M.Capitelli Dipartimento di Chimica, Università di Bari, Italy IMIP-CNR, Bari, Italy.

CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005

DYNAMICS, KINETICS AND MODELING OF MOLECULAR AND

ATOMIC PLASMAS: THE STATE TO STATE APPROACH

M.Capitelli

Dipartimento di Chimica, Università di Bari, ItalyIMIP-CNR, Bari, Italy


COLLABORATORS

C.GORSE, S.LONGO, P.DIOMEDE, D.PAGANO, D.PIETANZADepartment of Chemistry, University of Bari, Bari, Italy

O.DE PASCALE, F.ESPOSITO, A.LARICCHIUTA, M.RUTIGLIANO, M.CACCIATOREIMIP(CNR), Bari, Bari, Italy

R.CELIBERTODICA Politecnico di Bari, Bari, Italy

AND

A.GICQUEL, K.HASSOUNILIMHP-CNRS, Université Paris Nord, Villetaneuse, France

B.M.SMIRNOV, A.V.K OSARIMInstitute for High Temperatures of RAS, Moscow, Russia


QUANTUM CHEMISTRY

MOLECULAR DYNAMICS

COLLISION INTEGRALSground stateexcited states

Maxwell Distribution(DSMC)

Boltzmann Equation for electrons (PIC-MCC)

RATE COEFFICIENTS

KINETICS

LASER-PLASMAInteraction

DIVERTOR Plasmas

MULTICUSP(Magnetic Plasmas)

FilamentRF

H-/D- Production

MICROWAVE DISCHARGES

(Maxwell Equations)

Diamond Film Production

PARALLEL PLATE(PIC-MCC)

Microelectronics

Chapman-Enskog

TRANSPORT PROPERTIES

RF TORCHES

Waste Discharges

Metallurgy

AEROSPACE

ReentryProblems

FLUIDYNAMICS

ELECTRON-IMPACT induced PROCESSES

(inelastic+reactive)

SemiclassicalImpact Parameter

Method

HEAVY PARTICLE COLLISIONS

(inelastic+reactive)

QuasiclassicalTrajectory

Method

GAS-SURFACEINTERACTION

SemiclassicalCollisional

Model


OUTLINE

- Open problems (1985-1995) in Multipole Magnetic Plasmasa) Validation of Bari code with FOM experimentsb) Extension to D2 plasmasc) Pulsed dischargesd) Rydberg statese) Wall effects

- Cross Section Improvements (1995-2005) a) Electron-molecule cross sections

b) Heavy particle collision cross sections c) Gas surface interaction

- Kinetic models Improvements(1995-2005)a) New multipole zerodimensional codeb) Parallel-plate 1D codec) RF and MW quasi 1D code

- Air Plasmasa) N2 and O2 State-to-State Cross Sections


OUTLINE







€

∂n ε,t( )∂t

= −∂Jel

∂ε

⎛ ⎝ ⎜

⎞ ⎠ ⎟e−M

−∂Jel

∂ε

⎛ ⎝ ⎜

⎞ ⎠ ⎟e−e

+ In + Ion + Sup + S − L

VIBRATIONAL EXCITATION and NEGATIVE ION KINETICS

Time Evolution (heavy species)

€

dNv

dt

⎛ ⎝ ⎜

⎞ ⎠ ⎟=

dNv

dt

⎛ ⎝ ⎜

⎞ ⎠ ⎟e−V

+dNv

dt

⎛ ⎝ ⎜

⎞ ⎠ ⎟E−V

+dNv

dt

⎛ ⎝ ⎜

⎞ ⎠ ⎟

V−V

+dNv

dt

⎛ ⎝ ⎜

⎞ ⎠ ⎟

V−T

+

dNv

dt

⎛ ⎝ ⎜

⎞ ⎠ ⎟e−D

+dNv

dt

⎛ ⎝ ⎜

⎞ ⎠ ⎟e−I

+dNv

dt

⎛ ⎝ ⎜

⎞ ⎠ ⎟e−da

+dNv

dt

⎛ ⎝ ⎜

⎞ ⎠ ⎟e−E

+dNv

dt

⎛ ⎝ ⎜

⎞ ⎠ ⎟wall

€

InTerm due to inelastic collisions

€

Ion Term due to ionization collisions

€

Sup Term due to superelastic collisions

€

L Electron loss term€

−∂Jel

∂ε

⎛ ⎝ ⎜

⎞ ⎠ ⎟e−M

Flux of electrons along energy axis due to elastic collisions

€

−∂Jel

∂ε

⎛ ⎝ ⎜

⎞ ⎠ ⎟e−e

Flux of electrons along energy axis due to electron-electron collisions

Electron source term:

€

S =I

VeΔε p

MULTIPOLE MAGNETIC PLASMAS:

!! Self-consistent non equilibrium vibrational kinetics coupled to the Boltzmann equation for the electron energy distribution function!!


VALIDATION of BARI CODE with the FOM EXPERIMENTS (GORSE ET AL. 1992)

109

1011

1013

1015

0 2 4

p=2.25 mtorrp=4.5 mtorrp=7.5 mtorrp=15 mtorr

population densities (cm

-3)

vibrational quantum number

a)

1010

1012

1014

1016

0 2 4

p= 2.25mtorrp=4.5 mtorrp=7.5 mtorrp=15 mtorr


-3)


b)

comparison between experimental (a) and theoretical (b) vdfs at several pressures

109

1011

1013

1015

0 2 4

Id=5 AId=10 AId=20 AId=30 A


-3)


a)

1010

1012

1014

1016

0 2 4

Id=5 AId=10 AId=20 AId=30 A


-3)


b)

comparison between experimental (a) and theoretical (b) vdfs at several discharge currents I d


!!PROBLEMS!!- calculations overestimate by a factor 10 the high lying vibrational levels giving satisfactory agreement

with negative ion concentrations- FOM experimental vibrational distributions limited to v=5 !!New: experimental determination by Mosbach and Dobele up to v=13!!

