cnr - bari, italy from elementary processes to plasma modeling · 1st research coordination meeting...

1st Research Coordination Meeting onAtomic Data for Vapour Shielding in Fusion Devices

I.A.E.A. Vienna, March 2019

Roberto CelibertoRoberto Celiberto

From elementary processes

to plasma modeling

From elementary processes

to plasma modeling

Polytechnic of Bari, Italy Institute of NanotechCNR - Bari, Italy

Non-Boltzmann population

Non-Maxwellian electron energy distributionsfunction

Non-equilibrium low-temperature plasmas

State-to-state vibrational kinetics

Large sets of cross section data

Molecular plasmas

Vibrational kinetics of electronicallyexcited states in H2 discharges

The evolution of atmospheric pressure hydrogen plasmaunder the action of repetitively ns electrical pulse

Colonna et al., Eur. Phys. J. D (2017)

Input data===============================================Em/N = 200 Td;Pulse = 20 ns;Gas temperature = 1000 KGas pressure = 1 bar.Molar fractions:

===============================================

2

10

H10

eχ χ +

−= =9

H 2 10χ −= ⋅

3H H H0χ χ χ+ − += = =

H2/H STATE-TO-STATE KINETICS

Ground state vibrational kinetics

Ground state vibrational kinetics Atomic level kinetics

Electron impact induced processes

Molecular ion kinetics

Singlets vibrational kinetics

Triplets kinetics

Negative Ions kinetics cation kinetics

Updated model

H2/H STATE-TO-STATE KINETICS

The European Physical Journal D (2017), Vibrational kinetics of electronically excited states in H2 discharges

Colonna, G., Pietanza, L. D., D’Ammando, G., Celiberto, R., Capitelli, M., & Laricchiuta, A.

1

1

1

: , ’, ”

: ,*

, ’

g

g

B B B

C DY

D

+ Σ

Π=

3 3 3, ,u g ub a c+ +Σ Σ Π

+3H

✓ state-to-state

✓ radiative processes



✓ s ta te-to-s ta te

✓ ra dia tive proces s es

U. Fantz, D. Wünderlich, ADNDT (2006)



✓ state-to-state


✓ energy profile cross section

υ = 0

semiclassical IPM - R. Celiberto et al., ADNDT (2001)



1 1 12 2H ( , ) H ( , , ')g u uX v e B C v

+ +Σ + → Σ Π

1Bu+ C1Πu0→0

0→5

10→70→0

0→5

0→10

5→10

5→20Cro

ss s

ectio

n Å

2

Collision energy (eV)Collision energy (eV)

Ajello et al., Physical Review A (1984)

Wrkich et al., Journal of Physics B (2002)

υ = 0

✓ state-to-state


✓ energy profile cross sections

✓ accuracy

CCC approachM.C. Zammit et al., Physical Review Letters (2016)

BEf scalingTanaka et al. Reviews of Modern Physics (2016)

Kim, J Chem Phys (2007)



semiclassical IPM - R. Celiberto et al., ADNDT (2001)

Fast (ns-pulsed) discharges in hydrogenexcited state concentration

& singlets vibrational distributions



0 5 10 15 200

50

100

150

200

250

E0/

N (T

d)

time (ns)







… no quenching… no quenching

Fast (ns-pulsed) discharges in hydrogenFast (ns-pulsed) discharges in hydrogenhydrogen negative ion concentrationhydrogen negative ion concentration



no quenching

Dense plasmas

λD = [kBTe/(4πne)]1/2 is the Debye length

H+/H RESONANT CHARGE EXCHANGE in DEBYE PLASMAS

/ Dre

Ur

λ−

= −

H + H+ → H+ + H

Resonant charge exchange for H-H+ in Debye plasmas

A. Laricchiuta, G. Colonna, M. Capitelli1, A. Kosarim, and B. M. SmirnovEur. Phys. J. D (2017)

10–2 10–1 100 101 102

102

103

104

Ecmf [eV]

Cha

rge-

Exc

hang

e cr

oss

sect

ion

[a02 ]

1.4 a0

λD = ∞

3.0 a0

1.2 a0

0.9 a0

1.0 a0


ASYMPTOTIC APPROACH

Laricchiuta, A., Colonna, G., Capitelli, M., Kosarim, A., & Smirnov, B. M.. Resonant charge exchange for H–H+ in Debye plasmas

European Physical Journal D (2017).

