max-planck-institut für plasmaphysik crp on ‘atomic and molecular data for plasma modelling’,...
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Max-Planck-Institut für Plasmaphysik
CRP on ‘Atomic and Molecular Data for Plasma Modelling’, IAEA, Vienna 26-28 September 2005
Compilation and Extension of a Database for
Systematic Studies on Diatomic Molecules
Ursel Fantz and Dirk Wünderlich
Franck-Condon factors, transition probabilities
Vibrational population
Collisional radiative and dissociation modelling
Rate coefficients
TraDiMo
Yacora
Yacora
IPProg
Examples for molecular hydrogen and hydrocarbons
Future applications to CH, BH, BeH and its hydrogen isotopomeres, C2
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Transitions of Diatomic Molecules: TraDiMo
TraDiMobound-bound
and bound-free
transitions
TraDiMobound-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 moment
Effective mass
+
Compilation of dataCompilation of data
Basic molecular dataBasic molecular data
vibrational resolution
H2, D2, T2
HD, DT
HT
Already available U. Fantz, D. WünderlichINDC(NDS)-457 (2004)
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
TraDiMo for molecular hydrogen
Energy level diagram and potential curves
repulsive
double well
plotted n=1,2,3, data up to n=4plotted n=1,2,3, data up to n=4
v=0 metastable
data compilationpolynomial fits
data compilationpolynomial fits
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
TraDiMo for molecular hydrogen
Vibrational levels in double minima curves: GK 1g+
H2: v = 2 GK2H2: v = 2 GK2
Isotope effectIsotope effect
D2: v = 2 K1D2: v = 2 K1
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
TraDiMo for molecular hydrogen
Franck-Condon factors: X 1g+ → d 3u
v
v‘
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
TraDiMo for molecular hydrogen
Transition probabilities: d 3u → a 3g+
v‘‘
v‘
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
TraDiMo for molecular hydrogen
Transition probabilities for bound to free transitions: a 3g+ → b 3u
+
Isotope shiftsIsotope shifts
Continuum radiationContinuum radiation
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Vibrational population in excited states of hydrogen
Singlet system B 1u+Triplet system d 3u
v0v
vv'0p'
v'p' nqn
v'p'
v0v
vv'0p'v'
p' A
nqn
but also cascading, predissociation, quenching and …
Projection of n0v via Franck Condon matrix versus excitation and de-excitation
ground statepopulation
Tvib(X)
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
TraDiMo for C2, CH, BH, BeH, …
Potential curves and Franck-Condon factors: C2
X 1g+
- D 1u+X 1g
+ - D 1u
+
a 3u - d 3ga 3u - d 3g
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
TraDiMo for C2, CH, BH, BeH, …
Potential curves: CH and BH
Polynomial fits Polynomial fits
CHCH BHBH
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
TraDiMo for C2, CH, BH, BeH, …
Franck-Condon factors: X 2 - A 2
Isotope shiftsIsotope shifts
CHCH CDCD
CTCT
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
TraDiMo for C2, CH, BH, BeH, …
Transition probabilities: X 2 - A 2 CHCH
CH: = 540 ns measured valueAik= 1.85106 s-1
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Yacora: a flexible code for calculating particle densities
Self-consistent solution of coupled systems of linear and non-linear differential equations
Collisional radiative modellingCollisional radiative modelling Population densities of excited states
Dissociation modellingDissociation modelling Particle densities of radicals
+
Coupled systemCoupled system Particle and populationdensities
= 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 + radiationElectron collisions + heavy particle collisions + radiation
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Yacora for hydrogen: collisional radiative modelling
Vibrational resolution in ground state and electronically excited states
Extension of data base
Gryzinski method
optically forbidden transitions
Impact parameter method
optically allowed transitions
Additional processes
predissociation
autoionisation,
quenching, ….
