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Max-Planck-Institut für Plasmaphysik Max-Planck-Institut für Plasmaphysik

CRP on ‘Atomic and Molecular Data for Plasma Modelling’, IAEA, Vienna 17-19 November 2008

Fundamental Data of Diatomic Molecules Relevant for Fusion

Ursel Fantz and Dirk Wünderlich

Beryllium Beryllium

Be W C

Molecules in the plasma edge

Recycling H2, D2, T2, HD, HT, DT Plasma wall interaction: CH, CD, CT, C2 BeH, BeD, BeT BH, BD, BT Vibrationally resolved data FCF, Aik, σ, X, CR and dissociation model

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 2 CRP Meeting, 17-19 November 2008

Transitions of Diatomic Molecules: TraDiMo

TraDiMo

bound-bound and bound-free transitions

TraDiMo

bound-bound and bound-free transitions Vibrational energies Franck-Condon factors Transition probabilities Isotope relations Potential curves Based on Schrödinger equation with Born-Oppenheimer approximation Dipole transition moment Effective mass

+

Compilation of data Compilation of data Basic molecular data Basic molecular data vibrational resolution H2, D2, T2 HD, DT HT Already available

• U. Fantz, D. Wünderlich

INDC(NDS)-457 (2004)

presented at the 1st RCM, September 2005

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 3 CRP Meeting, 17-19 November 2008

1 2 3 4 5 2 4 6 8 10 12 14 16 18 20

H(1s)+H(1s)

g3Σ+

g

X1Σ+

g

H(1s)+H(3l) H(1s)+H(2l)

B1Σ+

u

b3Σ+

u

Singlet Triplet

Potential energy [eV] Internuclear distance [Å]

EF1Σ+

g

a3Σ+

g c3Πu

H+

2

i3Πg I1Πg d3Πu D1Πu B'1Σ+

u

e3Σ+

u

h3Σ+

g

GK1Σ+

g

HH1Σg

+

J1Δg j3Δg C1Πu

TraDiMo for molecular hydrogen

E [eV] H2

+

E,F C B a c b v=3 v=2 v=1 v=0

· · · Singlet Triplet system 10 2 4 6 8 12 14 16 n=2 n=3

H2

v=14

Energy level diagram and potential curves

repulsive double well plotted n=1,2,3, data up to n=4 plotted n=1,2,3, data up to n=4 v=0 metastable

data compilation polynomial fits data compilation polynomial fits

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 4 CRP Meeting, 17-19 November 2008

TraDiMo for molecular hydrogen

Example: transition probabilities: d 3Πu → a 3Σg

+

1 2 3 4 12.0 14.0 16.0 18.0

• 3x10-29
• 2x10-29
• 1x10-29

1x10-29

v'=3

a3Σ+

g

d3Πu Potential energy [eV] Internuclear distance [Å]

v''=3

Mel [Cm] Mel

1 2

• 4
• 3
• 2
• 1

1 v'=3→v''=3 Ψ*MelΨ'

v‘‘ v‘

q 1 2 3 4 2.41E+07 1.66E+06 9.27E+03 7.75E-02 5.62E-02 1 1.53E+06 2.07E+07 3.26E+06 2.97E+04 2.82E+00 2 1.07E+05 2.84E+06 1.74E+07 4.80E+06 6.23E+04 3 8.40E+03 3.19E+05 3.89E+06 1.43E+07 6.24E+06 4 5.87E+02 3.64E+04 6.22E+05 4.64E+06 1.15E+07 ...

