 800.2 nm )

Correction factors for excitation rate coefficients X →

ug IX11 ug EX

11

D2 2.9eV

n Singlet Triplet

2 E 4.35E+00 a 3.95E-01

3

H 1.98E+01 h 7.91E-01

B' 1.19E+01 e 3.95E-01

D- 3.95E+00 d- 3.95E-01

D+ 2.37E+01 d+ 3.95E-01

G 2.77E+01 g 5.93E-01

I- 2.57E+01 i- 4.74E-01

I+ 2.57E+01 i+ 4.74E-01

J- 7.91E+00 j- 2.77E-01

J+ 7.91E+00 j+ 2.77E-01

4

O 1.19E+00 f 1.19E+00

B" 5.93E+00 k- 1.19E+00

D'- 3.95E+00 k+ 1.58E+00

D'+ 3.10E+01 p 1.19E+00

P 5.53E+01 r- 9.88E-01

R- 1.58E+01 r+ 3.16E+00

R+ 2.37E+01 s- 7.91E-01

S- 3.95E-01 s+ 1.98E-01

S+ 3.95E-01

Calculated emission intensity (for each upper level)

After correction

After correction ( 762.9 nm – 800.2 nm ) good !

before

after

After correction ( 458.5 nm – 469.6 nm ) ???

before

after

Correction of excitation rate coefficients

and

estimation of cross section

ug EX11

Cross section Rate coefficient

Estimated rate coefficient and cross section

ug EX11

Rate coefficient Cross section

Cross section fitting parameters

Singlet ??? H2(X) + e → H2* + e ?

D2 2.9eV

n Singlet Triplet

2 E 4.35E+00 a 3.95E-01

3

H 1.98E+01 h 7.91E-01

B' 1.19E+01 e 3.95E-01

D- 3.95E+00 d- 3.95E-01

D+ 2.37E+01 d+ 3.95E-01

G 2.77E+01 g 5.93E-01

I- 2.57E+01 i- 4.74E-01

I+ 2.57E+01 i+ 4.74E-01

J- 7.91E+00 j- 2.77E-01

J+ 7.91E+00 j+ 2.77E-01

4

O 1.19E+00 f 1.19E+00

B" 5.93E+00 k- 1.19E+00

D'- 3.95E+00 k+ 1.58E+00

D'+ 3.10E+01 p 1.19E+00

P 5.53E+01 r- 9.88E-01

R- 1.58E+01 r+ 3.16E+00

R+ 2.37E+01 s- 7.91E-01

S- 3.95E-01 s+ 1.98E-01

S+ 3.95E-01

After correction ( 458.5 nm – 469.6 nm ) ???

Singlet ???

D2 2.9eV

n Singlet Triplet

2 E 4.35E+00 a 3.95E-01

3

H 1.98E+01 h 7.91E-01

B' 1.19E+01 e 3.95E-01

D- 3.95E+00 d- 3.95E-01

D+ 2.37E+01 d+ 3.95E-01

G 2.77E+01 g 5.93E-01

I- 2.57E+01 i- 4.74E-01

I+ 2.57E+01 i+ 4.74E-01

J- 7.91E+00 j- 2.77E-01

J+ 7.91E+00 j+ 2.77E-01

4

O 1.19E+00 f 1.19E+00

B" 5.93E+00 k- 1.19E+00

D'- 3.95E+00 k+ 1.58E+00

D'+ 3.10E+01 p 1.19E+00

P 5.53E+01 r- 9.88E-01

R- 1.58E+01 r+ 3.16E+00

R+ 2.37E+01 s- 7.91E-01

S- 3.95E-01 s+ 1.98E-01

S+ 3.95E-01

After correction ( 458.5 nm – 469.6 nm ) ???

(1) H2(X) + e → H2* + e ?

(2) Electron impact excitation from metastable ?

(3) Radiation rapping (Photon absorption) ?

(4) H3+ + e -> H2* + H ?

(5) Non Maxwell distribution of electron kinetic energy ?

Electron impact excitation from metastable ?