108

109

1010

4 6 8 10 12 14

number density (cm

-3)


vibrational distribution Nv measured in a H2 multicusp source (p = 11.25 mtorr, Id = 0.5 A, Vd = 100 V)


EXTENSION to D2 PLASMAS

105

107

109

1011

0 40 80

EEDF (cm

-3eV

-1)

energy (eV)

D2

H2

a)

1010

1012

1014

0 5 10 15 20


-3)


H2

D2

b)

theoretical EEDF (a) and Nv (b) in H2 and D2 sources

(p = 4.5 mtorr, Id = 10 A, Vd = 115 V, plasma potential Vp = 2.9 V)

10-18

10-16

10-14

10-12

10-10

10-8

0 5 10 15 20

B


H2

D2

rate coefficients (cm

3 s-1)

dissociative attachment rates versus vibrational quantum number for H2 and D2 molecules


0

2

4

6

8

10

0 2 4 6 8 10 12 14

electron density (10

11

cm-3

)

pressure (mtorr)

D2

a)H

2

0,7

0,8

0,9

1

1,1

1,2

1,3

2 4 6 8 10 12 14

electron temperature (eV)

pressure (mtorr)

D2

H2

b)

5

10

15

20

25

2 4 6 8 10 12 14atom D/H concentration (10

12

cm-3

)

pressure (mtorr)

D2

H2

c)

2

4

6

8

10

12

14

2 4 6 8 10 12 14D-/H

- ion concentration (10

9 cm

-3)

pressure (mtorr)

D2

H2

d)

(a) behavior of electron density ne(b) electron temperature Te(c) atomic concentration [H]/[D] (d) negative ion concentration [H-]/[D-]for H2 and D2 systems versus pressure p (Id = 10 A, Vd = 115 V)


2

4

6

8

10

0 4 8 12 16 20 24 28 32

electron density (10

11

cm-3

)

discharge current (A)

D2

a)H

2

0,6

1

1,4

0 4 8 12 16 20 24 28 32

electron temperature (eV)


D2

H2

b)

5

15

25

35

0 4 8 12 16 20 24 28 32atom D/H concentration (10

12

cm-3

)


D2

H2

c)

2

6

10

14

18

0 4 8 12 16 20 24 28 32D-/H

- ion concentration (10

9 cm

-3)


D2

H2

d)

(a) behavior of electron density ne(b) electron temperature Te(c) atomic concentration [H]/[D] (d) negative ion concentration [H-]/[D-]for H2 and D2 systems versus current Id (p = 7.5 mtorr, Vd = 115 V)


DISSOCIATIVE ATTACHMENT: H2 (X 1g,) + e H2- H- + H

E = 4.5 eV

10-9

10-8

10-7

10-6

10-5

10-4

10-3

0.0 0.5 1.0 1.5 2.0 2.5 3.0

H2

D2

σ

DISSOCIATIVE ATTACHMENT

(Å2)

( )INITIAL VIBRATIONAL EIGENVALUE eV


RESONANT VIBRATIONAL EXCITATION: H2 (X 1g, i) + e H2

- H2 (X 1g, f) + e

E = 5 eV

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

H2

D2

FINAL VIBRATIONAL EIGENVALUE (eV)

i = 0

σ

VIBRATIONAL EXCITATION

(Å2)


PULSED DISCHARGES: MODEL

2 1010

6 1010

1 1011

0 1 2 3 4

tpd

= 0 µs

tpd

= 15 µs

tpd

= 25 µs

tpd

= 60 µs

tpd

= 200 µsEEDF (eV

-1cm

-3)

energy (eV)

a)

2 10-9

6 10-9

1 10-8

8 12 16 20

tpd

= 4 µs

tpd

= 16 µs

tpd

= 193 µs

dissociative attachment rate (cm

3s-1)


b)

109

1011

1013

0 10 20

tpd

= 5.8 µs

tpd

= 25.8 µstpd

= 73.7 µstpd

= 203.7 µs

D2 population densities (cm

-3)


c)

2,0 109

2,3 109

2,6 109

4,0 109

4,6 109

5,2 109

0 100 1,5 10 -3 3 10-3

D- negative ion density (cm

-3)

time (s)

d)

Relaxation of several quantities in the D2 post-discharge regime

(a) EEDF, (b) e-da rate coefficient, (c) Nv, (d) D- density


PULSED DISCHARGES: EXPERIMENT

0

0,1

0,2

0,3

0 1 2 3

extracted H

-

current (mA)

time (ms)

extracted H- current in a pulsed hydrogen discharge with a 2.7 ms pulse length and a 87 Hz repetition rate (p = 2.4 mtorr, Id = 15 A)


RYDBERG STATES: HYSTORICAL SCENARIO/1

Pinnaduwage et al. [Phys. Rev. Lett. 70, 754 (1993)]

e + H2* H + H- Kda(Ryd)=10-6 cm3/sec

Garscadden and Nagpal [Plasma Sources Sci. Technol. 4, 268 (1995)]

