Revision of collisional-radiative

models and neutral-transport code for

hydrogen and helium species

Keiji Sawada Shinshu University, Japan Motoshi Goto NIFS, Japan

2011.8.10-12 IAEA

Neutral-Transport Code

Introduction : Our models

Hydrogen atom

Hydrogen molecule (H2)

Helium atom (Dr. Goto)

elastic collision

CollisionalRadiative Models

Neutral-Transport Code for LHD (NIFS Japan) plasmas

1.0x1019

0.80.60.40.20.0

H2 density [m-3

]

7x1016

6543210

H density [m-3

]

H2 H

Main plasma Main plasma

Trace H and H2(X,v=0-14)

H and He RF plasma

Z

Coil Coil

Gas

Pump

AntennaPyrex glass 50 mm

Matching box

RF oscillatorf = 13.56 MHz

1 m

Baratrongauge

RF

800 13.56

B 100

Gas pressure

0.144torr

He flow

H2 flow

(1) H and He Collional-Radiative Models

Application of H and He models to the RF plasma

Radiation trapping

(2) H2 Collisional Radiative Model

Revision to include rotational states

in addition to electronic and vibrational states

Calculation of effective reaction rate coefficient

Determination of ne, Te, Tv, Trot

Table of Contents

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

CR 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

CR 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/(cm3s)]

Griems

boundary

S(1)n(1)ne=6.92E1 [1/(cm3s)]

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

Byrons

boundary

Griems

boundary

(1)ne+(1))nzne=4.69E-1 [1/(cm3s)]

Recombining component

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

H and He RF plasma

Z

Coil Coil

Gas

Pump

AntennaPyrex glass 50 mm

Matching box

RF oscillatorf = 13.56 MHz

1 m

Baratrongauge

RF

800 13.56

B 100

Gas pressure

0.144torr

He flow

H2 flow

He and H emission line intensities

Before Abel Inversion After Abel Inversion

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

4

He Collisional-Radiative Model : Determination of Te and ne Inclusion of radiation trapping

QSS

Fitting parameters

M.GOTO, JQSRT, 76, 331 (2003)

)(),( qnnpqF e

)(),( pnnqpC e

q

i

p

de-excitation spontaneous transition

Ionization

3-body rec. radiative rec.

ie nnp2)(

)(),( qnpqA

)()( pnnpS e

iennp)(

excitation

Convergent close-coupling method

D.V. Fursa and I. Bray, Phys. Rev. A 52, 1279 (1995)

I. Bray and D.V. Fursa, J. Phys. B 28, L197 (1995).

D.V. Fursa and I. Bray, J. Phys. B 30, 757 (1997).

R-Matrix with pseudostates method

K. Bartschat, J. Phys. B 31, L469 (1998).

He excitation cross sections

M.GOTO

Collisional-Radiative model for neutral helium in plasma revisited

JQSRT, 76, 331 (2003)

He population : ne dependence

He population : Te dependence

He population

Fitting parameters

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

4

ne and Te

Z

Coil Coil

Gas

Pump

AntennaPyrex glass 50 mm

Matching box

RF oscillatorf = 13.56 MHz

1 m

Baratrongauge

Estimation of molecular density from Flcher band spectra intensity

Determined by Flcher Corona Model

nH2 =7.61013 -3 , Tv=4200K, Trot=350K

H2 dissociative

excitation is negligible.

[1] R.K.Janev, D.Reiter, U.Samm,

Collision Processes in Low-Temperature

Hydrogen Plasmas,

http://www.eirene.de/report_4105.pdf

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

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

[3] G.R.Mhlmann and F.J.De Heer,

Chem.Phys.Letters 43,240 (1976).

X -> d electron impact excitation rate coefficient

H atom Balmer line intensity

nH =1.01014 cm-3

Determined from H

intensity

Plasma

Spectroscopic measurement

Position B atom

Ground state

Excited state 1

Excited state 2

Electron

impact

Photo

emission

Emission line 1

Emission line 2 absorbed

Radiation Trapping and Spectroscopic measurement

Photo

absorption

Position A atom

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

32 )1(

0

1

0

0

)1(

1

0

0

0

)2,1(

)3,1(

.

.

).2()2(

)3()3(

.

.

)2(

)3(

.

.

....

....

....

....

)2(

)3(

.

.

LnLnnn

C

Cnn

n

n

n

n

n

ndt

deHeH

e

e

Emission

absorption

Iterative calculation )1(})()(),1({ 11 ngpB p

total

p

Lp

Iterative CR model for radiation trapping

0

H atom Balmer line intensity

Determined by Flcher

Corona Model

nH2 =7.61013 -3

Radiation trapping >> H2 dissociative excitation

Determined by Iterative

Collisional-Radiative

Model

nH =1.01014 -3

TH = 0.7 eV

H atom Excitation

Rate oefficient

in CR MODEL

and

H. Anderson

et al.

