Ab-initio calculation of state-resolvedcross sections and rate coefficientsfor electron-O2 and -N2 scattering

61st Course Hypersonic Meteoroid Entry Physics3-8 October 2017 Erice (Italy)

V. LaportaLaboratoire Onde et Milieux Complexes

Université du Havre-CNRS, Le Havre (France)

Plan of the talk:

Ab initio state-resolved cross sections database

• Atmospheric modelling: electron-O2 and electron-N2

• Astrophysics: electron-He2+

• Fusion plasma: electron-BeH+

Main collaborators:R. Celiberto (Politecnico di Bari, Italy)K. Chakrabarti (Scottish Church College, Kolkata, India)M. Panesi (University of Illinois at Urbana Champaign, IL, USA)I.F. Schneider (Université du Havre, France)J. Tennyson (University College London, UK)

electron-O2(X, v) scattering

In order to describe the low-energy electron-O2(X3Σ𝑔

−) resonant scattering it needs to include

four resonant states, 2Π𝑔,2Π𝑢,

4Σ𝑢−, 2Σ𝑢

− of O2−.

Potential energy curves and resonance widths obtained from MOLPRO and R-matrix withinaug-cc-pvQZ basis-set and MR-CI model.

The O2 target was represented using the corresponding orbital configurations:3 core orbitals (2ag, 1b1u)6 of frozen electrons and9 valence orbitals up to (3ag, 2b3u, 2b2u, 3b1u, 1b2g, 1b3g)10.

For the scattering calculations:(2ag, 1b1u)6 (5ag, 2b3u, 2b2u, 4b1u, 2b2g, 2b3g)11

and(2ag, 1b1u)6 (5ag, 2b3u, 2b2u, 4b1u, 2b2g, 2b3g)10 (6ag, 3b3u, 3b2u, 1b1g, 5b1u, 3b2g, 3b3g, 1au)1.

𝐞− + 𝐎𝟐 𝐗 𝟑𝚺𝐠−; 𝒗 ⟶ 𝐎𝟐

− 𝟐𝚷𝐠,𝟐𝚷𝐮,

𝟒𝚺𝐮−, 𝟐𝚺𝐮

− ⟶

𝐞− + 𝐎𝟐 𝐗 𝟑𝚺𝐠− ; 𝒗′ (VE)

𝐎 𝟑𝐏 + 𝐎− 𝟐𝐏 (𝐃𝐀)

𝐞− + 𝐎 𝟑𝐏 + 𝐎 𝟑𝐏 (𝐃𝐄)

V. Laporta, R. Celiberto and J. Tennyson, Phys. Rev. A91, 012701 (2015).

V. Laporta, R. Celiberto and J. Tennyson, Plasma Sources Sci. Technol. 22, 025001 (2013)

At energy below 2 eV the VE cross sections are dominated by 2Π𝑔 symmetry; comparison with Allan’s results

Resonance at 10 eV dominated by 4Σ𝑢− symmetry

𝑒− + O2 X 3Σ𝑔−; 𝑣 ⟶ O2

− 2Π𝑔,2Π𝑢,

4Σ𝑢−, 2Σ𝑢

− ⟶ 𝑒− + O2 X 3Σ𝑔− ; 𝑣′

Vibrational-Excitation process:

Set of calculated cross sections for j = 1

and the corresponding rate coefficients

𝑒− + O2 X 3Σ𝑔−; 𝑣 ⟶ O2

− 2Π𝑔,2Π𝑢,

4Σ𝑢−, 2Σ𝑢

− ⟶ 𝑒− + O2 X 3Σ𝑔− ; 𝑣′

𝑒− + O2 X 3Σ𝑔−; 𝑣 ⟶ O2

− 2Π𝑔,2Π𝑢,

4Σ𝑢−, 2Σ𝑢

− ⟶ O 3P + O−(2P)

Dissociative-electron-attachment

DeA cross section for v = 0 and j = 1Contributions from the four symmetries and comparison with some

theoretical and experimental data present in literature

Electron energy (eV)

Set of calculated cross sections and the corresponding rate coefficients for some vibrationallevels v and for j = 1

J = 1

J = 1

𝑒− + O2 X 3Σ𝑔−; 𝑣 ⟶ O2

− 2Π𝑔,2Π𝑢,

4Σ𝑢−, 2Σ𝑢

− ⟶ O 3P + O−(2P)

𝒆− + 𝐎𝟐 𝐗𝟑𝜮𝒈−; 𝒗 ⟶ 𝐎𝟐

− 𝟐𝜫𝒈,𝟐𝜫𝒖,

𝟒𝜮𝒖−, 𝟐𝜮𝒖

− ⟶ 𝒆− + 𝟐 𝐎 𝟑𝐏

Electron-impact dissociation:

J = 1J = 1

v = 0J = 1

Set of vibrational-resolved cross sections and the corresponding rate coefficients for j = 1

Effect of target rotation

j = 1 v1 = 0…41

j = 50 v50 = 0…33

j = 100 v100 = 0…23

j = 150 v150 = 0…9

j = 170 v170 = 0…2

Number of vibrational levels as a function of therotational quantum number j

Thermal averaged energy of the ro-vibrational level 𝜖𝑣,𝑗:

