state-to-state kinetics of molecular and atomic hydrogen ... · state-to-state kinetics of...

IAEA TECHNICAL MEETING: SECOND MEETING OF THE INTERNATIONAL CODE CENTRES NETWORK

27–28 SEPTEMBER 2010, IAEA HEADQUARTERS, VIENNA, AUSTR I A

State-to-State Kinetics ofMolecular and Atomic Hydrogen Plasmas

MARIO CAPITELLI

Department of Chemistry, University of Bari (Italy)CNR Institute of Inorganic Methodologies and Plasmas Bari (Italy)



MOLECULARDYNAMICS

KINETICMODELS

FLUID DYNAMICS

state-resolvedelementary process probability

non-equilibrium distributionson internal degrees of freeedom



MOLECULAR DYNAMICS

electron-impactinduced processes

atom-moleculecollision processes

gas-surfaceinteraction processes

KINETICMODELS

FLUID DYNAMICS





ELECTRON-IMPACT INDUCED PROCESSES

PROCESSES vibronic excitation direct dissociation

THEORETICAL APPROACHES semiclassical impact parameter method similarity function approach

INPUT DATA molecular potential of involved electronic states transition moment Born high-energy cross section value

DYNAMICAL INFORMATION energy and vibrational dependence of cross sections (complete set) isotopic effect investigation state-resolved and macroscopic rate coefficients radiative-decay vibrational excitation cross sections (EV)

FEATURES satisfactory accuracy (agreement with experimental data within the error of other methods) low computational load (except in the ab-initio step) suitable only for dipole-allowed transitions no treatment of resonances

Adamson et al., Chem. Phys. Lett., 436 (2007)



GAMESS(General Atomic and Molecular

Electronic Structure System )

IMPACTCross Section

FAUSTBORN Cross Section

DYNAMIC CALCULATIONsolution of the radialSchroedinger equation forquantum vibrational levelsand estimation of structural anddynamical factors (evaluation ofintegrals)

AB-INITIO CALCULATIONpotentials, transition dipolemoments and GOS(Multi ReferenceConfiguration Interaction)

Radiative-DecayVibrational Excitation

maxwellianeedf distribution

Einstein coeffsof spontaneousemission

Rate Coefficients

INTERFACING SCHEME of DIFFERENT CODES



GAMESS(General Atomic and Molecular

Electronic Structure System )

IMPACTCross Section

FAUSTBORN Cross Section

DYNAMIC CALCULATION

AB-INITIO CALCULATION

maxwellianeedf distribution

Rate Coefficients

SIMILARITYAPPROACHCross Section

rapid estimation ofcross sections fromoscillator strengthand transition energy




X 1Σg (νi=0) → B 1Σu X 1Σg (νi=0) → C 1Πu

Impact Parameter MethodCeliberto 2001

recommended valuesItikawa 2008

similarity approach


recommended valuesItikawa 2008

similarity approach

D’Ammando, in preparationItikawa et al., J. Phys. Chem. Ref. Data, 37 (2008)Celiberto et al., ADNDT, 77 (2001)

electron-impact induced VIBRONIC EXCITATION CROSS SECTIONS for H2comparison of different approaches



X 1Σg (νi) → B 1Σu


similarity approach

VIBRATIONALLY-RESOLVED CROSS SECTIONS for H2



X 1Σg (νi) → C 1Πu


similarity approach

VIBRATIONALLY-RESOLVED CROSS SECTIONS for H2



PROCESSES dissociative attachment resonant vibrational excitation (eV processes)

THEORETICAL APPROACH local resonance theory

INPUT DATA molecular potential of involved electronic states resonance characterization (width and energy dependence)

DYNAMICAL INFORMATION angular, energy and vibrational dependence of cross sections (complete set) isotopic effect investigation

FEATURES excellent agreement with experimental data resonable computational load

RESONANT PROCESSES in e- H2 collisions



LIVX

Calculation of complete rovibrational ladders

relative to all the possible reactants/products,

including quasibound states by WKB method

DINX

Quasiclassical dynamics of atom-diatom collision

processes. Distribution of computations on a wide

computational grid with periodic check of results,

automatic re-calculations for uncompleted jobs and

collection of good ones

PES from literature

ATOM-MOLECULE COLLISIONS: from PES to complete sets of rovibrationalCROSS SECTIONS and RATES



QCTX

Trajectory analysis and cross section results for

reactive and non-reactive processes as well as

dissociation. The quasibound states are here

considered as bound states. Various reactant and

product weight functions can be used to analyze the

trajectory results

XRATE

From translational energy dependent rovibrational cross

sections to rate coe fficient. This module includes the

possibility of selecting and mixing rate coe fficients on

the base of lifetime of initial/final states and of the level

of detail requested (e.g. total thermal rate, sum of rates

on final rotation, dissociation summed to state-to-state

rate coefficients with low lifetime, etc.)