Simplified model: (lumped excitation cross section on Rydberg states + lifetime of Rydberg states of 10-6sec + Kda(Ryd)=10-6 cm3/sec)

Result: Contribution from Rydberg states 10 times the one from vibrationally excited states

Gorse et al. [AIP Conf. Proc. 380, 109 (1995)]Model: Insertion of Garscadden model in the self-consistent kinetics in multipole magnetic plasmasResult: enhancement by a factor 2

Hiskes [Appl. Phys. Lett. 69, 755 (1996)]Model: collisional radiative model for H2

* Rydberg states + Kda(Ryd)=10-6 cm3/secResult: lifetime of Rydberg states of the order of 10-8secConsequence: contribution of Rydberg states 1%


RYDBERG STATES: HYSTORICAL SCENARIO/2

Pinnaduwage et al. [Phys. Rev. A 55, 4131 (1997)]e + H2* = H + H- Kda(Ryd) = 510-5 cm3/sec

Hassouni et al. [Chem. Phys. Lett. 290, 502 (1998)]Model: collisional radiative model for H2* Rydberg states + Kda(Ryd)=5 10-5 cm3/secResult: enhancement by factor 2.7Problem: Rydberg state from n>3

Pinnaduwage et al. [J.Appl.Phys. 85, 7064 (1999)]scaling law for Rydberg states which corresponds to n=12An estimation

For a plateau between 1010-1012cm-3 Rydberg concentrations of the order of 1/6 107 to 1/6 109 cm-3 can be of the same importance as the dissociative attachment from vibrationally excited molecules

€

kda (n) =10−8n7 / 2cm3 / s

€

6 ×10−5 H (n)n>12∑ =10−8 H2 (ν )ν>4∑


FUTURE IMPROVEMENTS

• COLLISIONAL RADIATIVE MODEL FOR RYDBERG STATES

• SCALING LAW FOR THE EXCITATION OF RYDBERG STATES

• LIFETIMES OF RYDBERG STATES

• SCALING LAW FOR DISSOCIATIVE ATTACHMENT FROM RYDBERG STATES


WALL EFFECTS: HYSTORICAL SCENARIO

Hiskes & KaroModel: trajectory calculationsResults: strong deactivation of vibrationally excited molecules on iron surfaces - widely used in multicusp modelling

Billing & CacciatoreModel: semiclassical/classical for describing atoms and molecules reaching the surface; quantum description of the interaction of the molecule/atom with the phononic and electronic structure of the metalResults : small deactivation of vibrationally excited molecules on copper surfaces


Dissociation Probabilities and Energy Accommodation for H2(v,j) Colliding with a Cu(100) Surface

as a Function of Vibrational and Rotational Angular Momenta v and j and Initial Kinetic Energy

j Ekin [eV] PD a) ’ b) j’ b) Eint b,c) [eV]

5 0 1,0 0,0 5 0,1 0,016

2,0 0,70 5 1 0,026

6 0 0,2 0,0 6 0,1 0,0024

0,4 0,0 6 0,1 0,0060

0,6 0,0 6 1 0,0095

1,0 0,62 6 1 0,014

8 0 0,05 0,0 8 (7) 0 0,001

0,2 1,0

10 0 0,05 0,95

0,1 1,0

a) Dissociation probabilityb)Averaged values for reflected trajectoriesc) Energy transferred to surface phonons


FORMATION OF VIBRATIONALLY EXCITED STATES

from HETEROGENEOUS ATOM RECOMBINATION

H(gas) + Hads H2() DIRECT ELEY RIDEAL (E-R) MECHANISM

H(gas) H (trapped)

H(trapped) + Hads H2() HOT ATOM (HA) MECHANISM

Hads + Hads H2() HINSHELWOOD-LANGMUIR (H-L) MECHANISM

!!Different energetics depending on the nature of the adsorbed atom e.g. physi-adsorbed; chemi-adsorbed!!

PHYSI-ADSORBED: practically all the recombination energy can go into vibrational excitation of

desorbed molecules in both E-R and H-L mechanisms

CHEMI-ADSORBED: only the difference between the dissociation energy of the diatom and the adsorption

energy of atom(s) can go into vibrational energy of the desorbed molecules


semiclassical collisional method

Hads equilibrium distance of 1.5 Å

in thermal equilibrium with the surface

Hgas

TS

(;) Ekin

MD

energetic fluxes

H2 vibrationaldistribution

recombinationprobabilities

reaction probabilitiesfor different reaction products

surface temperature effect

ELEY-RIDEL MECHANISM


VIBRATIONAL DISTRIBUTIONS from PHYSIADSORBED H and D ATOMS on COPPER

(E-R mechanism, BILLING&CACCIATORE)

0

0,05

0,1

0,15

0,2

0 2 4 6 8 10 12 14

vibrational contribute to rate constant


Hgas

+ Hads

H2(v,j) →

= 5000 T K

0

0,05

0,1

0,15

0,2

0 2 4 6 8 10 12 14

vibrational contribute to rate constant


T = 5000 K

Dgas

+ Dads

D2(v,j) →


VIBRATIONAL DISTRIBUTIONS from CHEMIADSORBED H ATOMS on COPPER (HA-SHALASHILIN et al.) for the REACTION Hgas + Dads HD()

P (

)



VIBRATIONAL DISTRIBUTIONS from PHYSIADSORBED H ATOMS on GRAPHITE (E-R mechanism, H-L mechanism, SIDIS&MORISSET)