H(1s) + H+

. Wu, J.G. Wang, P.S. Krstic, R.K. Janev, J. Phys. B 43, (2010)

10–2 10–1 100 101 102

102

103

104

Ecmf [eV]

Cha

rge-

Exc

hang

e cr

oss

sect

ion

[a02 ]

1.4 a0

λD = ∞

3.0 a0

1.2 a0

0.9 a0

1.0 a0


ASYMPTOTIC APPROACH vs QUANTUM

Laricchiuta, A., Colonna, G., Capitelli, M., Kosarim, A., & Smirnov, B. M.Resonant charge exchange for H–H+ in Debye plasmas


H(1s) + H+

10–2 10–1 100 101 102

102

103

104

Ecmf [eV]

Cha

rge-

Exc

hang

e cr

oss

sect

ion

[a02 ]

λD = ∞

0.9 a0

7.0 a0

λD = ∞

5.0 a0

4.6 a0 2pxy

1s

10–2 10–1 100 101 102

102

103

104

Ecmf [eV]

Cha

rge-

Exc

hang

e cr

oss

sect

ion

[a02 ]

λD = ∞

20 a0

λD = ∞

3dm=2

1s

11 a0

15 a0


EXCITED STATES H*

Laricchiuta, A., Colonna, G., Capitelli, M., Kosarim, A., & Smirnov, B. M.. Resonant charge exchange for H–H+ in Debye plasmas


n = 2, 3) + H+

2pm=1

Kinetic and divertor modeling

F. Taccogna, P. Minelli, D. Bruno, S. Longo, R. SchneiderChem. Phys. (2012)

Reduction of the Divertor Region to 1 Dimension

o Input data: - e/H+ density: np=1021 m-3

(detached divertor plasma condition) - e/H+ Temperature : Tp=5 eV

- B=1 Tesla; θ=85 °

o Simulation domain: l=0.3 mm

o Every Particle carries: - species: e, H+, H2+, H-; H, H2(X

1Σg+)

- axial position, velocities: (z, vx, vy, vz)

- quantities averaged over x,y (uniformity)

- quantum energy levels: - electronic: n=1s-3s for H

- vibrational: v=0-14 for H2

o Collision Methodology: - Plasma-Plasma (e+H2+/H-+H+/H-+e)

- Plasma-Neutral

- Neutral-Neutral relaxation (Vt/VT/VV)

o Boundary module:

- H2(v) wall relaxation-dissociation

- H wall recombinative desorption (ER/LH) -> H2(v) vibrational excitation (A-V)

- H+/H2+/ wall Auger neutralization -> H2(v) vibrational excitation (s-V)

Z

20

Particle-in-Cell / Direct Simulation Monte Carlo Model of Plasma-Gas Coupling in the Divertor Region (PIC-DSMC)

Calculation of force

acting on particles

Fi = Ei + vi x Bi

Solution of Poisson’s

equation

Φ, E

Plasma source and

boundary effects

ri, vi

Plasma parameters

np, vp, Tp, …

Particle collisions viDSMC

PIC

Integration of particle

motion equations

ri, vi

Plasma source and

boundary effects

ri, vi, H(n), H2(v)

Particle collisions vi

Gas parameters

ng, vg, Tg, …

e, H+ H2+

H(n=1-3)H2(X 1Σg

+ (v=0-14))

Results: Plasma

non-Maxwellianbehavior

agreement with probe measurement

bulkDistance from divertor plate z(mm)

E(eV)z(mm)

dens

ity (

m-3

)−1.6 −1.2 −0.8 −0.4 0

wall

z(mm)