ഥ𝜖𝑣 𝑇𝑟 =

𝑗

𝜖𝑣,𝑗(2𝑗 + 1)𝑒−𝜖𝑣,𝑗/𝑘𝐵𝑇𝑟

𝑄𝑣(𝑇𝑟)

𝑇𝑟 is the rotational temperature

Thermal averaged vibrational-excitation cross section, 𝑇𝑟 is the rotational temperature:

ത𝜎𝑣,𝑣′ 𝜖, 𝑇𝑟 =

𝑗

𝜎𝑣,𝑣′,𝑗(𝜖)(2𝑗 + 1)𝑒−𝜖𝑣,𝑗/𝑘𝐵𝑇𝑟

𝑄𝑣(𝑇𝑟)

j = 1

j = 50

j = 100

Tr = 102 K

Tr = 104 K

0 → 1

Thermal averaged rate coefficient by assuming therotational temperature in equilibrium with electrontemperature

j = 1, 50, 100

j = 1500 → 1

Thermal averagedrate coefficient

j-resolved cross section for v = 0 → v’= 1

j = 1

j = 50

j = 100

j = 150

Thermal averagedrate coefficient

v = 0 v = 0 j = 1

j = 50

j = 100

j = 150

Thermal averagedrate coefficient

Rotational j-resolved rate coefficients (solid lines) as a function of the electron temperatureand

Thermal averaged rate coefficient (dashed line) by assuming the rotational temperature inequilibrium with electron temperature

dissociative-electron-attachment dissociative-excitation

Application: Electron-vibration relaxation in oxygen plasmas

V. Laporta, K.L. Heritier and M. Panesi, Chemical Physics 472 (2016) 44–49

• State-to-State vibrational kinetics• Vibrational relaxation time is comparable to chemical relaxation: vibrational non-equilibrium

• Time evolution of non-equilibrium vibrational distribution function:

• Vibrational relaxation time:

Equilibriumdistribution

Non-equilibriumdistribution

electron-N2 resonant scattering

The resonance at 2.3 eV in electron-N2 scattering is described in term of the resonant state N2− X 2Π𝑔

The quantum chemistry codes MOLPRO and R-Matrix have been used to calculate potential energycurves, resonance width:

cc-pvQZ basis set MR-CI modelCAS (1𝜎𝑔, 1𝜎𝑢)

4(2𝜎𝑔, 2𝜎𝑢, 1𝜋𝑢, 3𝜎𝑔, 1𝜋𝑔, 3𝜎𝑢)10 128 configurations

V. Laporta et al., Plasma Sources Sci. Technol. 23, 065002 (2014)

V. Laporta et al., Plasma Sources Sci. Technol. 21, 055018 (2012)

𝑒− + N2 X 1Σ𝑔+; 𝑣, 𝐽 ⟶ N2

− X 2Π𝑔 ⟶ 𝑒− + N2 X 1Σ𝑔+; 𝑣′, 𝐽

Vibrational-excitation process:

Elastic

transitions (𝑣 → 𝑣)

Inelastic

transitions (20 → 𝑣)

VE cross sections

parameterized on N2

rotational quantum

number J

𝑒− + N2 X 1Σ𝑔+; 𝑣, 𝐽 ⟶ N2

− X 2Π𝑔 ⟶ 𝑒− + 2 N 4S

v = 0

v = 10

v = 20

v = 30

v = 40

v = 50

0 2 4 6 8 10 12 14

10 11

10 9

10 7

10 5

0.001

0.1

Electron energy eV

Cro

ssse

ctio

n2

v = 0

v = 10

v = 20

v = 30

v = 50v = 40

0 10000 20000 30000 40000 5000010 10

10 8

10 6

10 4

0.01

1

Electron temperature K

Rat

eco

effi

cien

t10

9cm

3se

c

Electron-impact dissociation:

Electron-vibration relaxation in nitrogen plasmas

𝑒− + N2 X 1Σ𝑔+; 𝑣, 𝐽 ⟶ N2

− X 2Π𝑔 ⟶ 𝑒− + N2 X 1Σ𝑔+; 𝑣′, 𝐽

• Time evolution of non-equilibrium vibrational distribution function:

N2 relaxation time

electron-He2+ dissociation cross sections

R Celiberto, KL Baluja, RK Janev and V Laporta, Plasma Phys. Control. Fusion 58 (2015) 014024

Adiabatic nuclei approximation

electron-BeH+ Dissociative Recombination cross sections

V Laporta, K Chakrabarti, R Celiberto, RK Janev, JZs Mezei, S Niyonzima, J Tennyson and IF Schneider, PPCF 59, 045008 (2017)

Thank you for your attention

Work in progress…

• We are planning with our collaborations to calculate ab initio cross sections for the mainelementary processes for electron-molecule scattering (dissociative attachment, dissociativeexcitation, dissociative recombination and vibrational excitation) ;

• Work is in progress on electron-CO2 scattering, electron-N2+, improvement of electron-NO….