E LEMENTARY P ROCESSES, T HERMODYNAMICS AND T RANSPORT OF H 2, O 2 AND N 2 P LASMAS

CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING” VIENNA, NOVEMBER 2008

M. CAPITELLI

CNR IMIP BARI – ITALY

DEPT OF CHEMISTRY, UNIVERSITY OF BARI – ITALY

ELEMENTARY PROCESSES, THERMODYNAMICS AND TRANSPORT OF

H2, O2 AND N2 PLASMAS


C.GORSE, S.LONGO, P.D IOMEDE, C.CATALFAM O, G.D’AMMANDO, M.C.COPPOLA Department of Chemistry, University of Bari, Bari , Italy

D.BRUNO, G.COLONNA, O.DE PASCALE, F.ESPOSITO, A.LARICCHIUTA

M.CACCIATOR E, M.RUTIGLIANO

IMIP(CNR), Bari, Bari, Italy

R.CELIBERT O

Department of Water Engineering an d Chemistry Polytechnic of Bari, Bari, Italy

COLLABORATORs


a) photodissociation of H2(), D2(), HD() and H2+()

b) heavy particle collision cross sections : H2(), D2() from recombinationc) H2() formation on graphited) heavy particle collision cross sections for O-O2 and N-N2 : fitting relationsd) collision integrals for O-O and O-O+ interactionse) collision integrals for N-N and N-N+ interactions: a phenomenological

approach

a) thermodynamic properties of atomic hydrogen plasmab) transport properties of atomic hydrogen plasma: cut-off criteriac) negative ion source modeling

ELEMENTARY PROCESSES

OUTLINE

THERMODYNAMICS, TRANSPORT AND KINETICS OF PLASMAS


PHOTODISSOCIATION PROCESSES for H2(), D2(), HD() and H2+()

• LYMAN and WERNER SYSTEMS• HIGH-ENERGY EXTRAPOLATION for STATE-DEPENDENT CROSS SECTIONS• derivation of

• STATE-DEPENDENT PHOTODISSOCIATION RATE COEFFICIENTS• MACROSCOPIC PHOTODISSOCIATION RATE COEFFICIENT (ktot) • FITTING FORMULAS


D.R.G. Schleicher et al. Astronomy&Astrophysics 490 (2008) 521

10-5

10-3

10-1

101

103

105

107

103 104

TEMPERATURE [K]

i=0

ktot

10-5

10-3

10-1

101

103

105

107

103 104

TEMPERATURE [K]

i=0

ktot

10-5

10-3

10-1

101

103

105

107

103 104

TEMPERATURE [K]

i=0

ktot

MACROSCOPIC PHOTODISSOCIATION RATE COEFFICINTS for H2() and H2

+() : COMPARISON with LITERATURE

H2() LYMAN H2() WERNER

H2+()


HEAVY PARTICLE COLLISIONSVIBRATIONALLY EXCITED MOLECULES FROM RECOMBINATION

• QCT SIMULATION

• RECOMBINATION RATE COEFFICIENTs

• from QCT DISSOCIATION by DETAILED BALANCE THREE-BODY RECOMBINATION

• from RBC (Roberts, Bernstein & Curtiss) THEORY TWO-STEP BINARY COLLISION

Potential Energy

Internuclear Distance

rotational barrier

quasi-bound state


T = 1,000 K T = 300 K

10-35

10-34

10-33

10-32

0 2 4 6 8 10 12 14

VIBRATIONAL QUANTUM NUMBER

detailed balance

RBC theory

10-36

10-35

10-34

10-33

10-32

10-31

10-30

0 2 4 6 8 10 12 14

VIBRATIONAL QUANTUM NUMBER

detailed balance

RBC theory

H2() FROM RECOMBINATION


O2(), N2() FROM RECOMBINATION

O2 N2


ATOMIC RECOMBINATION on GRAPHITE SURFACEH2 (, j) NASCENT DISTRIBUTIONs

• SEMI-CLASSICAL MODEL• ELEY-RIDEAL MECHANISM (H CHEMISORBED at the SURFACE with a chemisorption well of 0.52eV )• PROBABILITIES dependence on

