Collisional-Radiative Model of Molecular Hydrogen...H 2 and D 2 Collisional-Radiative Model (EvJ...
Transcript of Collisional-Radiative Model of Molecular Hydrogen...H 2 and D 2 Collisional-Radiative Model (EvJ...
-
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