0 1 2 3 4 5 6 7 8 9 0.0 5.0x106 1.0x107 1.5x107 2.0x107 2.5x107 2 4 6 8 A

v ' v ' '

[s

• 1

]

v ' ( d

3Πu

) v''(a

3Σ + g

)

Fulcher band

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 5 CRP Meeting, 17-19 November 2008

TraDiMo for molecular hydrogen coupled to H2

+(v)

Franck-Condon factors for H2*(v) - H2

+(v) transitions: data up to n=4

2 4 6 8 12.0 14.0 16.0 18.0 20.0

B

1Σ + u

H

+ 2(X 2Σ + g)

Potential energy [eV] Internuclear distance [Å]

v v‘

q 1 2 3 4 4.76E-01 3.17E-01 1.36E-01 4.82E-02 1.54E-02 1 3.75E-01 2.73E-02 2.07E-01 1.96E-01 1.12E-01 2 1.26E-01 3.32E-01 2.93E-02 5.59E-02 1.51E-01 3 2.10E-02 2.53E-01 1.75E-01 1.15E-01 6.82E-04 4 1.56E-03 6.44E-02 3.22E-01 5.91E-02 1.49E-01 ...

0 1 2 3 4 5 6 7 8 9 0.0 0.2 0.4 0.6 2 4 6 8 FCF

v ' ( H

+ 2

( X

2Σ+ g

) ) v (B

1Σ + u

)

Example: B 1Σu → H2(X 2Σg)

+ + +

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 6 CRP Meeting, 17-19 November 2008

TraDiMo for molecular hydrogen coupled to H2

+(v)

Franck-Condon factors for H2*(v) - H2

+(v) transitions: H2, D2, T2, HD, DT,HT 0 1 2 3 4 5 6 7 8 9 0.0 0.2 0.4 0.6 2 4 6 8

F C F v' (H+

2(X2Σ+ g))

v ( B

1

Σ

+ u

) H2

0 1 2 3 4 5 6 7 8 9 0.0 0.2 0.4 0.6 2 4 6 8

FCF v' (D+

2(X2Σ+ g))

v ( B

1Σ+ u

) D2

0 1 2 3 4 5 6 7 8 9 0.0 0.2 0.4 0.6 2 4 6 8

FCF v' (T

+ 2

(X

2

Σ

+ g

)) v ( B

1Σ + u

) T2

Isotope shifts Isotope shifts H2 H2 D2 D2 T2 T2 B 1Σu → H2(X 2Σg)

+ + +

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 7 CRP Meeting, 17-19 November 2008

0 1 2 3 4 5 6 7 8 9 0.0 0.5 1.0 1.5 2.0 2 4 6 8

A

vv'

[ 1

6

s

• 1

] v (X2Π) CH v' (A2Δ)

TraDiMo for CH

1 2 3 4 5 2 4 6 8 10

H Hettema and D R Yarkony, J. Chem. Phys 100, 1994, 8991 G C Lie, J Hinze and B Liu, J. Chem. Phys 59, 1973, 1872

A2Δ C2Σ+ B2Σ−

Potential energy [eV] Intenuclear distance [Å]

X2Π

CH

CH CH Potential curves and transition probabilities A 2Δ -X 2Π A 2Δ -X 2Π

Avv’ [106 s-1]

0 1 2 3 4 5 6 7 8 9 1 2 3 4 2 4 6 8

Avv' [106 s-1] v ' ( B

2Σ-

) v (X2Π)

0 1 2 3 4 5 6 7 8 9 2 4 6 8 10 2 4 6 8

A

vv'

[ 1

6

s

• 1

] v ' ( C

2

Σ

+

) v (X2Π)

B 2Σ- -X 2Π B 2Σ- -X 2Π C 2Σ+ -X 2Π C 2Σ+ -X 2Π

Gerö band

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 8 CRP Meeting, 17-19 November 2008

TraDiMo for C2

Potential curves and Einstein coefficients

1 2 3 4 2 4 6 8 10 12 14

Energy gap a 3Πu - X 1Σ+

g

0.0887 eV

ground state metastable d3Πg a3Πu X1Σ+

g

D1Σ+

u

Potential energy [eV] Internuclear distance [Å]