R-Matrix

J.Phys.B 33,

1255 (2000).

J.Phys.B 35,

1613 (2002).

H atom Excitation

Rate oefficient

in CR MODEL

and

H. Anderson

et al.

R-Matrix

J.Phys.B 33,

1255 (2000).

J.Phys.B 35,

1613 (2002).

H. Anderson et al. R-Matrix

J.Phys.B 33, 1255 (2000),

J.Phys.B 35, 1613 (2002).

0.5 eV < Te < 25 eV

5s,5p,5d,5f,5g

4s,4p,4d,4f

3s,3p,3d

2s,2p

1s

H(n,l) model is necessary for low ne.

H(n,l) model is necessary

for radiation trapping (?)

H (n,l) CR model

Born approximation cross section

Other reactions for H atom Balmer line intensity diagnostics

1.0x1019

0.80.60.40.20.0

H2 density [m-3

]

7x1016

6543210

H density [m-3

]

H2 H

Main plasma Main plasma

Trace H and H2(X,v=0-14)

35

30

25

20

15

10

5

0

Po

ten

tia

l E

ne

rgy

(e

V)

43210Internuclear Distance ()

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

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

3

4

5

6

7

8

90.01

2

3

4

5

6

PR

OD

UC

TIO

N C

RO

SS

SE

CT

ION

(a

02)

102 3 4 5 6 7 8 9

1002 3 4 5 6 7 8 9

1000

ENERGY (eV)

Eth

Hemission

PRESENT E.R.Williams, J.V.Martinez, and G.H.Dunn, Bull. Am. Phys. Soc. 12, 233 (1967).

D.A.Vroom and F.J.de Heer, J. Chem. Phys. 50, 580 (1969).

L.D.Weaver and R.H.Hughes, J. Chem. Phys. 52, 2299 (1970).

R.S.Freund, J.A.Schiovone, and D.F.Brader, J. Chem. Phys. 64, 1122 (1976).

G.A.Khayarallah, Phys. Rev. A 13, 1989 (1976).

C.Karolis and E.Harting, J.Phys. B 11, 357 (1976).

G.R.Mohlmann, F.J. de Heer, and J.Los, Chem. Phys. 25, 103 (1977).

J.M.Kurepa, M.D.Tasic, and Z.L.Petrovic (private communication).

J.M.Ajello, D.E.Shemansky, B.Franklin, J.Watkins, S.Srivastava, G.K.James, W.T.Simms,

C.W.Hord, W.Pryor, W.McClintock, V.Argabright, and D.Hall, Appl. Opt. 27, 890 (1988). (L )

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

rate

co

eff

icie

nt

(

cm

3/s

)

2 3 4 5 6 7 8 9

102 3

principal quantum number

10eV

100eV

1000eV

H(1) + e -> H(p) + e

H2 + e ->

H(1) + H(p) + e

eHH

eei

e

e

nn

C

Cnn

C

Cnn

n

n

n

n

n

ndt

d

H

22

)2(

)3(

.

.

)1(

)2,1(

)3,1(

.

.

).2()2(

)3()3(

.

.

)2(

)3(

.

.

....

....

....

....

)2(

)3(

.

.

2

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

eHeei nnpRnnpRnnpRpn 2210 )()1()()()(

Collisional-Radiative Model : Inclusion of H2 + e -> H + H(p) + e

0

p>=2

(QSS) Ionizing

component

Recombining

component

unknown

eHH nnpC 22 )(

New term

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

MAR (Molecular Assisted Recombination)

22 HeMARHe2He1He0)()()()()( nnpRnnpRnnpRnnpRpn

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

MA

R r

ate

co

eff

icie

nt

(c

m3/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

DA

10-25

10-24

10-23

10-22

10-21

10-20

10-19

10-18

10-17

H P

op

ula

tio

n C

oe

ffic

ien

t (

cm

3)

1098765432

Principal Quantum Number

CX MAR(v=0)

CX MAR(v=12)

CX MAR(v=8)

H+ + e -> H*

H(1s) + e -> H* + e

H2(v=0) + e -> H + H* + e

T=2.0eV

ne1014

cm-3

R0

R1

RCXMAR

CX MAR(v=4)

DA MAR(v=0)

DA MAR(v=4)

DA MAR(v=8)

R2

RDAMAR

35

30

25

20

15

10

5

0

Po

ten

tial

En

erg

y

(eV

)

43210

Internuclear Distance (A)