Recombination can be obtained

in this module by two methods:

detailed balance applied to

dissociation rates and

orbiting resonance applied to

rovibrational state-to-state rates



the two mechanisms can be used in a complementaryway, by choosing accurately the states involved in thecalculations

a detailed database of rate coefficients including initialand final rotation and state selected dissociation forH+H2 collision process is necessary

Two possible mechanisms: orbiting resonance theory and directthree body recombination (by detailed balance of dissociation data)

TERMOLECULAR HYDROGEN RECOMBINATION



normalized recombination vsfinal vibrational quantum number

recombination rates vsfinal rotational quantum number

Esposito&Capitelli J. Phys. Chem. A 133 (2009)

TERMOLECULAR HYDROGEN RECOMBINATION



PES used:L.P. Viegas, A. Alijah & A.J.C. Varandas, J. Chem. Phys. 126 (2007)

couplings calculated from the potential matrix, withparticular care for sign consistency of eigenvectorsEsposito, in preparation

a vibrationally detailed database of rate coefficientsshould be calculated, using trajectory surface hopping,including initial/final rotation and dissociationEsposito, in preparation

ION-MOLECULE COLLISION PROCESSES

comparison between cross sectionsobtained by DSM (Downhill SimplexMethod - full lines) and by QCT (QuasiClassical Trajectory - symbols)

This method is useful when, for a given chemical process, there are not cross sections data, but there are informationabout rate coefficients in a given range of temperatures (Minelli, to be published). The only data required are a goodfunctional form for cross section and a temperature dependent rate. The reference rate coefficients are input to astandard nonlinear optimization algorithm (Downhill Simplex Method, DSM (Nelder and Mead, Computer Journal 7(1965)) to give reconstructed cross sections that satisfy a convergence criterion.

Case study to test methoddissociation of the hydrogen molecule by atom impact

Experimental or TheoreticalRate Coefficients Cross Sections

deconvolution

DECONVOLUTION of temperature-dependent RATE COEFFICIENTSto energy-dependent CROSS SECTIONS



MOLECULAR DYNAMICS for GAS/SURFACE INTERACTION PROCESSES



ISOTOPIC EFFECT: H/D RECOMBINATION on GRAPHITE

ionsources

plasma-walltransition

electrostaticprobe

laser-inducedplasma

hypersonicplasma flow

Electric thrusters Negative ion sources Plasma shock tube

Divertor region Sheath physics: - see - instability - electronegativity

Ion collection Electron collection Dusty

LIBS Under-water cavitation bubble dynamics

MHD bow shock Space charge region

fluid models (CFD,MHD,SPH)kinetic models (Vlasov, PIC-MCC)

PLASMA NUMERICAL EXPERIMENTS



0

10000

20000

30000

40000

50000

-3 -2 -1 0 1 2 3 4 5

Gas T

em

pera

ture

(K

)

spatial coordinate x (m)

x=0 shock front

upstream

T1 = 5000 K

P1 = 10

-2 atm

u1 = 5

downstream

T2(x=0) > T

1

P2 (x=0)> P

1

u2 (x=0)< u

1

x = 1.6 m x = 3.1 m

10-4

10-3

10-2

10-1

100

101

-3 -2 -1 0 1 2 3 4 5

Mola

r F

ractions

spatial coordinate x(m)

H

H+ - e

-

thick! = 0

thin! = 1

Euler Equations

Radiative Transfer Equation

CR Master &Electron Boltzmann Equations

H2 kinetics

ATOMIC HYDROGEN under SHOCK WAVE



10-13

10-11

10-9

10-7

10-5

10-3

10-1

0 2 4 6 8 10 12 14

x(m) = 1.6

Ni /(

NH g

i)

level energy (eV)

! = 1

Ne = 1.20 10

13 cm

-3

NH = 5.44 10

16 cm

-3

Nn=2

= 3.32 1010

cm-3

!=0

Ne = 1.30 10

15 cm

-3

NH = 3.32 10

17 cm

-3

Nn=2

= 2.02 1011

cm-3

10-17

10-15

10-13

10-11

10-9

10-7

10-5

10-3

10-1

0 5 10 15 20 25 30

x(m) = 1.6

eedf (e

V-3

/2)

electron energy (eV)

!=0

Ne = 1.30 10

15 cm

-3

NH = 3.32 10

17 cm

-3

Nn=2

= 2.02 1011

cm-3

! = 1

Ne = 1.20 10

13 cm

-3

NH = 5.44 10

16 cm

-3

Nn=2

= 3.32 1010

cm-3

10-18

10-16

10-14

10-12

10-10

10-8

10-6

10-4

10-2

100

0 5 10 15 20 25 30

x(m) = 3.1

ee

df

(eV

-3/2

)

electron energy (eV)

