Max-Planck-Institut für Plasmaphysik CRP on ‘Atomic and Molecular Data for Plasma Modelling’,...

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)



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




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




Franck-Condon factors: X 1g+ → d 3u

v

v‘




Transition probabilities: d 3u → a 3g+

v‘‘

v‘




Transition probabilities for bound to free transitions: a 3g+ → b 3u

+

Isotope shiftsIsotope shifts

Continuum radiationContinuum radiation



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)



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




Potential curves: CH and BH

Polynomial fits Polynomial fits

CHCH BHBH




Franck-Condon factors: X 2 - A 2

Isotope shiftsIsotope shifts

CHCH CDCD

CTCT




Transition probabilities: X 2 - A 2 CHCH

CH: = 540 ns measured valueAik= 1.85106 s-1



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



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




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)




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)



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




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




IPProg for CH, C2

IPProg for CH, BH

Optically allowed transitions Excitation energy Statistical weights Transition probability




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



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




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.





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





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





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



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



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)



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+ +

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