H2

X1

g

+

b3

u

+

X2

g

+

H2+

n=3

n=4

E,F1

g

+

a3

g

+

B1

u

+

C1

u

c3

u

H++ H

H + H

H2+

(1) H and He Collional-Radiative Models

Application of H and He models to the RF plasma

Radiation trapping

(2) H2 Collisional Radiative Model

Revision to include rotational states

in addition to electronic and vibrational states

Calculation of effective reaction rate coefficient

Determination of ne, Te, Tv, Trot

Table of Contents

H2 Collisional-Radiative Model (ver.1)

Calculation of effective reaction rate coefficients

K. Sawada, K. Eriguchi, T. Fujimoto: Hydrogen-atom spectroscopy of the ionizing plasma containing molecular hydrogen: line intensities and ionization rate; J. Appl. Phys. 73, 8122-8125, 1993. K. Sawada, T. Fujimoto: Effective ionization and dissociation rate coefficients of molecular hydrogen in plasma; J. Appl. Phys. 78, 2913-2924, 1995.

35

30

25

20

15

10

5

0

Po

ten

tial

En

erg

y

(eV

)

43210

Internuclear Distance (A)

H2X

1

g

+

b3

u

+

X2

g

+

H2+

n=3

n=4

E,F1

g

+

a3

g

+

B1

u

+

C1

u

c3

u

H++ H

H + H

H2 Collisional-Radiative Model (ver.2)

Vibrational levels for n 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

DA

MAR rate coefficient

K. Sawada and T. Fujimoto: Effect of initial vibrational excitation of molecular hydrogen on molecular assisted recombination in divertor plasmas; Contrib. Plasma Phys. 42, 603-607, 2002.

Construction of Collisional-Radiative Model for H2

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)

25

20

15

10

5

0

En

erg

y (e

V)

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

4

H2 He atom

Tv=4500K

Trot=300K

Determination of ne, Te, Tv, Trot

from observed spectra

Tv,Trot -> Population X1g+(v,J)

Calculation of effective

reaction rate coefficients

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

H2 energy levels

The Hydrogen Molecule

Wavelength Tables of

GERHARD HEINRICH DIEKE,

Edited by H. M. Crosswhite,

John Wiley & Sons Inc (1972)

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)

Hunds case (b)

(K) (N)

2131 levels are included in H2

CR model.

H2 Transition Probability Annie Hansson and James K.G. Watson, Journal of Molecular Spectroscopy 233 (2005) 169-173

Hnl-London

factor

Transition moment

25

20

15

10

5

0

Po

ten

tial en

erg

y (e

V)

6543210

Internuclear distance ()

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

Potential U(R) and Re(R)

Calculated by

Kolos and Wolniewicz et al.

except for P, G, p, s, j states

H2 Transition moment

Hunds case (b)

HERZBERG, MOLECULAR SPECTRA

and MOLECULAR STRUCTURE

I. SPECTRA OF DIATOMIC

MOLECULES

Numerov method

d

X

H2 Transition Probability Hnl-London Factor James K.G. Watson, Journal of Molecular Spectroscopy 252 (2008) 5-8

SJJ

25

20

15

10

5

0

Po

ten

tial en

erg

y (e

V)

6543210

Internuclear distance ()

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

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 e -> a transition probability

P-branch A[107 s-1] R-branch A[107 s-1]

v' v'' N' Present ref.1 Present /ref.1 Present ref.1 Present /ref.1

1 0 1 0.497 0.522 0.951 0.274 0.298 0.919

2 0.431 0.447 0.964 0.339 0.372 0.910

3 0.395 0.405 0.975 0.373 0.414 0.902

4 0.370 0.374 0.989 0.396 0.441 0.898

5 0.349 0.349 1.002 0.414 0.463 0.895

2 0 1 0.107 0.124 0.863 0.063 0.086 0.737

2 0.091 0.100 0.915 0.080 0.113 0.706

3 0.082 0.085 0.965 0.090 0.132 0.682

4 0.076 0.075 1.014 0.097 0.147 0.665

5 0.071 0.067 1.056 0.104 0.159 0.654

2 1 1 0.675 0.649 1.040 0.362 0.352 1.028

2 0.591 0.565 1.046 0.443 0.432 1.026

3 0.546 0.519 1.052 0.482 0.471 1.024

4 0.515 0.485 1.061 0.507 0.495 1.025

5 0.489 0.458 1.069 0.524 0.511 1.027

3 0 1 0.023 0.032 0.721 0.014 0.016 0.892

2 0.019 0.029 0.659 0.019 0.019 0.960

3 0.017 0.029 0.590 0.021 0.020 1.052

3 1 1 0.239 0.259 0.923 0.136 0.168 0.814

2 0.205 0.213 0.965 0.171 0.218 0.784

3 0.186 0.185 1.010 0.190 0.250 0.760

4 0.173 0.164 1.054 0.205 0.278 0.736

5 0.162 0.147 1.101 0.217 0.303 0.716

3 2 1 0.647 0.564 1.148 0.336 0.291 1.153

2 0.572 0.497 1.150 0.406 0.350 1.158

3 0.533 0.462 1.155 0.436 0.373 1.167

4 0.507 0.437 1.159 0.451 0.384 1.175

5 0.485 0.416 1.165 0.460 0.387 1.187

P-branch A[107 s-1] R-branch A[107 s-1]