)(''
'' e
ppvv
ppvv EFq
)()( ''
'' e
ppvv
ppvv EDAS
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Yacora for hydrogen: collisional radiative modelling
Electronically excited states: triplet system
n=3: electronically resolved
Differences in dependence on neDifferences in dependence on ne
Calculations of individual levels requiredCalculations of individual levels required
d 3u: vibrationally resolved (change in data base)
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Yacora for hydrogen: collisional radiative modelling
v'p'
v0v
vv'0p'v'
p' A
nqn
Projection of n0v via qvv’ and Aik versus collisional radiative modelling
v'p'n vib. resolved excitation and de-excitation
Triplet system d 3u Singlet system B 1u+
CR modelling is essentialCR modelling is essential
ground statepopulation
Tvib(X)
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Yacora for C2, CH, BH, … : collisional radiative modelling
Compilation of energy level diagrams and potential curvesCHCHA. Kalemos, A. Mavridis, A. Metropoulos
J. Chem. Phys. 111 (1990) 9536
C2C2
B.M. Smirnov, A.S. Yatsenko
Physics-Uspekhi 39 (1996) 2116
U, 104 cm-1 U, eV
Electronic states and optically allowed transitions
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Yacora for C2, CH, BH, … : collisional radiative modelling
Compilation of rate coefficients: CH
IPProgIPProgA Burgess, H P Summers, IPProg code,
Mon. Not. R. Astr. Soc. 174 (1976) 345
Validation and isotope investigationsValidation and isotope investigations
and measurements in laboratory plasmas
Discrepancies between data sourcesDiscrepancies between data sources
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Yacora for C2, CH, BH, … : collisional radiative modelling
IPProg for CH, C2
IPProg for CH, BH
Optically allowed transitions Excitation energy Statistical weights Transition probability
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Yacora for C2, CH, BH, … : collisional radiative modelling
Dissociative excitation for CH, C2
Direct excitation
CH + e CH* + e
C2 + e C2* + e
CH4 + e CH* + 3H + e
C2Hy + e CH* + CHx + e
C2Hy + e C2* + Hm + e
phCH
HC
CH
effHC XB
D
22
22
Particle flux Photon flux
phCH
CH
CH
effCH XB
D
4
4
Example: Photon efficiencies of CHExample: Photon efficiencies of CH
phCH
CH
CH
effCH XB
D
and/or
and/or
Dissociation modelling
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Yacora for hydrocarbons: dissociation modelling
Density ratios
C2 Swan radiationC2 Swan radiation
Direct excitationdominates
C2* ~ C2 ~ C2H2C2* ~ C2 ~ C2H2
Rate coefficients [m3/s]
CH A-X radiationCH A-X radiation
CH* ~ CH, CH4CH* ~ CH, CH4
Direct + dissociativeexcitation
… and collisional radiative modelling: effective rate coefficients
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Yacora for hydrocarbons: dissociation modelling
Dissociation model for hydrocarbons: model for methane
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)
Exchangeof data base
Exchangeof data base
Importance ofheavy particle collisions
Importance ofheavy particle collisions
Formation ofhigher hydrocarbons (ethane family)
Formation ofhigher hydrocarbons (ethane family)
H. Tahara et al., Jpn. J. Appl. Phys. 34 (1995) 1.
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Yacora for hydrocarbons: dissociation modelling
Dissociation model for hydrocarbons: model for methane
Check data bases (electron impact processes only)Check data bases (electron impact processes only)
CH4(t=0) = 1020 m-3, Te = 4 eV, ne = 1019 m-3
Janev&Reiter dataErhardt&Langer with Brooks data
Deviations by a factor of two
Formation of higher hydrocarbons is negligible
Deviations by a factor of two
Formation of higher hydrocarbons is negligible
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Yacora for hydrocarbons: dissociation modelling
Dissociation model for hydrocarbons: model for methane
Check data bases: electron impact processes and heavy particlesCheck data bases: electron impact processes and heavy particles
CH4(t=0) = 1020 m-3, Te = 4 eV, ne = 1019 m-3
Janev&Reiter dataErhardt&Langer with Brooks data
Different pattern for higher hydrocarbons
Factor of two difference in C2 formation
Different pattern for higher hydrocarbons
Factor of two difference in C2 formation
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Yacora for hydrocarbons: dissociation modelling
Dissociation model for hydrocarbons: model for methane
Importance of heavy particle collisions at low TeImportance of heavy particle collisions at low Te
CH4(t=0) = 1020 m-3, ne = 1019 m-3
Janev&Reiter data
Te = 4 eV Te = 2 eV
Less electron impact dissociationLess electron impact dissociation
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Yacora for hydrogen: dissociation modelling
Manifold of hydrogen species
Surface recombination
HH+
H2
Ionisation
Dissociation
Recombination
Charge exchange
Vibrational excitation
···
Relevance of vibrational excitation: resonant processes heavy particle collisions: formation of H3
+, H-,
H2(v), H2*
H, H*
H2+, H3
+, H+, Hˉ
H2(v), H2*
H, H*
H2+, H3
+, H+, Hˉ… Te = 2.5 eV, ne = 1017 m-3
Tvib = 3000 K, Tgas = 450 K, p = 10 Pa
Preliminary resultsPreliminary results
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Yacora for hydrogen: dissociation modelling
Consequences on population of atomic hydrogen: coupling to hydrogen species
H(n)
H
H+ H2+
H2
H-
eHH
eHH
eHH
eHH
eHH
nnpR
nnpR
nnpR
nnpR
nnpRpn
)(
)(
)(
)(
)()(
22
22
recombinationdissociativerecombination
dissociativeexcitation
effectiveexcitation
mutual neutralisationH־ + H+ H* + H
Collisional radiative and dissociation modellingCollisional radiative and dissociation modelling
Input data described in:D. Wünderlich, PhD ThesisUniversity of Augsburg (2004)
Max-Planck-Institutfür Plasmaphysik
Ursel Fantz CRP Meeting, 26-28 September 2005
Summary
Compilation and Extension of a Database for Systematic Studies on Diatomic Molecules
Tools availableTools available Already doneAlready done ProspectsProspects
TraDiMoH2, 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
CompilationCompilation ExtensionExtension Systematic studiesSystematic studies+ +