! = 1

Ne = 1.88 10

15 cm

-3

NH = 2.54 10

17 cm

-3

Nn=2

= 7.52 1010

cm-3

! = 0

Ne = 7.64 10

14 cm

-3

NH

= 3.43 1017

cm-3

Nn=2

= 9.99 1010

cm-3

10-10

10-8

10-6

10-4

10-2

100

0 2 4 6 8 10 12 14

x(m) = 3.1

Ni /(

NH g

i)

level energy (eV)

! = 0

Ne = 7.64 10

14 cm

-3

NH

= 3.43 1017

cm-3

Nn=2

= 9.99 1010

cm-3

! = 1

Ne = 1.88 10

15 cm

-3

NH = 2.54 10

17 cm

-3

Nn=2

= 7.52 1010

cm-3

x = 1.6 m x = 1.6 m

x = 3.1 mx = 3.1 m



1000

10000

100000

-2 -1 0 1 2 3 4 5

TGAS

(K)

TH[0-1]

Te-

Te

mp

era

ture

(K

)x [m]

!

S" = j" /#"

!

S" = B" (T )

Source function isthe ratio of emissivity

over absorption coefficient

at equilibriumequals the blackbody intensity

upstream condition

P1=10-2atmT1=1000Ku=20

non-equilibrium distributionsof spectral quantities

LOCAL SOURCE FUNCTIONoptically thin plasma (λ=1)

10-10

10-9

10-8

10-7

10-6

0 2 4 6 8 10 12 14 16

Sn=je

n/k

n

Bn(T)

E [ev]

B(T

) and je

!/k! [J

m-2

s-1sr

-1H

z-1]

(5)T=12775 K

10-9

10-8

10-7

10-6

10-5

0 2 4 6 8 10 12 14 16

S!=je

!/"

!

B!(T)

B(T

) and je

!/k! [J

m-2

s-1sr

-1H

z-1]

E [ev]

T=17817 K(4)

x = 3.29mTgas = 17817 K

10-10

10-9

10-8

10-7

10-6

0 2 4 6 8 10 12 14 16

Sn=je

n/k

n

Bn(T)

B(T

) and je

!/k! [J

m-2

s-1sr

-1H

z-1]

E [ev]

(6)T=11461 K

x = 3.28mTgas = 12775 K

x = 3.30mTgas = 11461 K

x=0 shock front

Tgas (K)

Telectrons (K)

TH[1-2] (K)

Capitelli et al., J. Phys. B, 43 (2010)



MOLECULAR DYNAMICS

KINETICMODELS

FLUID DYNAMICS



electron-impactinduced processes

atom-moleculecollision processes

gas-surfaceinteraction processes

TRANSPORTTHEORY

transportproperties

collisionintegrals

THERMODYNAMICS



THERMODYNAMIC PROPERTIES of multicomponent plasmasincluding Debye-Hückel correction

SIMPLIFIED TWO and THREE-LEVEL PARTITION FUNCTION

ATOMIC HYDROGEN LEVELS in a BOX in the presence of Coulomband Debye-Hückel potentials

THERMODYNAMIC PROPERTIES



• the method is based on the idea of combining a multitude of atomic energy levels into two or threegrouped levels. The partition function for atomic hydrogen can be approximated as

• the method has been applied to many atomic and ionic systems

D’Ammando et al., Spectrochim. Acta B, 65 (2010)

SIMPLIFIED TWO-LEVEL PARTITION FUNCTION

nmax =100nmax =10



Capitelli&Giordano, Physical Review A, 80 (2009)

n

box radius = 103 ao

Bohr atomparticle in a spherical box

ENERGY LEVELS for ATOMIC HYDROGEN in a SPHERICAL BOX

Coulomb potential

screened Coulombpotential (Debye length = 102 ao)



DATABASE OF TRANSPORT CROSS SECTION and COLLISIONINTEGRALS for He-H2 interactions in a wide temperature range [100-50000 K]

EFFECT OF MAGNETIC FIELD (tensorial reformulation)

EFFECT OF ELECTRONICALLY EXCITED STATES (EES)

Bruno et al., Physics of Plasmas (2010) in press

TRANSPORT PROPERTIES



OMEGA

CHAPMAN-ESKOGCODE

TRANSPORT PROPERTYCALCULATION

solution of a system of linearequations algebraic equations oforder n*K, n being the numberof species and K theorder of approximation of theexpansion in Sonine polynomials

DYNAMICAL CALCULATION

classical collision integrals forelastic collision between speciesfrom (accurate, model orphenomenological) interactionpotentials

HIERARCHICAL CODE

calculation of the species-concentrationas a function of temperature

heat flux &diffusion




ground-state collisionintegrals

including EEScollision integrals

Bruno et al., Physics of Plasmas 14 (2007)

INTERNAL CONDUCTIVITY for HYDROGEN PLASMA including EES

state-to-state kinetics of molecular and atomic hydrogen ... · state-to-state kinetics of...

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