From elementary processes From elementary processes to plasma - - PowerPoint PPT Presentation

1st Research Coordination Meeting on Atomic Data for Vapour Shielding in Fusion Devices I.A.E.A. Vienna, March 2019

Roberto Celiberto Roberto Celiberto

From elementary processes to plasma modeling From elementary processes to plasma modeling

• lytechnic of Bari, Italy

Institute of Nanot CNR - Bari, Ital

Non-Boltzmann population Non-Maxwellian electron energy distributions function

Non-equilibrium low-temperature plasmas

State-to-state vibrational kinetics Large sets of cross section data Molecular plasmas

Vibrational kinetics of electronically excited states in H2 discharges

The evolution of atmospheric pressure hydrogen plasma under 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 K Gas pressure = 1 bar. Molar fractions: ===============================================

2

10 H

10

e

χ χ

+

−

= =

9 H

2 10 χ

−

= ⋅

3

H H H

χ 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 D Y D

+

 Σ   Π =  

3 3 3

, ,

u g u

b a c

+ +

Σ Σ Π

+ 3

H

✓ state-to-state ✓ radiative processes

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.

✓ state-to-state ✓ radiative processes

• U. Fantz, D. Wünderlich, ADNDT (2006)

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.

✓ state-to-state ✓ radiative processes ✓ energy profile cross section

υ = 0 semiclassical IPM - R. Celiberto et al., ADNDT (2001)

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 2 2

H ( , ) H ( , , ')

g u u

X v e B C v

+ +

Σ + → Σ Π

1Bu +

C1Πu

0→0 0→5 10→7 0→0 0→5 0→10 5→10 5→20

Cross section Å2 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 ✓ radiative processes ✓ energy profile cross sections ✓ accuracy

CCC approach

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

BEf scaling

Tanaka et al. Reviews of Modern Physics (2016) Kim, J Chem Phys (2007)

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.

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

Fast (ns-pulsed) discharges in hydrogen

excited state concentration & singlets vibrational distributions

Fast (ns-pulsed) discharges in hydrogen

excited state concentration & singlets vibrational distributions

5 10 15 20 50 100 150 200 250 E0/N (Td) time (ns)

Fast (ns-pulsed) discharges in hydrogen

excited state concentration & singlets vibrational distributions

Fast (ns-pulsed) discharges in hydrogen

excited state concentration & singlets vibrational distributions

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.

… no quenching … no quenching

Fast (ns-pulsed) discharges in hydrogen Fast (ns-pulsed) discharges in hydrogen

hydrogen negative ion concentration hydrogen negative ion concentration

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.

no quenching

Dense plasmas

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

H+/H RESONANT CHARGE EXCHANGE in DEBYE PLASMAS

/

D

r

e U r

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. Smirnov
• Eur. Phys. J. D (2017)

10–2 10–1 100 101 102 102 103 104 Ecmf [eV] Charge-Exchange cross section [a0

2] 1.4 a0

λD = ∞

3.0 a0 1.2 a0 0.9 a0 1.0 a0

H+/H RESONANT CHARGE EXCHANGE in DEBYE PLASMAS ASYMPTOTIC APPROACH icchiuta, A., Colonna, G., Capitelli, M., Kosarim, A., & Smirnov, B. M..

• nant charge exchange for H–H+ in Debye plasmas

European Physical Journal D (2017).

(1s) + H+

u, 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] Charge-Exchange cross section [a02]

1.4 a0

λD = ∞

3.0 a0 1.2 a0 0.9 a0 1.0 a0

H+/H RESONANT CHARGE EXCHANGE in DEBYE PLASMAS ASYMPTOTIC APPROACH vs QUANTUM icchiuta, A., Colonna, G., Capitelli, M., Kosarim, A., & Smirnov, B. M.

• nant charge exchange for H–H+ in Debye plasmas

European Physical Journal D (2017).