• SURFACE TEMPERATURE• IMPACT ENERGY• ISOTOPES

SURFACE TEMPERATURE=500 K ENERGY = 0.07 eV

M.RUTIGLIANO, M.CACCIATORE, CHEM.PHYS.CHEM. 9 (2008) 171

vibrational distribution is obtained summing up population

of rotational levels


HEAVY PARTICLE COLLISION CROSS SECTIONS for O-O2 and N-N2 SYSTEMSFITTING RELATIONS

• ACCURATE QCT CROSS SECTIONS for• VIBRATIONAL DEACTIVATION VT processes• DISSOCIATION

F.ESPOSITO, I.ARMENISE, G.CAPITTA, M.CAPITELLI, CHEM.PHYS 351 (2008) 91

fitting bidimensional

relations

EASY INCLUSION in KINETIC MODEL

TEMPERATURE

RA

TE

CO

EF

FIC

IEN

T [

cm3 s

-1]

TEMPERATURE

RA

TE

CO

EF

FIC

IEN

T [

cm3 s

-1]

i=30

i=40

i=46

i=010

20

30


COLLISION INTEGRALS for O-O and O-O+ INTERACTIONS involving LOW-LYING EXCITED STATES

SCHEME OF CLASSICAL APPROACH

ab-initio INTERACTION POTENTIALSfor molecular (atom-atom)

or molecular ion (atom-ion) states

exchange cross sectionsQex

DEVOTO formula

splitting gerade-ungerade

orasymptoticapproach

ELASTIC COLLISIONS

Morse interpolation(bound states)

exponential interpolation(repulsive states)

Smith&Munntabulated collision integrals

Kalinin&Dubrovitskiiformulas

Ω(1,1)( )nΩ(2,2)

( )n

averaging procedure

Ω(2,2)

[(Ω(1,1))2 + (Ω(1,1))2]1/2el ex

INELASTIC COLLISIONS excitation or charge exchange

Ω(1,1)

= 1/2[ - ( )]Q C D ln g2ex

Ω( , )s= € l Σ w Ω( ,s)(n) (n) € lΣ w(n)

viscosity-typecollision integrals

diffusion-typecollision integrals


A.LARICCHIUTA, D.BRUNO, M.CAPITELLI, R.CELIBERTO, C.GORSE, G.PINTUS, CHEM.PHYS.LETT. 344 (2008) 13

EFFECTIVE DIFFUSION-TYPE COLLISION INTEGRALSfor O-O+ INTERACTIONS involving LOW-LYING EXCITED STATES

ELASTIC CONTRIBUTION from POTENTIALS andINELASTIC CONTRIBUTION from CHARGE-EXCHANGE CROSS-SECTIONS


A PHENOMENOLOGICAL MODEL forHEAVY PARTICLE COLLISION INTEGRALS

CLASSICAL COLLISION INTEGRALS

INTERACTION POTENTIAL

PHENOMENOLOGICAL APPROACHAVERAGE INTERACTION

fitting formulas up to (4,4) orderA. LARICCHIUTA, G.COLONNA et al. Chemical Physics Letters 445 (2007) 133

“tuplet” ( ) characterising the colliding system


PHENOMENOLOGICAL APPROACH

ION-NEUTRAL4

6

INTERACTION POTENTIAL FEATURES

correlation formulas from physical properties of colliding partnersPOLARIZABILITY, CHARGE and

NUMBER of ELECTRONS EFFECTIVE in POLARIZATION

F.PIRANI et al. International Review in Physical Chemistry 25 (2006) 165

NEUTRAL-NEUTRAL

PREDICTION of POTENTIAL PARAMETERfor UNKNOWN SYSTEMS

hard interactionssoft interactions


3 100

4 100

5 100

6 100

7 100

8 100

9 100

101

1000 10000

O(3P)-O(1D)

O(1D)-O(1D)

O(3P)-O(1S)

O(1D)-O(1S)

O(1S)-O(1S)

TEMPERATURE [K]

COLLISION INTEGRALSCOMPARISON between CLASSICAL and PHENOMENOLOGICAL APPROACHES

LARICCHIUTA et al. (2008)

CAPITELLI et al. (1972)

phenomenological approach


INELASTIC (CHARGE TRANSFER) DIFFUSION-TYPE COLLISION INTEGRALs for N*-N+ INTERACTIONs

involving HIGH-LYING EXCITED STATES

Dependence of diffusion-type collision integrals for the interaction N+(3P)-N on the principal quantum number of the atom valence shell electrons, n, at T=10,000 K (different electronic states of N, arising

from the same electronic configuration have been considered. n=2 N(2p3 4S,2D,2P), n=3 N(2p23s 2P,4P;), n=4 N(2p24s 2P,4P;), n=5 N(2p25s 2P,4P;)


