m.capitelli dipartimento di chimica, università di bari, italy imip-cnr, bari, italy
TRANSCRIPT
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
€
∂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!!
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
population densities (cm
-3)
vibrational quantum number
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
population densities (cm
-3)
vibrational quantum number
a)
1010
1012
1014
1016
0 2 4
Id=5 AId=10 AId=20 AId=30 A
population densities (cm
-3)
vibrational quantum number
b)
comparison between experimental (a) and theoretical (b) vdfs at several discharge currents I d
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
!!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 quantum number
vibrational distribution Nv measured in a H2 multicusp source (p = 11.25 mtorr, Id = 0.5 A, Vd = 100 V)
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
population densities (cm
-3)
vibrational quantum number
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
vibrational quantum number
H2
D2
rate coefficients (cm
3 s-1)
dissociative attachment rates versus vibrational quantum number for H2 and D2 molecules
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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)
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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)
discharge current (A)
D2
H2
b)
5
15
25
35
0 4 8 12 16 20 24 28 32atom D/H concentration (10
12
cm-3
)
discharge current (A)
D2
H2
c)
2
6
10
14
18
0 4 8 12 16 20 24 28 32D-/H
- ion concentration (10
9 cm
-3)
discharge current (A)
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)
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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)
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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)
vibrational quantum number
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)
vibrational quantum number
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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)
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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%
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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∑
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
vibrational quantum number
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
vibrational quantum number
T = 5000 K
Dgas
+ Dads
D2(v,j) →
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
VIBRATIONAL DISTRIBUTIONS from CHEMIADSORBED H ATOMS on COPPER (HA-SHALASHILIN et al.) for the REACTION Hgas + Dads HD()
P (
)
vibrational quantum number
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
VIBRATIONAL EXCITATION
(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
VIBRATIONAL EXCITATION
(Å2)
f =
i+2
RESONANT VIBRATIONAL EXCITATIONH2 (X 1g, ni) + e H2
- H2 (X 1g, nf) + e
E = 5 eV
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
RATE COEFFICIENTS for the PROCESS: H+H2(,Trot) 3H
Trot=500 K
H2 D2
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
HYDROGEN VIBRATIONAL MONOQUANTUM DEACTIVATION RATE COEFFICIENTS
€
H2 (ν ,Trot = 500K )+ H → H2 (ν −1,Trot = 500K )+ H
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
!! 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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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:
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
p = 10 mtorr d = 36 cm Vrf = 300 V
num
ber
dens
ity
(m-3)
position (m)
VD
F (
m-3)
vibrational quantum number
mea
n ki
neti
c en
ergy
(eV
)
position (m)
EE
DF
(eV
-3/2)
energy (eV)
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
HARPOON REACTION INVOLVING CESIUM ATOM AND HYDROGEN MOLECULE
€
Cs+H2∗⇔ Cs−+H2
+
€
σ =1.5 ×10−13cm2
€
k = 3×10−8cm3 / s
Asymptotic Approach
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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)
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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)
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
DISSOCIATION RATE COEFFICIENTS FOR OXYGEN
T = 300, 1000, 3000 K
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
VIBRATIONAL DE-EXCITATION RATE COEFFICIENTS FOR OXYGEN
-1 T=1000 K
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
VIBRATIONAL DE-EXCITATION RATE COEFFICIENTS FOR OXYGEN
-5 T=1000 K
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
VIBRATIONAL DE-EXCITATION RATE COEFFICIENTS FOR OXYGEN
-15 T=1000 K
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
VIBRATIONAL DE-EXCITATION RATE COEFFICIENTS FOR OXYGEN
-25 T=1000 K
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
VIBRATIONAL DE-EXCITATION RATE COEFFICIENTS FOR OXYGEN
-35 T=1000 K
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
VIBRATIONAL DE-EXCITATION RATE COEFFICIENTS FOR OXYGEN
comparison of rate coefficients with Laganà&Garcia results on the same PES
-1(yellow) -5(black)
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
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A(i)+e−(ε)kij →
k ji←
A( j)+e−( ′ ε )
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A(i)+e−(ε)kic →
kci←
A+ +e−( ′ ε )+eb−(εb)
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A(i) λijAij → A( j)+h ij with i> j
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A+ +e−(ε) βi → A(i)+h
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
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dne
dt=dn+
dt=− dni
dti∑
Quasi-Stationary Solution(QSS)
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dni
dt=0 ∀i
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dni
dt≠0 ∀i
Stationary solution
Time-dependent solution
€
dni
dt=0 i≥2
dn1dt
≈−dne
dt=−dn+
dt
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
QSS approximation
€
dni
dt=0 i≥2
dn1dt
≈−dne
dt=−dn+
dt
⎧
⎨ ⎪
⎩ ⎪
€
X i =ni
niSB
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dX1dt
=a11X1+ a1jX jj=2
i*
∑ −b1
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X i≥2 =X i≥20 +Ri≥2
1 X1
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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
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X i≥20 =f(ne,Te)
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Ri≥21 =f(ne,Te)
Xj (j>1) can be calculated when X1, ne, Te are given
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X i≥2 =f(X1,ne,Te)
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
Time-dependent solution
CR rate equations Boltzmann equation
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dni
dt≠0 ∀i
Rate coefficients for electron impact processes
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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
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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
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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)
CRP (COORDINATED RESEARCH PROJECT), IAEA MEETING “ATOMIC and MOLECULAR DATA for PLASMA MODELING”VIENNA, SEPTEMBER 26-28, 2005
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