(1s) + H+

10–2 10–1 100 101 102 102 103 104 Ecmf [eV] Charge-Exchange cross section [a0

2]

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] Charge-Exchange cross section [a0

2]

λD = ∞ 20 a0 λD = ∞

3dm=2

1s

11 a0 15 a0

H+/H RESONANT CHARGE EXCHANGE in DEBYE PLASMAS EXCITED STATES H* icchiuta, A., Colonna, G., Capitelli, M., Kosarim, A., & Smirnov, B. M..

• nant charge exchange for H–H+ in Debye plasmas

European Physical Journal D (2017).

n = 2, 3) + H+

2pm=1

Kinetic and divertor modeling

• F. Taccogna, P. Minelli, D. Bruno, S. Longo, R. Schneider
• Chem. Phys. (2012)

Reduction of the Divertor Region to 1 Dimension

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

(detached divertor plasma condition)

• e/H+ Temperature : Tp=5 eV
• B=1 Tesla; θ=85 °
• Simulation domain: l=0.3 mm
• Every Particle carries: - species: e, H+, H2

+, H-; H, H2(X1Σg +)

• 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
• Collision Methodology: - Plasma-Plasma (e+H2

+/H-+H+/H-+e)

• Plasma-Neutral
• Neutral-Neutral relaxation (Vt/VT/VV)
• 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 vi

DSMC 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-Maxwellian behavior

agreement with probe measurement

bulk

Distance from divertor plate z(mm)

E(eV) z(mm) density (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 wall due to high vibrational excitation H2(v)

−0.25 −0.2 −0.15 −0.1 −0.05 0

z (mm)

−0.25 −0.2 −0.15 −0.1 −0.05 0

z (mm)

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

+,

H2

+ + e → H + H

Aerospace Sciences

Motivation

Planet 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 entries

• P. Reynier, G. D'Ammando, D. Bruno,

Progress in Aerospace Sciences (2018)

Chemical input data Cross sections for all the processes included in the model. Heavy particle collisions H−He, He−He, H−–He, H–He+, He–He H+–H, H+–H2, H+–He, H–H–, He–He2

+

H2–H2

+

Electron interactions e-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 data Flight data, i.e. probe velocity, gas density, gas temperature and pressure as a function

• f 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 the stagnation line at 180 km 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 processes A+BC(v, j) → A+BC(v’, j’) Reactive processes A+BC(v,j) → B+AC(v’, j’), C+AB(v’, j’) Dissociation A+BC(v, j) → A+B+C

Collision processes of heavy particles

Inelastic processes A+BC(v, j) → A+BC(v’, j’) Reactive processes A+BC(v,j) → B+AC(v’, j’), C+AB(v’, j’) Dissociation A+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).

QCT QM

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 1 2 3 4 5 6 7 8

Potential energy (eV) Internuclear distance (a.u.)

H(1s) + H(1s) H(n=2) + H

• (1s

2)

H

(2Σ

, )

Dissociative attachment: H + H− Vibrational excitation Resonant dissociation: H + H + e

H + esonant collisions

0.0 2.0 4.0 6.0 8.0 10 12 14 1 2 3 4 5 6 7 8

Potential energy (eV) Internuclear distance (a.u.)

H(1s) + H(1s) H(n=2) + H

• (1s

2)

H

(2Σ

, )

Dissociative attachment: H + H− Vibrational excitation Resonant dissociation: H + H + e

H + esonant collisions V V

• V(R), V

(R) and Γ(R

0.0 2.0 4.0 6.0 8.0 10 12 14 1 2 3 4 5 6 7 8

Potential energy (eV) Internuclear distance (a.u.)

H(1s) + H(1s) H(n=2) + H

• (1s

2)

H

(2Σ

, )

Dissociative attachment: H + H− Vibrational excitation Resonant dissociation: H + H + e

H + esonant collisions − ℏ 2

• + () +

2 Γ() − ! = −#

$ ()&' ()

− ℏ 2

• + () +

2 Γ() − ! = −#

$%()&'%()

V V

• V(R), V

(R) and Γ(R

0.0 2.0 4.0 6.0 8.0 10 12 14 1 2 3 4 5 6 7 8

Potential energy (eV) Internuclear distance (a.u.)