SCHEME OF THE REACTION PATH

(v, j) distribution of the H2 product


VIBRATIONAL DISTRIBUTIONS from PHYSIADSORBED H ATOMS on GRAPHITE (E-R mechanism, BILLING&CACCIATORE)

TS = 500K

0.00

0.10

0.20

0.30

0.40

0.50

0 2 4 6 8 10 12

VIBRATIONAL QUANTUM NUMBER


OUTLINE







ELECTRONIC EXCITATION to the lowest SINGLETS

X 1 g ( i) C 1uX 1g (i) B 1 u

0.0

0.4

0.8

1.2

1.6

0.0 50.0 100.0 150.0 200.0

Energy (eV)

= 0

1

3

4

6

9-10

12

13 14

11

0.0

0.2

0.4

0.6

0.8

1.0

0.0 50.0 100.0 150.0 200.0

Energy (eV)

12-14

= 0

2 4 6 8

10

CROSS SECTIONS IMPROVEMENTS


THEORETICAL APPROACH IMPACT PARAMETER METHOD

TOTALCROSS SECTION

€

σ i

α i→α f (E) = Σν fσ ν i ,ν f

α i→α f (E) + dεdσ ν i,ε

α i→α f (E)

dε∫

VIBRONIC EXCITATION

DISSOCIATIVE EXCITATION

SEMICLASSICAL Method (quantal target - classical projectile) ALLOWED Transitions (selection rules) degenerate rotational levels

€

σ i

α i→α f (E) = Sν i ,ν f

α i→α f ⋅Dν i ,ν f

α i→α f (E)

STRUCTURAL FACTOR

DYNAMICAL FACTOR

€

σ i

α i→α f (E) = dR χ ν f

α fμ(R)∫ χ ν i

α i

€

Dν i,ν f

α i→α f (E,ρ0,ΔEν i ,ν f

α i→α f )

IMPACT PARAMETER(BORN cross section)

TRANSITION DIPOLE MOMENT


0.40

0.60

0.80

1.00

1.20

1.40

0 5 10 15 20 25

H2

D2

DT

T2

Vibrational Quantum Number

0.40

0.60

0.80

1.00

1.20

1.40

0.0 1.0 2.0 3.0 4.0 5.0

H2

D2

DT

T2

Vibrational Eigenvalues (eV)

CROSS SECTIONS for H2 ISOTOPIC VARIANTS

E = 40 eVX 1g (i) B 1 u


0.00

0.20

0.40

0.60

0.80

1.00

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

H2

D2

T2

bi H2

bi D2

bi T2

INITIAL VIBRATIONAL EIGENVALUE (eV)

f =

i+1

σ


(Å2)

f =

i+2

0.00

0.20

0.40

0.60

0.80

1.00

0 1 2 3 4 5 6

H2

D2

T2

bi H2

bi D2

bi T2

INITIAL VIBRATIONAL LEVEL

f =

i+1

σ


(Å2)

f =

i+2

RESONANT VIBRATIONAL EXCITATIONH2 (X 1g, ni) + e H2

- H2 (X 1g, nf) + e

E = 5 eV


EXCITATION of low-lying RYDBERG STATES

0.00

0.03

0.06

0.09

0.12

0.15

0.0 50.0 100.0 150.0 200.0

1413v = 0

v = 9

Energy (eV)

1

3

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.0 50.0 100.0 150.0 200.0

14

v =04

Energy (eV)

3

9 1011

12,13

12

8

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.0 50.0 100.0 150.0 200.0

v = 0

14

1312

Energy (eV)

87

9

10

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.0 50.0 100.0 150.0 200.0

14

v = 0

Energy (eV)

23

1

910

1112

13

X 1 g ( i) D 1uX 1g (i) B’ 1 u

X 1 g ( i) D’ 1uX 1g (i) B” 1 u


0.00

0.20

0.40

0.60

0.80

1.00

2 3 4

=0=10

σTOTAL

(Å2)

PRINCIPAL QUANTUM NUMBER n

=40 E eV

C u [2pπ]

D u [3pπ]

D' u [4pπ]

H2 ( X

g, )+ e→ H

2(

u [npπ])+e

1

1

1

1 1

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

2 3 4

=0=10

σ

DISSOCIATION

(Å2)

PRINCIPAL QUANTUM NUMBER n

=40 E eV

C u [2pπ]

D u [3pπ]

D' u [4pπ]

H2 ( X

g,)+ e→ H

2(

u [npπ])+ e→ ( )+ ( )+H H n e

1

1

1

1 1 1

σ n-4


DISSOCIATION

DIRECT DISSOCIATION through EXCITED STATES

€

H2 (X 1g

+ , i ) +e→ H2 (b 3u

+ ,ε) +e→ H +H +e

€

H2 (X 1g

+ , i ) +e→ H2 (singlets, ′ ε ) +e→ H +H +e

B 1 u and C 1 u + low-lying RYDBERG STATES B’, B” 1 u , D, D’ 1 u

i

pure repulsive state

excited bound state

DISSOCIATION

DISSOCIATION

’

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

20.0 40.0 60.0 80.0 100.0

Energy (eV)

911

13

= 0

1

2

7

6

4,5

3

810

12


theoretical approach in atom-molecule collisions:QCT Method

atomic motion is considered classical on the potential energy surface (PES)

initial and final states are approximated with pseudoquantization rules

COMPUTATIONAL LOAD RELIABILITY of METHOD

goodmonths on fast processor


RATE COEFFICIENTS for the PROCESS: H+H2(,Trot) 3H

Trot=500 K

H2 D2


HYDROGEN VIBRATIONAL EXCITATION RATE COEFFICIENTSas a FUNCTION of FINAL VIBRATIONAL QUANTUM NUMBER

€

H2 (ν =10,Trot = 500K )+ H → H2 (ν =10 + n,Trot = 500K )+ H


HYDROGEN VIBRATIONAL DEACTIVATION RATE COEFFICIENTS as a FUNCTION of FINAL VIBRATIONAL QUANTUM NUMBER

€

H2 (ν =10,Trot = 500K )+ H → H2 (ν =10 − n,Trot = 500K )+ H


HYDROGEN VIBRATIONAL MONOQUANTUM DEACTIVATION RATE COEFFICIENTS

€

H2 (ν ,Trot = 500K )+ H → H2 (ν −1,Trot = 500K )+ H


!! normalized to total recombination, at different temperatures !!