C2

0 1 2 3 4 5 6 7 10 20 30 40 50 60 70 2 4 6 Aik [ 1 06 s-1 ]

v(D1

Σ+

u)

v(X1Σ+

g)

0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 2 4 6

Aik [ 1 06 s-1 ] v'(d

3Π g

) v ( a3

Π

u)

D 1Σu

+ - X 1Σg +

D 1Σu

+ - X 1Σg +

d 3Πg - a 3Πu d 3Πg - a 3Πu

Swan band Mulliken band

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 9 CRP Meeting, 17-19 November 2008

TraDiMo for BH

1 2 3 4 5 2 4 6 8 10

W-T Luh and W C Stwalley, J. Molec. Spectr. 102, 1983, 212

BH B1Σ+ A1Π X1Σ+ Potential energy [eV] Intenuclear distance [Å]

BH BH

0 1 2 3 4 5 6 7 8 0.0 0.5 1.0 2 4 6 8

FCF v ( A

1Π

) v (X1Σ+)

X1Σ+→A1Π

A 1Π - X 1Σ+ A 1Π - X 1Σ+

0 1 2 3 4 5 6 7 8 0.0 0.5 1.0 2 4 6 8

FCF v ( B

1Σ +

) v ( X

1

Σ

+

)

X1Σ+→B1Σ+

B 1Σ+ - X 1Σ+ B 1Σ+ - X 1Σ+ Potential curves and Franck Condon factors

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 10 CRP Meeting, 17-19 November 2008

TraDiMo for BeH

1 2 3 4 5 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000

• J. Pitarch-Ruiz et al,
• J. Chem. Phys. 129, 2008, 054310

62Σ+ 52Σ+ Be(1P)+H(2S) Be(3P)+H(2S) 22Δ 14Π 14Σ+ 12Σ- 32Σ+ 22Π 42Σ+ 22Σ+

A2Π

Potential energy [cm-1] Internuclear distance [Å]

X2Σ+

Be(1S)+H(2S) 32Π 12Δ 42Π 52Π

BeH BeH

0 1 2 3 4 5 6 7 8 9 0.0 0.5 1.0 1.5 2.0 2 4 6 8

Avv' [ 1 06 s-1 ] v (X2Π) CH v ' ( A2

Δ

)

CH CH A2Δ- -X2Π A2Δ- -X2Π

0 1 2 3 4 5 6 7 8 9 2 4 6 8 10 2 4 6 8 Av'v'' [106 s-1] v ' ( A

2

Π

) v ' ' ( X2

Σ

+)

BeH

BeH BeH A 2Π - X 2Σ+ A 2Π - X 2Σ+

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 11 CRP Meeting, 17-19 November 2008

TraDiMo for BeH

0 1 2 3 4 5 6 7 8 9 2 4 6 8 10 2 4 6 8 Av'v'' [106 s-1] v' (A2Π) v ' ' ( X2Σ+ ) BeT 0 1 2 3 4 5 6 7 8 9 2 4 6 8 10 2 4 6 8 Av'v'' [106 s-1] v' (A2Π) v'' (X2

Σ

+)

BeD

• G. Duxbury et al., EFDA–JET–CP(04)03-54

Einstein coefficients: A 2Π - X 2Σ+ Isotope shifts Isotope shifts BeD BeD BeT BeT

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 12 CRP Meeting, 17-19 November 2008

Yacora: a flexible code for calculating particle densities

Self-consistent solution of coupled systems of linear and non-linear differential equations Collisional radiative modelling Collisional radiative modelling Population densities of excited states Dissociation modelling Dissociation modelling Particle densities of radicals

+

Coupled system Coupled system Particle and population densities

=

10-10 10-8 10-6 10-4 10-2 100 10-8 10-6 10-4 10-2 100 ne=1017 m-3 Te=4 eV

v=0 metastable

c3Πu v=2 v=3 v=4 v=5 v=6 v=8 v=14 v=1 B1Σ+

u

Relative population ni/n0 Temporal development [s]

Example: molecular hydrogen Flexible code Easy to extend for new processes Simple change of input data Based on cross sections (EEDF) Electron collisions + heavy particle collisions + radiation Electron collisions + heavy particle collisions + radiation

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 13 CRP Meeting, 17-19 November 2008

Yacora for molecular hydrogen: CR modelling

Vibrational resolution in ground state and electronically excited states 11 12 13 14 15 16 H+

2

. . .