H(1s) + H(1s) H(n=2) + H

• (1s

2)

H

(2Σ

, )

Dissociative attachment: H + H− Vibrational excitation Resonant dissociation: H + H + e

H + esonant 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.) Potential energy (eV) CF (X 1Σ+)

3Σ− 1Σ+ 1∆

CF molecule

75 vibrational levels

Rozum, Mason & Tennyson,

• J. Phys. B (2013)

CF−

Bond length, R (a.u.) Resonance width, Γ(R) (eV)

3Σ− 1Σ+ 1∆

CF molecule

Rozum, Mason & Tennyson,

• J. Phys. B (2013)

Energy (eV) Cross section (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 vi = 40 vi = 20 CF molecule

Dissociative attachment

CF (X 1Σ+;vi) + e → CF− ( 1Σ+;v’) → CF (X 1Σ+;vf) + e CF (X 1Σ+;vi) + e → CF− ( 1Σ+;v’) → CF (X 1Σ+;vf) + e 0 = 0 0 = 10 0 = 40 0 = 20

Energy (eV) Cross section (Å2)

CF molecule

Resonant vibrational excitation

CF (X 1Σ+;vi) + e → CF− ( 1∆; v’) → C + F + e CF (X 1Σ+;vi) + e → CF− ( 1∆; v’) → C + F + e vi = 0 vi = 10 vi = 40 vi = 20

Energy (eV) Cross section (Å2)

CF molecule

Dissociative excitation

Rate coefficient (10-9 cm3⋅s-1) Temperature (eV) vi = 0 vi = 20 vi = 5 vi = 20 vi = 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

Rate coefficient (10-9 cm3⋅s-1) Temperature (eV) 0 → 0 CF (X 1Σ+;vi) + e → CF− ( 1Σ+v’) → CF (X 1Σ+;vf) + e CF (X 1Σ+;vi) + e → CF− ( 1Σ+v’) → CF (X 1Σ+;vf) + e 0 → 40 0 → 20 0 → 5 0 → 10

Resonant vibrational excitation

Rate coefficient (10-9 cm3⋅s-1) Temperature (eV) vi = 0 vi = 10 vi = 5 vi = 20 vi = 40 CF (X 1Σ+;vi) + e → CF− ( 1∆) → C + F + e CF (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)

Potential energy (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) Cross section (Å2) Energy (eV)

TMMM = Threshold Modified Mott-Massey

BeH

0.0 2.0 4.0 6.0 8.0 10 12 14 16 2 4 6 8 10 12 14 16

Cross section (Å2) Energy (eV) Born R-matrix TM MM

X(0)→A(0)

R Celiberto, K L Baluja & R K Janev Plasma Source Science & Technology, 2013

Cross section (Å2) Energy (eV) 0 → 0 0 → 10 0 → 20 X (0 ) → A (v’)

10 → 27 10 → 20 10 → 10 Cross section (Å2) Energy (eV) X (10 ) → A (v’)

20 → 27 20 → 25 20 → 20 Cross section (Å2) Energy (eV) X (20 ) → A (v’)

• M. Capitelli

– Università di Bari, Italy

• D. Bruno

– CNR, Italy

• G. Colonna

– CNR, Italy

• A. D’Angola – Università della

Basilicata, Italy

• F. Esposito

– CNR, Italy

• V. Laporta

– CNR, Italy

• A. Laricchiuta – CNR, Italy
• P. Minelli

– CNR, Italy

• F. Taccogna

– CNR, Italy

• K. Baluja

– Dely University, India

• R. K. Janev

– Macedonian Academy of Science, Macedonia

• I. Schneider

– University of Pari Sud, France

• J. Tennyson

– University College, UK

• J. M. Wadehra – Wayne State University, USA