15

10

5

0

En

erg

y (

eV)

E

B

H

C

B'D G J 3 3

3 3 33

22

2

1g

+

ns np np nd nd nd

1u

+ 1u

1g

+ 1g

1g

ns np np nd nd nd

3

3

3 3 3 3

2 2a c

he

d g i j

Singlet TripletX

1

b2

3g

+ 3u

+ 3u

3g

+ 3g

3g

O B'' D' P R S fk p r s4

4 4 4 4 4 44 4 4 4

I

H2+

repulsive

metastable(v=0)

After correction ( 458.5 nm – 469.6 nm ) ???

D2 2.9eV

n Singlet Triplet

2 E 4.35E+00 a 3.95E-01

3

H 1.98E+01 h 7.91E-01

B' 1.19E+01 e 3.95E-01

D- 3.95E+00 d- 3.95E-01

D+ 2.37E+01 d+ 3.95E-01

G 2.77E+01 g 5.93E-01

I- 2.57E+01 i- 4.74E-01

I+ 2.57E+01 i+ 4.74E-01

J- 7.91E+00 j- 2.77E-01

J+ 7.91E+00 j+ 2.77E-01

4

O 1.19E+00 f 1.19E+00

B" 5.93E+00 k- 1.19E+00

D'- 3.95E+00 k+ 1.58E+00

D'+ 3.10E+01 p 1.19E+00

P 5.53E+01 r- 9.88E-01

R- 1.58E+01 r+ 3.16E+00

R+ 2.37E+01 s- 7.91E-01

S- 3.95E-01 s+ 1.98E-01

S+ 3.95E-01

He

Radiation rapping (Photon absorption) ?

15

10

5

0

En

erg

y (

eV)

E

B

H

C

B'D G J 3 3

3 3 33

22

2

1g

+

ns np np nd nd nd

1u

+ 1u

1g

+ 1g

1g

ns np np nd nd nd

3

3

3 3 3 3

2 2a c

he

d g i j

Singlet TripletX

1

b2

3g

+ 3u

+ 3u

3g

+ 3g

3g

O B'' D' P R S fk p r s4

4 4 4 4 4 44 4 4 4

I

H2+

repulsive

metastable(v=0)

After correction ( 458.5 nm – 469.6 nm ) ???

D2 2.9eV

n Singlet Triplet

2 E 4.35E+00 a 3.95E-01

3

H 1.98E+01 h 7.91E-01

B' 1.19E+01 e 3.95E-01

D- 3.95E+00 d- 3.95E-01

D+ 2.37E+01 d+ 3.95E-01

G 2.77E+01 g 5.93E-01

I- 2.57E+01 i- 4.74E-01

I+ 2.57E+01 i+ 4.74E-01

J- 7.91E+00 j- 2.77E-01

J+ 7.91E+00 j+ 2.77E-01

4

O 1.19E+00 f 1.19E+00

B" 5.93E+00 k- 1.19E+00

D'- 3.95E+00 k+ 1.58E+00

D'+ 3.10E+01 p 1.19E+00

P 5.53E+01 r- 9.88E-01

R- 1.58E+01 r+ 3.16E+00

R+ 2.37E+01 s- 7.91E-01

S- 3.95E-01 s+ 1.98E-01

S+ 3.95E-01

He

15

10

5

0

En

erg

y (e

V)

E

B

H

C

B' D G J 3 33 3

3 3

22

2

1g

+

ns npnp ndndnd1u

+ 1u

1g

+ 1g

1g

ns npnp ndndnd

3 3

3

3 3 3

2 2a c

h

ed g i j

H2 Singlet

H2 Triplet

X1

b2

3g

+ 3u

+ 3u

3g

+ 3g

3g

O B'' D' P R S fk p r s4 4 4 4 4 4

44 4 4 4

I

H2+

repulsive

metastable(v=0)

V4

nf

1u

nf

m4

3u

+

H2(X) + H(1s)

H3+

3H(1s)

2H(1s) + H+

2H(1s) + H(2s)

H3+ ?