1 2 3 4 n= X j i g d e h c a B' GK I J D HH C B b EF Triplet system Singlet system Energy [eV]

d1Δg d1Πg d1Σ+

g

p1Πu p1Σ+

u

s1Σ+

g

d3Δg d3Πg d3Σ+

g

p3Πu p3Σ+

u

s3Σ+

g

Extension of data base Gryzinski method

• ptically forbidden transitions

Impact parameter method

• ptically allowed transitions

Additional processes predissociation autoionisation, quenching, …. ) (

' ' ' ' e p p v v pp vv

E F q ⋅ = σ ) ( ) (

' ' ' ' e p p v v pp vv

E D A S ⋅ = σ

Janev:

• R. Janev, D. Reiter, U. Samm

Juel-Report 4105 (2003) Sawada: K. Sawada and T. Fujimoto

• J. Appl. Phys. 78 (1995), 291

IPProg: A. Burgess, H. P. Summers,

• Mon. Not. R. Astr. Soc. 174 (1976) 345

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 14 CRP Meeting, 17-19 November 2008

Yacora for molecular hydrogen: CR modelling

1 2 3 4 5 10-11 10-10 10-9 10-8 10-7

n(I1Πg)/n0 Te [eV] I1Πg

H2 D2

Janev Miles/Sawada

Population densities: comparison with measurements

1 2 3 4 5 10-10 10-9 10-8 10-7 10-6

n(e3Σ+

u)/n0

Te [eV] e3Σ+

u

Miles/Sawada Janev

H2 D2 10-11 10-10 10-9 10-8 10-7 H2 D2

n(GK1Σ+

g)/n0

Miles/Sawada Janev

GK1Σ+

g

(low and high quenching)

Singlet Singlet

1 2 3 4 5 10-10 10-9 10-8 10-7 10-6

n(d3Πu)/n0 d3Πu

Miles/Sawada Janev

H2 D2

Triplet Triplet Overall agreement is not satisfying! Overall agreement is not satisfying!

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 15 CRP Meeting, 17-19 November 2008

Yacora for atomic hydrogen: CR modelling

Population densities: comparison with measurements Cross sections Cross sections

• R. Janev, D. Reiter, U. Samm: Juel-Report 4105 (2003)

12.0 12.5 13.0 13.5 10-10 10-9 10-8 10-7

n=3 n=4 n=5 n=6 n=7 n=9

ECR discharge, 0.5 Pa, 10%H2 in 5%Ar/He

E [eV]

ne = 2×1017 m-3 Te= 4.5 eV

Balmer lines: Boltzmann plot np/n0/gp

1 5 10 15 20 10-19 10-18 10-17 10-16 10-15 10-14

Yacora: Janev ADAS: Anderson Yacora: fit Anderson/Janev

Te=20 eV Te=5 eV Te=3 eV Te=2 eV

X [m3/s]

Main quantum number

• H. Anderson, C. P. Ballance, N. R. Badnell, H. P. Summers,
• J. Phys. B. 33 (2000) 1255

20 40 60 80 100 10-23 10-22 10-21 10-20

1→7 1→6 1→5 1→4 1→3

σ [m2]

Ee [eV]

1→2

Ground state excitation

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 16 CRP Meeting, 17-19 November 2008

Yacora for atomic hydrogen: CR modelling

Population densities: comparison with measurements

• D. Wünderlich et al. JQSRT(2008) in press

Balmer lines: Boltzmann plot np/n0/gp

Yacora now in agreement with experiments Yacora now in agreement with experiments