HYDROGEN RECOMBINATION RATE COEFFICIENTS as a FUNCTION of FINAL VIBRATIONAL QUANTUM NUMBER

€

H + H + H → H2 (ν )+ H


OUTLINE







KINETIC MODELS IMPROVEMENTS

MULTIPOLE H2 DISCHARGES!! Time dependent electron kinetics and vibrational kinetics treated at the same level!!

€

n ε,t( ) ≈ n ε i ,t( )

€

εi −12

Δε i ≤ ε ≤ ε i +12

Δε ifor

€

Δεi

εi

€

εi −1

2Δε i

€

εi +1

2Δε i

ELECTRON ENERGY DISCRETIZATION

each electron energy sub-interval a “different electron” characterized by a representative energy

εi (sub-interval mean energy)

ELECTRONS STATE-TO-STATE KINETICS

(electrons with different energies as molecular energy levels)

€

kie = σ i ε( )v ε( )

discretized electron rate coefficients:


VDF and EEDF as a function of PRESSURE

109

1010

1011

1012

1013

1014

0.0 1.0 2.0 3.0 4.0 5.0

P=2.25 mtorrP=4.5 mtorrP=7.5 mtorr

energy (eV)

106

107

108

109

1010

1011

1012

0.0 20.0 40.0 60.0 80.0 100.0 120.0

P=2.25 mtorrP=4.5 mtorrP=7.5 mtorr

energy (eV)

TG =500 K

DISCHARGE CURRENT=10 A

DISCHARGE VOLTAGE=100 V


VDF and EEDF as a function of CURRENT

109

1010

1011

1012

1013

1014

1015

0.0 1.0 2.0 3.0 4.0 5.0

Id=5 A

Id=10 A

Id=20 A

energy (eV)

106

107

108

109

1010

1011

1012

0.0 20.0 40.0 60.0 80.0 100.0 120.0

Id=5 A

Id=10 A

Id=20 A

energy (eV)

TG =500 K

PRESSURE=7.5 mtorr

DISCHARGE VOLTAGE=100 V


RF DISCHARGES: PARALLEL PLATES

1D(r)2D(v) self-consistent particle/continuum model

• PIC/MCC applied to ELECTRONS and IONIC SPECIES

• GRID-DISCRETIZED RELAXATION technique for REACTION-DIFFUSION part

€

∂∂t

+ vx

∂

∂x−

qs

ms

∂ϕ x,t( )

∂x

∂

∂vx

⎛

⎝ ⎜

⎞

⎠ ⎟fs x,v,t( ) = Cs Fc{ }( )

€

∂2ϕ x,t( )

∂x2= −

1

ε 0

qs d3vfs(x,v,t)∫s

∑

€

−Dc

∂2nc x( )

∂x2= ′ ν rc − ν rc( )kr fe t( )

r∑ n ′ c

ν rc

′ c ∏

Cs: Boltzmann collision integral for charged/neutral collisions

BOUNDARYCONDITIONS POISSON EQUATION

REACTION/DIFFUSIONEQUATIONS

CHARGED PARTICLE KINETICS

SPACE CHARGE

EEDF

ELECTR./IONDENSITY

ELECTRICFIELD

GAS COMPOSITION

SURFACEREACTIONS

(WALL)

ABSORPTION,SEC.EMISSION


p = 10 mtorr d = 36 cm Vrf = 300 V

num

ber

dens

ity

(m-3)

position (m)

VD

F (

m-3)


mea

n ki

neti

c en

ergy

(eV

)

position (m)

EE

DF

(eV

-3/2)

energy (eV)


FUTURE STEPS

• CONSTRUCTION OF A DATA BASE OF CROSS SECTIONS FOR H2 AND ISOTOPES

• RYDBERG KINETICS AND GAS-SURFACE INTERACTIONS

• INSERTION OF THE COMPLETE DATA BASE IN 1D-2D CODES

• EXTENSION TO SURFACE SOURCES

• VALIDATION OF THE PREDICTIVE CODE WITH DEDICATED EXPERIMENTS

• AGREEMENT PROTOCOL WITH ITER PROGRAMME


HARPOON REACTION INVOLVING CESIUM ATOM AND HYDROGEN MOLECULE

€

Cs+H2∗⇔ Cs−+H2

+

€

σ =1.5 ×10−13cm2

€

k = 3×10−8cm3 / s

Asymptotic Approach


OUTLINE







ELECTRON IMPACT induced PROCESSES in HOMONUCLEAR DIATOMIC MOLECULES

VIBRONIC EXCITATION and (PRE)DISSOCIATION of O2 and N2

NON-DISSOCIATIVE IONIZATION of N2

AIR PLASMAS

ATOM-DIATOM COLLISION PROCESSES

DISSOCIATION/RECOMBINATION of O2 and N2

ENERGY EXCHANGE (VT Processes) of O2 and N2


0.00

5.00

10.00

15.00

20.00

25.00

0.5 1 1.5 2 2.5 3 3.5 4

Internuclear Distance (Å)