0.0

10.0

20.0

30.0

40.0

50.0

60.0

0.0 1.0 2.0 3.0 4.0 5.0

ELECTRONIC LEVEL EIGENVALUE [eV]

inelastic

elastic

effective

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

0.0 1.0 2.0 3.0 4.0 5.0

ELECTRONIC LEVEL EIGENVALUE [eV]

inelastic

elastic

effective

EFFECTIVE DIFFUSION-TYPE COLLISION INTEGRALSfor N-N+ INTERACTIONS involving LOW-LYING EXCITED STATES

ELASTIC CONTRIBUTION from PHENOMENOLOGICAL POTENTIALS andINELASTIC CONTRIBUTION from CHARGE-EXCHANGE CROSS-SECTIONS

T = 10,000 K


a) photodissociation of H2(), D2(), HD() and H2+()

b) heavy particle collision cross sections : H2(), D2() from recombinationc) H2() formation on graphited) heavy particle collision cross sections for O-O2 and N-N2 : fitting relationsd) collision integrals for O-O and O-O+ interactionse) collision integrals for N-N and N-N+ interactions: a phenomenological

approach

a) thermodynamic properties of atomic hydrogen plasmab) transport properties of atomic hydrogen plasma: cut-off criteriac) negative ion source modeling


OUTLINE



• (curve a) energy levels from the Debye-Hückel potential [23]

• (curve b) energy levels from the Coulomb potential

• (curve c) only hydrogen ground state (fH= 2, cp,int(H)=0).

For curves a and b the number of l evels is truncated by using the Griem cut-off, calculatedself-consistently with the plasma composition.

THERMODYNAMIC PROPERTIES for ATOMIC HYDROGEN PLASMA

M. Capitelli, D. Giordano, G. ColonnaThe role of Debye-Hückel electronic energy levels on the thermodynamic properties of hydrogen plasmas including isentropic coefficientsPhysics of Plasmas 15(8) (2008) 082115


Internal partition function Internal specific heat


internal state contribution

reaction contribution

CONTRIBUTION TO SPECIFIC HEAT

Frozen Specific Heat Reactive Specific Heat


HYDROGEN MIXTURE ISENTROPIC COEFFICIENT

Total Frozen


GROUND STATE METHODS

DEBYE HÜCKEL CRITERION

CONFINED ATOM APPROXIMATION

internal energy = 0

particle density

IN ANY CASE

DRASTICALLY DECREASES

INCREASING PRESSURE

or ELECTRON DENSITY!!!

TRANSPORT PROPERTIES for ATOMIC HYDROGEN PLASMA : CUT-OFF CRITERIA


1018

1020

1022

1024

1026

1 104

2 104

3 104

4 104

5 104

nH

, m

-3

Temperature, K

p=1000atm

p=1atm

p=100atm

EFFECT of DIFFERENT CUT-OFF CRITERIA on ATOMIC HYDROGEN NUMBER DENSITY

GROUND-STATE

DEBYE-HUCKEL

CONFINED-ATOM

Trampedach et al. Astrophys. J. (2006)


10

0

10

1

10

2

10

3

10

4

10

5

1 10

4

2 10

4

3 10

4

4 10

4

5 10

4

Temperature, K

H

+

-H(n=12)

H

+

-H(n=6)

H

+

-H

+

(1atm)

H

+

-H

+

(1000atm)

H

+

-H(n=1)

H

+

-H

+

(100atm)

σ

2

Ω

(1,1)*

, A

2

10

0

10

1

10

2

10

3

1 10

4

2 10

4

3 10

4

4 10

4

5 10

4

Temperature, K

σ

2

Ω

(2,2)*

, A

2

H

+

- ( =12)H n

H

+

- ( =6)H n

H

+

- ( =1)H n

H

+

-H

+

(1000 )atm

H

+

-H

+

(100 )atmH

+

-H

+

(1 )atm

DIFFUSION-TYPE COLLISION INTEGRALS VISCOSITY-TYPE COLLISION INTEGRALS

COLLISION INTEGRALs for H(n)-H+ INTERACTIONs compared withCOULOMB COLLISION INTEGRALs