12.0 12.5 13.0 13.5 10-10 10-9 10-8 10-7

n=3 n=4 n=5 n=6 n=7 n=9

ECR discharge, 0.5 Pa, 10%H2 in 5%Ar/He

E [eV]

ne = 2×1017 m-3 Te= 4.5 eV 1 5 10 15 20 10-19 10-18 10-17 10-16 10-15 10-14

Yacora: Janev ADAS: Anderson Yacora: fit Anderson/Janev

Te=20 eV Te=5 eV Te=3 eV Te=2 eV

X [m3/s]

Main quantum number 20 40 60 80 100 10-23 10-22 10-21 10-20

1→7 1→6 1→5 1→4 1→3

σ [m2]

Ee [eV]

1→2

Ground state excitation

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 17 CRP Meeting, 17-19 November 2008

Yacora for hydrogen: CR modelling

Coupling to other hydrogen species H(n) H H+ H2

+

H2 H-

e H H e H H e H H e H H e H H

n n p R n n p R n n p R n n p R n n p R p n

− − + + + +

+ + + + = ) ( ) ( ) ( ) ( ) ( ) (

2 2 2 2

recombination dissociative recombination dissociative excitation effective excitation mutual neutralisation H־+ H+ → H* + H

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 10-29 10-28 10-27 10-26 10-25 10-24 10-23 10-22 10-21 Population coefficient [m3] Te = 3 eV ne = 1017 m-3

H- H+

2

H+ H2 Quantum number n H

Lyα Hε Hδ Hγ Hβ Hα

Input data described in:

• D. Wünderlich, PhD Thesis

University of Augsburg (2004)

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 18 CRP Meeting, 17-19 November 2008

Yacora for hydrogen: CR modelling

0.01 0.1 1 10 100 10-22 10-21 10-20 10-19 10-18 10-17 10-16 σtotal [m2]

Ee [eV]

Janev 1987 Janev 2003 0.1 1 10 10-15 10-14 10-13

Janev 1987 Janev 2003

n=6 n=5 n=4 n=3 X [m3/s] Te [eV]

Relevance of dissociative recombination: H2

+ + e → H(n) + H R.K. Janev, W.D. Langer, J.K. Evans D.E. Post Elementary Processes in Hydrogen/Helium Plasmas Springer, Berlin (1987)

• K. Sawada und T. Fujimoto
• J. Appl. Phys. 78 (1995), 291

n=1: 0.1 n=4: 0.12 n=2: 0.45 n=5: 0.69 n=3: 0.22 n>5: 10/n3

fixed branching ratio

• R. Janev, D. Reiter, U. Samm:

Juel-Report 4105 (2003)

branching ratio vibrationally resolved and energy dependent

Data set changed Yacora now in better agreement with experimental data (H¯ sources) Yacora now in better agreement with experimental data (H¯ sources)

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 19 CRP Meeting, 17-19 November 2008

Yacora for hydrogen: CR modelling

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 10-28 10-27 10-26 10-25 10-24 10-23 10-22 10-21 H+

2

H H+

3

Populatin coefficient [m3] Quantum number n H2 Lyα Hε Hδ Hγ Hβ Hα

Te = 3 eV, ne = 1017 m-3

Coupling to other hydrogen species H(n) H H+ H2

+

H2 H-

recombination dissociative recombination dissociative excitation effective excitation

H3

+

• R. Janev, D. Reiter, U. Samm:

Juel-Report 4105 (2003)

branching ratio well known

• S. Datz et al., Phys. Rev. Lett. 74(1995) 896

branching ratio not known

all in n=2: F.C: Kulander et al., J. Phys. B 12 (1979) L501

Dissociative recombination H3

+

H3

+ + e → H + H + H

→ H2 + H(n)

• D2

+

H3

+, D3 +

D2

+

H3

+, D3 +

• pen

issue channel added

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 20 CRP Meeting, 17-19 November 2008