X1g+

A3u+

B3u

X2g+

A2u

B2u+

N2+

N2

F.R. Gilmore, J.Q.R.S.T. 5, 369 (1965)

N2-N2+ system POTENTIAL ENERGY CURVES

€

2e + N2+ (A2Π u )

€

e + N2 (X1Σg+ ,ν )

€

2e + N2+ (X2Σg

+ )

€

2e + N2+ (B2Σu

+ )

€

2e + N2+ (X2Σg

+ )

€

e + N2 (A3Σu+ ,ν )

€

e + N2 (B3Π g ,ν )

IONIZATION


IONIZATION CROSS SECTION of atoms by electron impact

CLASSICAL METHODS (THOMSON)

€

σ ION = n πe4

J2 ƒ

EJ

⎛ ⎝ ⎜

⎞ ⎠ ⎟ ƒ universal function

IONIZATION CROSS SECTION of vibrationally excited molecules

by electron impact

€

σION = ∑ν ' σ νν '

ION = ∑ν ' n πe4

Jνν '2

ƒE

Jν ′ ν

⎛

⎝ ⎜

⎞

⎠ ⎟ Sνν '

ionization potential

Franck-Condon factor

'ν"

R

U

M2

M2+

SIMPLIFIED APPROACH

€

σION = n

πe4

2

1

Jν ′ ν 2

ƒE

Jν ′ ν

⎛

⎝ ⎜

⎞

⎠ ⎟+

1

Jν ′ ′ ν 2

ƒE

Jν ′ ′ ν

⎛

⎝ ⎜

⎞

⎠ ⎟

⎡

⎣ ⎢

⎤

⎦ ⎥

ELECTRON-IMPACT IONIZATION: THEORETICAL APPROACH

€

Jν ′ ′ ν

€

Jν ′ ν


ELECTRON-IMPACT IONIZATION from GROUND STATEcross section [10-17 cm2]

0 0.82 2.1 3.44 0.87 2.2 3.58 0.92 2.2 3.612 0.92 2.2 3.616 0.92 2.3 3.620 0.97 2.3 3.724 1.0 2.4 3.828 1.0 2.4 3.832 1.1 2.5 3.936 1.1 2.5 3.940 1.1 2.5 3.9

0 0.79 2.9 5.24 0.90 3.1 5.38 0.95 3.2 5.412 1.0 3.3 5.516 1.2 3.5 5.820 1.4 3.7 6.124 1.5 3.9 6.428 1.6 4.1 6.632 1.8 4.3 6.836 1.8 4.4 6.940 1.9 4.5 7.3

0 0.13 1.0 2.04 0.16 1.1 2.18 0.20 1.2 2.212 0.26 1.3 2.316 0.32 1.4 2.520 0.39 1.5 2.624 0.47 1.6 2.828 0.56 1.7 2.932 0.65 1.9 3.136 0.75 2.0 3.340 0.83 2.1 3.4

€

N2 (X,ν) → N2+(X)

€

N2 (X,ν) → N2+(A)

€

N2 (X,ν) → N2+(B)

€

€

30eV

€

50eV

€

σ(E = 20eV)

€

€

30eV

€

50eV

€

σ(E = 20eV)

€

€

30eV

€

50eV

€

σ(E = 20eV)

[J.Geophys.Res. 100, 23755 (1995)]

ionic state Van Zyl this work0.320 0.300.535 0.500.145 0.20

€

N2+(X)

€

N2+(A)

€

N2+(B)

E=100eV


ELECTRON-IMPACT IONIZATION from EXCITED STATE

€

N2 (B,ν) → N2+ (X)

€

N2 (A,ν) → N2+ (X)

€

€

25eV

€

40eV

€

σ(E = 15eV)

0 9.6 11.6 1.4 3.1 4.24 8.8 12.0 1.7 3.5 4.68 8.2 12.4 2.1 4.0 5.112 7.6 12.8 2.6 4.5 5.616 7.1 13.2 3.0 5.1 6.220 6.8 13.6 3.4 5.5 6.624 6.6 14.0 3.7 5.8 6.8

€

Jν ′ ν [eV]

€

Jν ′ ′ ν [eV]

€

€

25eV

€

40eV

€

σ(E = 15eV)

€

Jν ′ ν [eV]

€

Jν ′ ′ ν [eV]

0 8.2 9.0 3.0 5.3 6.64 7.9 9.8 3.5 5.8 7.18 7.6 10.1 3.9 6.3 7.512 7.3 10.3 4.4 6.9 8.116 7.0 10.5 5.0 7.5 8.720 6.7 10.7 5.3 7.8 8.924 6.4 10.8 5.3 7.9 9.0


0

2

4

6

8

10

1.5 2 2.5 3 3.5 4 4.5 5

Potential Energy (eV)

Internuclear Distance (bohr)

X 3

g−

B 3

u−

3 u

1 u 5 u

2 3u+

O2 system POTENTIAL ENERGY CURVES:Schumann-Runge transition

O (3P) + O (3P)

O (3P) + O (1D)


0.00

0.20

0.40

0.60

0.80

0.0 20.0 40.0 60.0 80.0 100.0

Dissociative Cross Section (Å

2 )