D2 2.9eV

n Singlet Triplet

2 E 4.35E+00 a 3.95E-01

3

H 1.98E+01 h 7.91E-01

B' 1.19E+01 e 3.95E-01

D- 3.95E+00 d- 3.95E-01

D+ 2.37E+01 d+ 3.95E-01

G 2.77E+01 g 5.93E-01

I- 2.57E+01 i- 4.74E-01

I+ 2.57E+01 i+ 4.74E-01

J- 7.91E+00 j- 2.77E-01

J+ 7.91E+00 j+ 2.77E-01

4

O 1.19E+00 f 1.19E+00

B" 5.93E+00 k- 1.19E+00

D'- 3.95E+00 k+ 1.58E+00

D'+ 3.10E+01 p 1.19E+00

P 5.53E+01 r- 9.88E-01

R- 1.58E+01 r+ 3.16E+00

R+ 2.37E+01 s- 7.91E-01

S- 3.95E-01 s+ 1.98E-01

S+ 3.95E-01

Singlet ? H2(X) + e → H2* + e

D2 2.9eV

n Singlet Triplet

2 E 4.35E+00 a 3.95E-01

3

H 1.98E+01 h 7.91E-01

B' 1.19E+01 e 3.95E-01

D- 3.95E+00 d- 3.95E-01

D+ 2.37E+01 d+ 3.95E-01

G 2.77E+01 g 5.93E-01

I- 2.57E+01 i- 4.74E-01

I+ 2.57E+01 i+ 4.74E-01

J- 7.91E+00 j- 2.77E-01

J+ 7.91E+00 j+ 2.77E-01

4

O 1.19E+00 f 1.19E+00

B" 5.93E+00 k- 1.19E+00

D'- 3.95E+00 k+ 1.58E+00

D'+ 3.10E+01 p 1.19E+00

P 5.53E+01 r- 9.88E-01

R- 1.58E+01 r+ 3.16E+00

R+ 2.37E+01 s- 7.91E-01

S- 3.95E-01 s+ 1.98E-01

S+ 3.95E-01

After correction ( 458.5 nm – 469.6 nm ) ???

Calculation of

effective rate coefficient

Rate coefficient correction off

Rate coefficient correction on

15

10

5

0

En

erg

y (

eV)

E

B

H

C

B'D G J 3 3

3 3 33

22

2

1g

+

ns np np nd nd nd

1u

+ 1u

1g

+ 1g

1g

ns np np nd nd nd

3

3

3 3 3 3

2 2a c

he

d g i j

Singlet TripletX

1

b2

3g

+ 3u

+ 3u

3g

+ 3g

3g

O B'' D' P R S fk p r s4

4 4 4 4 4 44 4 4 4

I

H2+

repulsive

metastable(v=0)

Effect of the “correction” is small.

In calculating effective rate coefficients

the “correction” is not applied.

H2(X) → H

Table of Contents

2. Test for the spectroscopic diagnostic using RF plasmas

1. Introduction of CR model : H CR model

: H2 (D2 ) CR model

3. Calculation of effective rate coefficients

X(v,J) population (time dependent solution)

Examples

Time dependent population X(v,J)

Initial condition (at wall) 300 K equilibrium

Plasma Te = 2 eV , ne =1016 cm-3

TH2 = 300 K , nH2 =1015 cm-3

v=0-4

v=5-9

v=10-14

10-12

10-10

10-8

10-6

10-4

10-2

Po

pu

lati

on

/ (

Sta

tisti

cal

weig

ht)

(

m-3

)

10-9

2 4 6 8

10-8

2 4 6 8

10-7

2 4 6 8

10-6

Time (sec)

10-6

10-5

10-4

10-3

Distance from wall (m)

v=0 v=1 v=2 v=3 v=4

10-12

10-10

10-8

10-6

10-4

10-2

Po

pu

lati

on

/ (

Sta

tisti

cal

weig

ht)

(

m-3

)

10-9

2 4 6 8

10-8

2 4 6 8

10-7

2 4 6 8

10-6

Time (sec)

10-6

10-5

10-4

10-3

Distance from wall (m)

v=5 v=6 v=7 v=8 v=9

10-12

10-10

10-8

10-6

10-4

10-2

Po

pu

lati

on

/ S

tati

sti

cal

weig

ht

(m

-3)

10-9

2 4 6 8

10-8

2 4 6 8

10-7

2 4 6 8

10-6

Time (sec)