Yacora for hydrogen: dissociation modelling

Manifold of hydrogen species

H2(v), H2*,H, H* H2

+, H3 +, H+, H¯

Surface recombination

H H+ H2

1016 1017 1018 1019 1014 1015 1016 1017 1018 1019 1020 1021

Te=2.5 eV, TN=450 K, Tvib=3000 K

Density [m-3] ne [m-3]

H2 H+ H− H+

3

H+

2

H

Dependence on electron density Dependence on electron density

1015 1016 1017 1018 1019 20 40 60 80 100 H+

3

Relative density [%] ne [m-3] H+ H+

2

n(H2)=2⋅1019 m-3

1015 1016 1017 1018 1019 20 40 60 80 100

n(H2)=1020 m-3

H+

3

Relative density [%] ne [m-3] H+ H+

2

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 21 CRP Meeting, 17-19 November 2008

Yacora for CH, C2: CR modelling

Energy level diagram and states selected CH CH

• A. Kalemos, A. Mavridis, A. Metropoulos
• J. Chem. Phys. 111 (1990) 9536

Processes considered, vibrationally resolved Ionisation: Gryzinski method Electron impact excitation: IPProg Electronic de-excitation: detailed balance Radiation: emission (TraDiMo)

B.M. Smirnov, A.S. Yatsenko Physics-Uspekhi 39 (1996) 2116 U, 104 cm-1 U, eV U, 104 cm-1 U, eV singlet system triplet system

C2 C2

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 22 CRP Meeting, 17-19 November 2008

IPProg: electron impact excitation rate coefficients

Check applicability: molecular hydrogen X1Σg(v) → B1Σu

+ +

1 2 3 4 5 6 7 8 9 10 10-16 10-15 10-14 10-13

v=14 v=10-11

X [m3/s] Te [eV]

Celiberto calculations

v=0

1 2 3 4 5 6 7 8 9 10 10-16 10-15 10-14 10-13

v=14 v=10-11

X [m3/s] Te [eV]

IPProg calculations

v=0

• R. Celiberto et al.

ADNDT 77 (2001) 161

X(IPProg) > X(Celiberto) X(IPProg) > X(Celiberto)

1 2 3 4 5 6 7 8 9 10 1.0 1.2 1.4 1.6 1.8 2.0

v=14 v=10-11

Ratio Te [eV]

v=0 reasonable agreement reasonable agreement

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 23 CRP Meeting, 17-19 November 2008

IPProg for CH, C2: vibrationally resolved data

CH CH

1 2 3 4 5 6 7 8 9 10 10-19 10-18 10-17 10-16 10-15 10-14 10-13 X2Π -C2Σ+ X2Π -B2Σ-

1-1 1-0 0-0

X [m3/s] Te [eV]

0-1 1-0 0-0 1-1 0-0 1-0 0-1

X2Π -A2Δ 2 3 4 5 6 10-16 10-15 10-14 10-13

Aik=1.24x107s-1 Aik=1.8x106s-1, v'=v''=0

BH: X 1Σ+ - A 1Π CH: X 2Π - A 2Δ

Te[eV]

1 2 3 4 5 6

10-15 10-14 10-13

Te [eV]

v'=v''=0-3 v'=v''=0

Mulliken: X 1Σ+

g - D 1Σ+ u

Swan: a 3Πu- d 3Πg

10-16

Rate coefficients C2 C2 X – A: BH and CH X – A: BH and CH

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 24 CRP Meeting, 17-19 November 2008

Yacora for CH, C2: CR modelling

Temporal evolution of population densities CH CH

9 7 5 3 1 1

10-6 10-5 10-4 10-3 10-2 10-1 100

v=10 v=9 v=4 v=3 v=2

Relative population X2Π

v=1

10-9 10-7 10-5 10-3 10-1 101

10-9 10-8 10-7 10-6 10-5 10-4 10-3

v=8 v=3 v=2

C2Σ+ B2Σ-

A2Δ Relative population Time [s]

v=1 v=1 v=2

1 2 3 4 5 6 C2Σ+ B2Σ− A2Δ

E [eV]