Energy (eV)

i = 0

4 8,1012 2024

30

2

6

14 26 28

0.00

0.10

0.20

0.30

0.40

0.50

0.0 20.0 40.0 60.0 80.0 100.0

Bound-Bound ExcitationCross Section (Å

2 )

Energy (eV)

i = 0

4

816

2024

30

2

6

26 28

18

14

12

1

€ e+O2(X 3Σg−,ν)€ e+O2(B 3Σu−,ε)→e+2O€ e+O2(B 3Σu−,ν)predissociation ⏐ → ⏐ ⏐ ⏐ ⏐e+2ODISSOCIATIVE O2 CHANNELS


0.0

5.0

10.0

15.0

20.0

1.0 2.0 3.0 4.0 5.0

POTENTIAL ENERGY (eV)

INTERNUCLEAR DISTANCE (a0)

X 1 g

+

b 1 u

dissociation limit

( N 4 ) + ( S N4 )S

( N 2 ) + ( D N2 )D

i

f

ε

€

N2 (X 1Σg+ ,ν i ) + e → N2 (b 1Π u ,ε) + e → N + N + e

Direct Dissociation through the excited state

€

N2 (X 1Σg+ ,ν i ) + e → N2 (b 1Π u ,ν f ) + e

Vibronic Excitation

D.Spelsberg, W.Meyer, Journal of Chemical Physics 115 (2001) 6438

The N2 Birge-Hopfield system

Dissociation through Predissociative Channels

€

N + N + e


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 20.0 40.0 60.0 80.0 100.0

Total cross section (Å

2)

Energy (eV)

i = 05

1015 20

253035

40

0.0

0.1

0.2

0.3

0.4

0.0 20.0 40.0 60.0 80.0 100.0

Dissociative cross section (Å

2)

Energy (eV)

5

10

1520 25

3035

40

X 1g (i) b 1u X 1g (i) b 1u (continuum)

E=40eV E=40eV


CROSS SECTION DEPENDENCE on the INITIAL VIBRATIONAL QUANTUM NUMBER

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 5 10 15 20 25 30 35 40

CROSS SECTION (Å

2 )

INITIAL VIBRATIONAL QUANTUM NUMBER

E=40 eVTOTAL

DISSOCIATIVE

VIBRONICEXCITATION


DISSOCIATION CROSS SECTIONS FOR NITROGEN

rotationally averaged cross sections from =40, Trot= 50, 1000, 3000 K

rotationally averaged cross sections from =40,50,60,65, Trot= 3000 K


DISSOCIATION RATE COEFFICIENTS FOR NITROGEN

T = 300, 1000, 3000 K!!interpolated with polynomials of order 3-4!!

comparison of total dissociation rate coefficient with experimental results

Roth&Thielen (1986)

Appleton (1968)


VIBRATIONAL DE-EXCITATION RATE COEFFICIENTS FOR NITROGEN

comparison with theoretical results ofLaganà&Garcia (1996) (T=1000 K)

!!lines without points are reactive rates!!

-1, -5, -15, -25, -35 T=1000 K


DISSOCIATION RATE COEFFICIENTS FOR OXYGEN

T = 300, 1000, 3000 K


VIBRATIONAL DE-EXCITATION RATE COEFFICIENTS FOR OXYGEN

-1 T=1000 K



-5 T=1000 K



-15 T=1000 K



-25 T=1000 K



-35 T=1000 K



comparison of rate coefficients with Laganà&Garcia results on the same PES

-1(yellow) -5(black)


DISSOCIATION CROSS SECTIONS FOR OXYGEN

rotationally averaged cross sections from =30, Trot= 50,1000,3000,10000 K

rotationally averaged cross sections from =20,25,30,35,40, Trot= 1000 K


QuickTime™ e undecompressore TIFF (LZW)

sono necessari per visualizzare quest'immagine.

TOTAL DISSOCIATION CROSS SECTIONS FOR OXYGEN!! COMPARISON with some EXPERIMENTAL FITS!!

• Our rate is similar to that of Shatalov within ±13% over the whole interval 1000-10000K

• NF: no correction factor

• VF: variable factor


1. Excitation and de-excitation by electron impact

2. Ionization by electron impact and three body recombination

3. Spontaneous emission and absorption

4. Radiative recombination

Collisional-Radiative Model for Atomic Plasma

€

A(i)+e−(ε)kij →

k ji←

A( j)+e−( ′ ε )

€

A(i)+e−(ε)kic →

kci←

A+ +e−( ′ ε )+eb−(εb)

€

A(i) λijAij → A( j)+h ij with i> j

€

A+ +e−(ε) βi → A(i)+h


Rate Equations

€

dni

dt=+ njA ji

*

j>i∑ +ne njk ji

j≠i∑ +ne

2n+kci+nen+βi −ni A ij*

j<i∑ −nine kij

j≠i∑ −ninekic ∀i

€

dne

dt=dn+

dt=− dni

dti∑

Quasi-Stationary Solution(QSS)

€

dni

dt=0 ∀i

€

dni

dt≠0 ∀i

Stationary solution

Time-dependent solution

€

dni

dt=0 i≥2

dn1dt

≈−dne

dt=−dn+

dt


QSS approximation

€

dni

dt=0 i≥2

dn1dt

≈−dne

dt=−dn+

dt

⎧

⎨ ⎪

⎩ ⎪

€

X i =ni

niSB

€

dX1dt

=a11X1+ a1jX jj=2

i*

∑ −b1

€

X i≥2 =X i≥20 +Ri≥2

1 X1

€

aijX jj=1

i*

∑ =bi i >1

The ground state density changes like the density of the charged particles andthe excited states are in an instantaneous ionization-recombination equilibrium with the free electrons

differential equation for the ground state

system of linear equation for excited levels

The system of equations is linear in X1

€

X i≥20 =f(ne,Te)