−0.25 −0.2 −0.15 −0.1 −0.05 0 z (mm)

−0.2 −0.15 −0.1 −0.05 0 z (mm)

−0.2 −0.15 −0.1 −0.05 0 z (mm)

Results: Gas

− 0.25 −0.2 −0.15 −0.1 −0.05 0 z (mm)

Results: MAR processes

production of precursors peaks close to the walldue to high vibrational excitation H2(v)

−0.25 −0.2 −0.15 −0.1 −0.05 0z (mm)

−0.25 −0.2 −0.15 −0.1 −0.05 0z (mm)

a) e + H2(v) → H + H−, H− + H+ → H + Hb) H+ + H2 (v) → H + H2

+, H2+ + e → H + H

Aerospace Sciences

MotivationPlanet Speed

(km/s)Heat flux(kW/cm2)

Enthalpy(kJ/cm2)

Acceleration(g)

Jupiter 47.4 30 300 250

Saturn 26.9 1.3 257

Uranus 22.3 5.1 32.8

Modelling chemical kinetics and convective heating in giant planet entriesP. Reynier, G. D'Ammando, D. Bruno,Progress in Aerospace Sciences (2018)

Chemical input dataCross sections for all the processesincluded in the model.

Heavy particle collisionsH−He, He−He, H−–He, H–He+, He–HeH+–H, H+–H2, H+–He, H–H–, He–He2

+

H2–H2+

Electron interactionse-He, e-H, e-H2

Charged particle interactions

The code couples the fluid-dynamics with the kinetic chemistry (Jupiter atmosphere modeled: H2/He)

Fluid-dynamics input dataFlight data, i.e. probe velocity, gas density,gas temperature and pressure as a functionof the altitude in the atmosphere.

Processes

[1] D. Bruno et al., Transport properties of high-temperature Jupiter atmosphere components, Physics of Plasmas, 17(11) (2010) 112315.[2] G. Palmer, D. Prabhu, B. A. Cruden, Aeroheating uncertainties in Uranus and Saturn entries by the Monte Carlo method, Journal of Spacecraft and Rockets, 51(3) (2014) 801–814.

Tt(K) = translational tempe-rature along thestagnation line at 180km of altitude;

Tv(K) = vibrational tempe-rapture;

X(m) = distance from the probe.

Convective Heat Flux

Ph. Reynier, G. D'Ammando, D. Bruno, Review: Modelling chemical kinetics and convective heating in giant planet entries, Progress in Aerospace Sciences 96 (2018) 1–22.

Elementary processes

Heavy particle collisions

Electron-molecule collisions

Collision processes of heavy particles

Inelastic processesA+BC(v, j) → A+BC(v’, j’)

Reactive processesA+BC(v,j) → B+AC(v’, j’), C+AB(v’, j’)

DissociationA+BC(v, j) → A+B+C

Collision processes of heavy particles

Inelastic processesA+BC(v, j) → A+BC(v’, j’)

Reactive processesA+BC(v,j) → B+AC(v’, j’), C+AB(v’, j’)

DissociationA+BC(v, j) → A+B+C

The general philosophy is to use approximated methods for cross section calculations to reduce the computational load

Quasi-classical trajectory method

Relaxation of He+H2

Comparison of QCT with QM Close Coupling calculations

R. Celiberto, M. Capitelli, G. Colonna, G. D’Ammando, F. Esposito,R. Janev, V. Laporta, A. Laricchiuta, L. Pietanza, M. Rutigliano, and J. Wadehra, Atoms 5, 18 (2017).N. Balakrishnan, M. Vieira, J. Babb, A. Dalgarno, R. Forrey, and S. Lepp, ApJ 524, 1122 (1999).

QCTQM

Reaction of H+HeH+→He+H2+

Comparison of QCT with accurate QM calculations

F. Esposito, C.M. Coppola, and D. De Fazio,JPCA 119, 12615−12626 (2015).

Reaction of H+HeH+→He+H2+

Normalized computational load in QCT and QM calculations

F. Esposito, C.M. Coppola, and D. De Fazio,JPCA 119, 12615−12626 (2015).

Electron-molecule collisions

Non-resonant collisions

Resonant collisions

0.0

2.0

4.0

6.0

8.0

10

12

14

0 1 2 3 4 5 6 7 8

Pot

enti

al e

nerg

y (e

V)

Internuclear distance (a.u.)