X2Π

Collisions, IPProg Radiation, TraDiMo Ionization, Gryzinski

CH+: Eion =12.6 eV

Gerö transition A2Δ – X2Π Gerö transition A2Δ – X2Π

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 25 CRP Meeting, 17-19 November 2008

Yacora for CH, C2: collisional radiative modelling

1 2 3 4 5 6 d3Πg c3Σ+

u

b3Σ−

g

C1Πg B'1Σ+

g

A1Πu a3Πu E [eV] X1Σ+

g

Collisions, IPProg Radiation, TraDiMo Collisions, Gryzinski Ionization, Gryzinski

D1Σ+

u

B1Δg

ground state metastable state

Swan transition: d3Πg – a3Πu Swan transition: d3Πg – a3Πu Populating and depopulating processes CR model for C2 CR model for C2

C2

+: Eion = 12.15 eV

0.0 0.2 0.4 0.6 0.8 1.0

electron de-excitation spontaneous emission electron excitation

Relative contribution 1015 1016 1017 1018 1019 1020 0.0 0.2 0.4 0.6 0.8 1.0

ionisation electron excitation electron de-excitation spontaneous emission

Relative contribution ne [m-3]

A 1Πu A 1Πu

depopulation population Te = 5 eV

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 26 CRP Meeting, 17-19 November 2008

Yacora for CH, C2: collisional radiative modelling

C2 Swan transition C2 Swan transition

1015 1016 1017 1018 1019 1020 0.0 0.2 0.4 0.6 0.8 1.0 ne [m-3] Relative contribution

spontaneous emission electron excitation electron de-excitation ionisation

0.0 0.2 0.4 0.6 0.8 1.0 Relative contribution

electron excitation spontaneous emission electron de-excitation

a 3Πu a 3Πu d 3Πg d 3Πg

0.0 0.2 0.4 0.6 0.8 1.0 Relative contribution

electron excitation spontaneous emission electron de-excitation

1015 1016 1017 1018 1019 1020 0.0 0.2 0.4 0.6 0.8 1.0 ne [m-3] Relative contribution

spontaneous emission electron excitation electron de-excitation ionisation

depopulation population depopulation population

(metastable)

Te = 5 eV

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 27 CRP Meeting, 17-19 November 2008

Photon efficiencies: CH and C2

Experimental validation of photon efficiencies: TEXTOR, ASDEX Upgrade, JET, DIII-D

• S. Brezinsek, …, U. Fantz, A. Manhard, …, et al., J. Nucl. Mat. 363-365 (2007) 1119

CxHy in D plasmas Te= 35 eV CxDy in H plasmas Te= 45 eV Gas puff experiments TEXTOR TEXTOR HYDKIN code HYDKIN code TEXTOR TEXTOR HYDKIN code HYDKIN code

www.eirene.de/eigen

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 28 CRP Meeting, 17-19 November 2008

Photon efficiencies: CH and C2

Experimental validation of photon efficiencies

ERO modelling of hydrocarbon transport and spectroscopy for injection experiments at TEXTOR D/XB values for CD and C2 are strongly dependent on local electron temperature, whereas their dependence on electron density is small Discrepancies between modelled and measured D/XB probably indicate the uncertainties of emission rate coefficients used in the modelling

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 29 CRP Meeting, 17-19 November 2008

Photon efficiencies: CH and C2

Experimental validation of photon efficiencies Problem of the uncertainty of CH emission rate coefficient still not solved! Problem of the uncertainty of CH emission rate coefficient still not solved!