• case USUAL EES considered as independent chemical species BUT EES collision integrals set equal to

ground state ones

• case ABNORMAL EES considered as independent chemical species withtheir own collision integrals


0

1

2

3

4

5

6

1 10

4

2 10

4

3 10

4

4 10

4

5 10

4

Temperature, K

λ

h

, / *W m K

=1000p atm

=1p atm

=100p atm

0 10

0

5 10

-5

1 10

-4

1,5 10

-4

2 10

-4

1 10

4

2 10

4

3 10

4

4 10

4

5 10

4

η

, /( * )Kg m s

, Temperature K

=1000p atm

=1p atm

=100p atm

EFFECT of DIFFERENT CUT-OFF CRITERIA on TRANSPORT PROPERTIES of HYDROGEN PLASMA

including ABNORMAL TRANSPORT CROSS SECTIONs for EES

HEAVY PARTICLE THERMAL CONDUCTIVITY VISCOSITY

GROUND-STATE

DEBYE-HUCKEL

CONFINED-ATOM

D. Bruno, M. Capitelli, C. Catalfamo, A. Laricchiuta Physics of Plasmas (2008) in press


0

1

2

3

4

5

6

1 10

4

2 10

4

3 10

4

4 10

4

5 10

4

λ

r, / *W m K

, Temperature K

=1p atm

=100p atm

=1000p atm

EFFECT of DIFFERENT CUT-OFF CRITERIA on TRANSPORT PROPERTIES of HYDROGEN PLASMA

including ABNORMAL TRANSPORT CROSS SECTIONs for EES

GROUND-STATE

DEBYE-HUCKEL

CONFINED-ATOM

0 10

0

2 10

-1

4 10

-1

6 10

-1

8 10

-1

1 10

0

0 10

0

5 10

-2

1 10

-1

1,5 10

-1

2 10

-1

1 10

4

2 10

4

3 10

4

4 10

4

5 10

4

λ

int

, / * W m K CA

λ

int

, / * W m K SCCP

, Temperature K

=1000p atm

=100p atm

=1p atm

REACTIVE THERMAL CONDUCTIVITY INTERNAL THERMAL CONDUCTIVITY


3 CRITICAL AREAS (“remote” source)• Source chamber (driver): ICP (transformer) heating at high RF power No sheath losses Hot electrons• Expansion region: H2 vibrational excitation• Extraction region: Magnetic filtering Cold electrons H- production (surface/volume) Electron removal

Length 0.35 m

Radius 0.2 cm

Input Power 170 kW

Current coil 100 A

Frequency 1 MHz

Pressure 0.6 Pa

Max magnetic field 160 G

Extraction grid potential -20 kV

RF-ICP NEGATIVE ION SOURCE


10-19

10-17

10-15

10-13

10-11

10-9

10-7

10-5

0,001

0,1

0 2 4 6 8 10 12 14

H2

(v) VDF

Vibrational level v

Boltzmann Tg VDF

€

Nv = N 1 − e−E v / k BTg

[ ]e−E v / k BTg

€

Ev = hω(v +1 / 2) − hωxe (v +1 / 2)2H2(v)

vibrational distribution function

(*) J. R. Hiskes et al., J. Appl. Phys. 53(5), 3469 (1982)(**) O. Fukumasa, K. Mutou, H. Naitou, Rev. Sci. Instrum. 63(4), 2693 (1992)

1015

1016

1017

1018

1019

1020

0 3 6 9 12 15

(eV + EV)(eV + EV) + AV(eV + EV) + AV + sV(eV + EV) + AV + sV + (Vt + VT)

vibrational distribution function (m

-3 )

vibrational level v

EXPANSION REGION: H2() EXCITATION

H2()VIBRATIONAL

DISTRIBUTION FUNCTION


FUTURE PERSPECTIVEs

a) elementary gas-phase processes involving Caesium b) direct approaches for gas-phase recombination

c) H2() formation on caesiated surfacesd) approaches for collision integral calculation

of highly excited states interactions

a) transport properties of air plasma with electronically excited statesb) transport of radiation

c) negative ion source modeling improvements



Documents

E LEMENTARY P ROCESSES, T HERMODYNAMICS AND T RANSPORT OF H 2, O 2 AND N 2 P LASMAS