v' v'' N' Present ref.1 Present /ref.1 Present ref.1 Present /ref.1

0 0 1 0.841 0.289 2.909 1.724 0.542 3.180

2 1.000 0.354 2.826 1.564 0.476 3.285

3 1.063 0.385 2.761 1.501 0.443 3.388

4 1.093 0.403 2.713 1.470 0.407 3.613

5 1.109 0.415 2.672 1.454 0.407 3.572

6 1.117 0.422 2.647 1.445 0.397 3.639

2 1 1 0.091 0.035 2.592 0.211 0.065 3.269

2 0.104 0.043 2.413 0.200 0.056 3.601

3 0.106 0.046 2.275 0.200 0.053 3.795

4 0.104 0.048 2.156 0.204 0.051 4.049

5 0.102 0.049 2.066 0.210 0.049 4.259

6 0.099 0.049 2.002 0.217 0.049 4.406

2 2 1 0.626 0.199 3.146 1.230 0.346 3.555

2 0.755 0.248 3.043 1.099 0.296 3.712

3 0.811 0.272 2.983 1.038 0.269 3.857

4 0.844 0.288 2.930 0.999 0.251 3.982

5 0.865 0.298 2.902 0.971 0.238 4.081

H2 d -> a transition probability

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(X) + e -> H2* + e

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)

X -> B, B, B, C, D, D

R.CELIBERTO, R.K.JANEV et al.

Atomic Data and Nuclear Data Tables 77, 161-213 (2001).

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

[1] R.K.Janev, D.Reiter, U.Samm,

Collision Processes in Low-Temperature

Hydrogen Plasmas,

http://www.eirene.de/report_4105.pdf

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

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

[3] G.R.Mhlmann and F.J.De Heer,

Chem.Phys.Letters 43,240 (1976).

X -> d electron impact excitation rate coefficient

Vibrationally and rotationally resolved rate coefficient X -> 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

X->

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)

Optically allowed

Rate coefficient Franck-Condon factor

and

Hnl-London Factor

Optically forbidden

Rate coefficient Franck-Condon factor

and

Evenly divided for J

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

H2 CORRELATION DIAGRAM, T.E SHARP,

ATOMIC DATA 2, 119-169(1971)

H2 electron impact excitation among excited levels

He data are used.

Energy difference is

taken into account.

He data labeled by

magnetic sublevel are

necessary.

We need H2 data.

H2(v,J=1) + H+ -> H + H2+

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

H2(v=0,J) + H2 -> H2(v=0,J) + H2

H2 (X) -> 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)

S. Green et al., The Astrophysical Journal

Supplement Series, 36, 483-496 (1978).

H2(,v,J) + e -> H2(,v,J) + e

under examination

X 1

E 302

B 334

C- 424

C+ 455

H 471

B* 485

D- 513

D+ 531

G 543

I- 578

I+ 598

J- 618

J+ 633

O 642

B** 662

D*- 677

D*+ 693

P 709

R- 717

R+ 726

S- 728

S+ 731

a 734

c- 882

c+ 969

h 1050

e 1094

d- 1244

d+ 1373

g 1439

i- 1524

i+ 1599

j- 1662

j+ 1725

f 1785

k- 1811

k+ 1913

r- 1931

r+ 2000

s- 2063

s+ 2099

H2 population

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)

Te=3.0eV, ne=2x1010cm-3

Tv=4200K, Trot=350K

Calculated spectra of H2

Te=3.0eV, ne=2x1010cm-3, Tv=4200K, Trot=350K

H emission line intensity diagnostics

(1) H(n,l) + e -> H(n,l) + e (n>5, Te>25eV)

(2) H2(X,v,J) + e -> H + H(n,l) + e

(3) H2+(X,v,J) + e -> H+ + H(n,l) + e

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

-> H + H + H H(n,l) ?

H2 CR model

(5) H2(,v,J) + e -> H2(,v,J) + e

(6) H2(X,v,J) + H+ -> H2

+ (X,v,J) + H

(7) H2(,v,J) + H2 -> H2(,v,J) + H2

(8) H2(,v,J) + e -> H2(,v,J) + e

Summary : Help !