H(1s) + H(1s)

H(n=2) + H -(1s2)

H��

(2Σ�� , �� )

Dissociative attachment: H + H−

Vibrational excitation

Resonant dissociation: H + H + e

H� + �

Resonant collisions

0.0

2.0

4.0

6.0

8.0

10

12

14

0 1 2 3 4 5 6 7 8

Pot

enti

al e

nerg

y (e

V)


H(1s) + H(1s)

H(n=2) + H -(1s2)

H��

(2Σ�� , �� )




H� + �

Resonant collisions

V��V��

�V��(R), V��

�(R) and Γ(R)

0.0

2.0

4.0

6.0

8.0

10

12

14

0 1 2 3 4 5 6 7 8

Pot

enti

al e

nerg

y (e

V)


H(1s) + H(1s)

H(n=2) + H -(1s2)

H��

(2Σ�� , �� )




H� + �

Resonant collisions

−ℏ

2�

�

��+ ��(�) +

�

2Γ(�) − ! � = −#$ (�)&' (�)−

ℏ�

2�

��

��+ ��(�) +

�

2Γ(�) − ! � = −#$%

(�)&'%(�)

V��V��

�V��(R), V��

�(R) and Γ(R)

0.0

2.0

4.0

6.0

8.0

10

12

14

0 1 2 3 4 5 6 7 8

Pot

enti

al e

nerg

y (e

V)


H(1s) + H(1s)

H(n=2) + H -(1s2)

H��

(2Σ�� , �� )




H� + �

Resonant collisions

V��V��

�V��(R), V��

�(R) and Γ(R)

CO, NO, N2, O2, CO2, H2, He2+, BeH, BeH+CO, NO, N2, O2, CO2, H2, He2+, BeH, BeH+

Bond length, R (a.u.)

Pot

enti

al e

nerg

y (e

V)

CF (X 1Σ+) 3Σ−

1Σ+

1∆

CF molecule

75 vibrational levels

Rozum, Mason & Tennyson,J. Phys. B (2013)

CF−

Bond length, R (a.u.)

Res

onan

ce w

idth

, Γ(R

)(e

V)

3Σ−

1Σ+1∆

CF molecule

Rozum, Mason & Tennyson,J. Phys. B (2013)

Energy (eV)

Cro

ss s

ecti

on (

Å2 )

vi= 0

CF (X 1Σ+;vi) + e → CF− ( 3Σ−, v’) → C + F−CF (X 1Σ+;vi) + e → CF− ( 3Σ−, v’) → C + F−

vi= 10 v

i= 40

vi= 20

CF molecule

Dissociative attachment

CF (X 1Σ+;vi) + e → CF− ( 1Σ+;v’) → CF (X 1Σ+;vf) + eCF (X 1Σ+;vi) + e → CF− ( 1Σ+;v’) → CF (X 1Σ+;vf) + e

0 = 0

0 = 10

0 = 400 = 20

Energy (eV)

Cro

ss s

ecti

on (

Å2 )

CF molecule

Resonant vibrational excitation

CF (X 1Σ+;vi) + e → CF− ( 1∆; v’) → C + F + eCF (X 1Σ+;vi) + e → CF− ( 1∆; v’) → C + F + e

vi= 0

vi= 10

vi= 40

vi= 20

Energy (eV)

Cro

ss s

ecti

on (

Å2 )

CF molecule

Dissociative excitation

Rat

e co

effi

cien

t(10

-9cm

3 ⋅s-1

)

Temperature (eV)

vi= 0

vi= 20

vi= 5

vi= 20v

i= 40

CF (X 1Σ+;vi) + e → CF− ( 3Σ−v’) → C + F−CF (X 1Σ+;vi) + e → CF− ( 3Σ−v’) → C + F−

