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 !