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 30 CRP Meeting, 17-19 November 2008

Yacora for hydrocarbons: dissociation modelling

Dissociation model for hydrocarbons Based on electron impact processes CxHy + e → CxHy-m + Hm + e CxHy + e → CxHy

+ + 2e; …

Erhardt&Langer data completed with Brooks data Janev&Reiter data heavy particle collisions (optional) CH3 + CH3 → C2H6 C2H + C2H → C2 +C2H2 Tahara data

A.B. Ehrhardt, W.D. Langer, PPPL-2477 (1987) J.N. Brooks et al., ANF/FPP/TM-297 (1999)

• R. Janev, D. Reiter, Jül3966 (2002) and Jül4005 (2003)

Exchange

• f data base

Exchange

• f data base

Importance of heavy particle collisions Importance of heavy particle collisions Formation of higher hydrocarbons (ethane family) Formation of higher hydrocarbons (ethane family)

• H. Tahara et al., Jpn. J. Appl. Phys. 34 (1995) 1.

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 31 CRP Meeting, 17-19 November 2008

Yacora for hydrocarbons: dissociation modelling

Dissociation model for methane CH4(t=0) = 1020 m-3 Te = 4 eV, ne = 1019 m-3

10-6 10-5 10-4 10-3 1015 1016 1017 1018 1019 1020 1021

C2H5 C2H6 C2H3 C2H C2H2 C2 C2H4 C CH CH2 CH3

Particle density [m-3] Temporal development [s]

CH4

10-6 10-5 10-4 10-3 1015 1016 1017 1018 1019 1020 1021

C CH CH2 CH3

Particle density [m-3]

CH4

with heavy particle collisions

Yacora Yacora

Janev&Reiter data

with heavy particle collisions Tahara Data

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 C2 Yacora C CH CH2 CH3

Particle density [1019 m-3]

CH4 Hydkin Yacora

τspecies= 1-100 µs

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 32 CRP Meeting, 17-19 November 2008

Yacora for hydrocarbons: dissociation modelling

1015 1016 1017 1018 1019 1020 1016 1017 1018 1019 1020 1021 Particle density [m-3] ne [m-3]

C2H5 C2H6 C2H3 C2H C2H2 C2 C2H4 C CH CH2 CH3 CH4

1016 1017 1018 1019 1020 1021 Particle density [m-3]

C CH CH2 CH3 CH4

1015 1016 1017 1018 1019 1020 1016 1017 1018 1019 1020 1021 Particle density [m-3] ne [m-3]

C2H5 C2H6 C2H3 C2H C2H2 C2 C2H4 C CH CH2 CH3 CH4

Dissociation model for methane CH4(t=0) = 1020 m-3, Te = 4 eV

Janev&Reiter data Janev&Reiter data Erhardt&Langer + Brooks data

Dependence on electron density Need for experimental data! Need for experimental data!

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 33 CRP Meeting, 17-19 November 2008

Summary

Compilation, Calculation and Validation of Fundamental Data for Diatomic Molecules

Tools available Tools available Already done Already done Prospects Prospects

TraDiMo H2, D2, T2, HD, HT, DT CH, C2, BH, BeH,… Yacora Collisional radiative model Dissociation model H2, H CH4 CH, C2, BH H2 IPProg CH, C2, BH CH, C2, BH, BeH, …

selected states states available

presented at the 1st RCM, September 2005

Max-Planck-Institut Max-Planck-Institut für Pl für Plasmaphy asmaphysik

Ursel Fantz, p. 34 CRP Meeting, 17-19 November 2008

Summary

Compilation, Calculation and Validation of Fundamental Data for Diatomic Molecules

Tools available Tools available Completed Completed

TraDiMo H2, D2, T2, HD, HT, DT CH, C2, BH, BeH,… Yacora Collisional radiative model Dissociation model H2, H CH4 CH, C2 H2 IPProg with C2Hy with H2,H2

+, H3 +,H¯

CH, C2, BH CH, C2, BH, BeH, …

selected states states available

presented at the final meeting, November 2008