CF molecule

Dissociative attachment

Rat

e co

effi

cien

t(10

-9cm

3 ⋅s-1

)

Temperature (eV)

0 → 0

CF (X 1Σ+;vi) + e → CF− ( 1Σ+v’) → CF (X 1Σ+;vf) + eCF (X 1Σ+;vi) + e → CF− ( 1Σ+v’) → CF (X 1Σ+;vf) + e

0 → 400 → 20

0 → 5

0 → 10

Resonant vibrational excitation

Rat

e co

effi

cien

t(10

-9cm

3 ⋅s-1

)

Temperature (eV)

vi= 0

vi= 10

vi= 5

vi= 20

vi= 40

CF (X 1Σ+;vi) + e → CF− ( 1∆) → C + F + eCF (X 1Σ+;vi) + e → CF− ( 1∆) → C + F + e

CF molecule

Dissociative excitation

CH + e− → CH* + e−

X 2Π(vi) → A 2∆(vi), B 2Σ−(vf) and C 2Σ+(vf)(R. Celiberto, R.K. Janev and D. Reiter, 2009)

BeH+ + e− → BeH+ * + e−

X 1Σ+(vi) → A 1Σ+ (vf), B 1Π (vf)(R. Celiberto, R.K. Janev and D. Reiter, 2012)

BeH + e− → BeH* + e−

X 2Σ+ (vi) → A 2Π (vf)(R. Celiberto, K.L. Baluja and R.K. Janev, 2013)

He(� + )� → He(

�* → He + He+ + )�

X 2Σ+ (vi) → A 2Σ+ (repulsive)(R. Celiberto, K.L. Baluja, R.K. Janev and V. Laporta, 2015)

Pot

enti

alen

ergy

(eV

)

R (a.u.)

Partridge & Langhoff, [J. Chem. Phys. (1981)]

Tung et al, [J. Chem. Phys. (2011)]

A 1Σ+

X 1Σ+

Trans. dipole moments (Partridge & Langhoff)

e + LiH (X 1Σ+,v) → e + LiH (A1Σ+,v)e + LiH (X 1Σ+,v) → e + LiH (A1Σ+,v)

LiH molecule

Antony_et_al; R-matrix (2004)

Born-Bethe approximation

TMMM approximation

X (v = 0) → A (v’ = 0)

Cro

ss s

ecti

on(Å

2 )

Energy (eV)

TMMM = Threshold ModifiedMott-Massey

BeH

0.0

2.0

4.0

6.0

8.0

10

12

14

16

2 4 6 8 10 12 14 16

Cro

ss s

ecti

on (

Å2 )

Energy (eV)

Born

R-matrix

TM MM

X(0)→A(0)

R Celiberto,K L Baluja& R K JanevPlasma Source Science & Technology, 2013

Cro

ss s

ecti

on(Å

2 )

Energy (eV)

0 → 0

0 → 10

0 → 20

X (0 ) → A (v’)

10 → 27

10 → 20

10 → 10

Cro

ss s

ecti

on(Å

2 )

Energy (eV)

X (10 ) → A (v’)

20 → 27

20 → 25

20 → 20

Cro

ss s

ecti

on(Å

2 )

Energy (eV)

X (20 ) → A (v’)

M. Capitelli – Università di Bari,Italy

D. Bruno – CNR, ItalyG. Colonna – CNR, ItalyA. D’Angola – Università della

Basilicata, ItalyF. Esposito – CNR, ItalyV. Laporta – CNR, ItalyA. Laricchiuta – CNR, ItalyP. Minelli – CNR, ItalyF. Taccogna – CNR, Italy

K. Baluja – Dely University, IndiaR. K. Janev – Macedonian Academy of

Science, MacedoniaI. Schneider – University of Pari Sud, France J. Tennyson – University College, UKJ. M. Wadehra – Wayne State University, USA

cnr - bari, italy from elementary processes to plasma modeling · 1st research coordination meeting...

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