10-6

10-5

10-4

10-3

Distance from wall (m)

v=10 v=11 v=12 v=13 v=14

Time dependent calculation Plasma

Te = 2 eV

ne =1016 cm-3

TH2 = 300 K

nH2 =1015 cm-3

time = 0 sec

10-12

10-10

10-8

10-6

10-4

10-2

Po

pu

lati

on

/ (

Sta

tis

tic

al

we

igh

t)

(

m-3

)

10-9

2 4 6 8

10-8

2 4 6 8

10-7

2 4 6 8

10-6

Time (sec)

10-6

10-5

10-4

10-3

Distance from wall (m)

v=0 v=1 v=2 v=3 v=4

10-36

10

-32 10

-28 10

-24 10

-20 10

-16 10

-12 10

-8 10

-4 100

H2(X

,v,J

) p

op

ula

tio

n (m

-3)

43210

Level energy (eV)

v=0 v=1 v=2 v=3 v=4

t=0 sec

Initial condition (at wall) 300 K equilibrium

Time dependent calculation Plasma

Te = 2 eV

ne =1016 cm-3

TH2 = 300 K

nH2 =1015 cm-3

time = 10-9 sec

10-12

10-10

10-8

10-6

10-4

10-2

Po

pu

lati

on

/ (

Sta

tis

tic

al

we

igh

t)

(

m-3

)

10-9

2 4 6 8

10-8

2 4 6 8

10-7

2 4 6 8

10-6

Time (sec)

10-6

10-5

10-4

10-3

Distance from wall (m)

v=0 v=1 v=2 v=3 v=4

10-36

10

-32 10

-28 10

-24 10

-20 10

-16 10

-12 10

-8 10

-4 100

H2(X

,v,J

) p

op

ula

tio

n

(m-3

)

43210

Level energy (eV)

t=1.0x10-9

sec

v=0 v=1 v=2 v=3 v=4 v=5 v=6 v=7 v=8 v=9 v=10 v=11 v=12 v=13 v=14

Time dependent calculation Plasma

Te = 2 eV

ne =1016 cm-3

TH2 = 300 K

nH2 =1015 cm-3

time = 10-8 sec

10-12

10-10

10-8

10-6

10-4

10-2

Po

pu

lati

on

/ (

Sta

tis

tic

al

we

igh

t)

(

m-3

)

10-9

2 4 6 8

10-8

2 4 6 8

10-7

2 4 6 8

10-6

Time (sec)

10-6

10-5

10-4

10-3

Distance from wall (m)

v=0 v=1 v=2 v=3 v=4

10-36

10-33

10-30

10-27

10-24

10-21

10-18

10-15

10-12

10-9 10

-6 10

-3 100

H2(X

,v,J

) p

op

ula

tio

n

(m-3

)

4321

Level energy (eV)

t=1.0x10-8

sec

v=0 v=1 v=2 v=3 v=4

Table of Contents

2. Test for the spectroscopic diagnostic using RF plasmas

1. Introduction of CR model : H CR model

: H2 (D2 ) CR model

3. Calculation of effective rate coefficients

Time dependent solution

Examples Fixed Trot is used.

10-13

10-12

10-11

10-10

10-9

10-8

Ra

te c

oe

ffic

ien

t

(cm

3/s

)

1012

1013

1014

1015

1016

1017

Electron Density (cm-3

)

from H2(X,v=0)

H2(X,v=0) depletion

v=1

v=14

v=2

v=13Te = 2 eV

Trot = 300 K

v=3

v=4

H2(X,v) + e → H2(X,v’) + e : v=0 →

Trot = 300 K , Te =2 eV

H2(X,v) → H : v=0

Trot = 300 K , Te =2 eV

H2(X,v) → H : v=0

Trot = 300 K , Te =10 eV

H2(X,v) → H : v=4

Trot = 300 K , Te =2 eV

H2(X,v) → H+ : v=0

Trot = 300 K , Te =2 eV

H2(X,v) → H+ : v=4

Trot = 300 K , Te =2 eV

Summary List of what we did

2. Test of the models using RF plasmas

3. Calculation of effective rate coefficients

1. Construction of

H2, D2 EvJ collisional-radiative models