€

Ri≥21 =f(ne,Te)

Xj (j>1) can be calculated when X1, ne, Te are given

€

X i≥2 =f(X1,ne,Te)


CR for Atomic Nitrogen Plasma: Energy-level Model

group Energy (cm-1) Statistical weight Terms1 0 4 2p34S2 19228 10 2p32D3 28840 6 2p32P4 83337 12 3s4P5 86193 6 3s”P6 95276 36 3p4S, 4P, 4D7 96793 18 3p2S,2P,2D8 103862 18 4s4P,2P9 104857 60 3d4P,4D,4F

10 104902 30 3d2P,2D,2F11 107125 54 4p4S,4P,4D,2S,2D,2P12 109951 18 5s4P,2P13 110315 90 4d4P,4D,4F,2P,2D,2F14 110486 126 4f4D,4F,4G,2D,2F,2G15 111363 54 5p4S,4P,4D,2S,2P,2D16 112691 18 6s4P,2P17 112851 90 5d4P,4D,4F,2P,2D,2F18 112955 288 5f,5g19 113391 54 6p20 114211 90 6d4P,4D,4F,2P,2D,2F21 114255 486 6f,6g,6h22 114914 882 n=723 115464 1152 n=824 115837 1458 n=925 116102 1800 n=1026 116298 2178 n=1127 116445 2592 n=1228 116560 3042 n=1329 116650 3528 n=1430 116724 4050 n=1531 116784 4608 n=1632 116834 5202 n=1733 116875 5832 n=1834 116910 6498 n=1935 116940 7200 n=20


CR for Atomic Nitrogen Plasma with QSS

Xi vs level energy

Te=5800 K Te=11600 K Te=17400 K

0.0001

0.001

0.01

0.1

1

10

8 104 8.5 104 9 104 9.5 104 1 105 1.05 105 1.1 105 1.15 105 1.2 105

ne=10

8 cm

-3

ne=1016 cm-3

level energy (cm-1

)

X1=1

0.0001

0.001

0.01

0.1

1

10

8 104 8.5 104 9 104 9.5 104 1 105 1.05 105 1.1 105 1.15 105 1.2 105

ne=108 cm-3

ne=1016 cm-3

level energy (cm-1

)

X1=1

0.0001

0.001

0.01

0.1

1

10

100

8 104 8.5 104 9 104 9.5 104 1 105 1.05 105 1.1 105 1.15 105 1.2 105

ne=108 cm-3

ne=1016 cm-3

level energy (cm-1

)

X1=1


Time-dependent solution

CR rate equations Boltzmann equation

€

dni

dt≠0 ∀i

Rate coefficients for electron impact processes

€

k= f(ε)Et

∞∫ σ(ε)v(ε)dεf(e) electron energy distribution functions(e) cross sectionv(e) electron velocity

level populationplasma composition

f(e)rate coefficients


ATOMIC HYDROGEN PLASMA

P=100 Torr, Tg=30000 K, Te(t=0)=1000 K H+ = e

- =10-8 , H=1, H(1)=1, H(i)=0 i>1

€

H(n≤25),H+ ,e−[ ]

0

5000

10000

15000

20000

25000

30000

35000

10-14 10-12 10-10 10-8 10-6 10-4 10-2 100 102 104 106

time (s)

108

1010

1012

1014

1016

10-5 10-4 10-3 10-2 10-1

H

H+

e-

time (s)

10-20

10-18

10-16

10-14

10-12

10-10

10-8

10-6

0.0001

0.01

1

100

104

10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1

i=1i=2i=5i=10i=15i=20i=25

time (s)

density (cm-3) vs time(s) Xi = ni/niSB vs time(s) Te vs time(s)


10-30

10-28

10-26

10-24

10-22

10-20

10-18

10-16

10-14

10-12

10-10

10-8

10-6

0.0001

0.01

1

0 5 10 15 20 25

t(s)=0 s

t(s)=10-10 s

t(s)=10-9 s

t(s)=5 10-9 s

t(s)=10-8 s

t(s)=3 10-8 s

t(s)=5 10-8 s

t(s)=8 10-8 s

t(s)=10-7 s

t(s)=10-6 s

t(s)=10-5

s

t(s)=10-4 s

t(s)=8 10-4 s

t(s)=9 10-4 s

t(s)=10-3 s

ε( )eV

Tfit = 30020 K

H(i)/g(i) vs Ei

10-30

10-28

10-26

10-24

10-22

10-20

10-18

10-16

10-14

10-12

10-10

10-8

10-6

0.0001

0.01

0 2 4 6 8 10 12 14

t(s)=0 s

t(s)=10-10

s

t(s)=10-9

s

t(s)=5 10-9 s

t(s)=10-8 s

t(s)=3 10-8 s

t(s)=5 10-8 s

t(s)=8 10-8 s

t(s)=10-7 s

t(s)=10-6 s

t(s)=10-5 s

t(s)=10-4 s

t(s)=8 10-4 s

t(s)=9 10-4 s

t(s)=10-3 s

( )level energy eV

Tfit = 29986 K

eedf(eV-3/2) vs E

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M.Capitelli Dipartimento di Chimica, Università di Bari, Italy IMIP-CNR, Bari, Italy.

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