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

2. COLLABORATORS

3. Diamond Film Production
QUANTUM CHEMISTRY
MOLECULAR DYNAMICS
ELECTRON-IMPACT
induced PROCESSES
(inelastic+reactive)
Semiclassical
Impact Parameter
Method
HEAVY PARTICLE
COLLISIONS
(inelastic+reactive)
Quasiclassical
Trajectory
Method
GAS-SURFACE
INTERACTION
Semiclassical
Collisional Model
COLLISION INTEGRALS
ground state
excited states
Maxwell Distribution
(DSMC)
Boltzmann Equation for electrons (PIC-MCC)
RATE COEFFICIENTS
Chapman-Enskog
TRANSPORT PROPERTIES
KINETICS
FLUIDYNAMICS
PARALLEL PLATE
(PIC-MCC)
Microelectronics
LASER-PLASMA
Interaction
MULTICUSP
(Magnetic Plasmas)
Filament RF
H-/D- Production
AEROSPACE
Reentry
Problems
RF TORCHES
Waste Discharges
Metallurgy
MICROWAVE DISCHARGES
(Maxwell Equations)
Diamond Film Production
DIVERTOR
Plasmas

4. OUTLINE - Open problems (1985-1995) in Multipole Magnetic Plasmas
a) Validation of Bari code with FOM experiments
b) Extension to D2 plasmas
c) Pulsed discharges
d) Rydberg states
e) Wall effects
- Cross Section Improvements ( )
a) Electron-molecule cross sections
b) Heavy particle collision cross sections
c) Gas surface interaction
- Kinetic models Improvements( )
a) New multipole zerodimensional code
b) Parallel-plate 1D code
c) RF and MW quasi 1D code
- Air Plasmas
a) N2 and O2 State-to-State Cross Sections

5. OUTLINE - Open problems (1985-1995) in Multipole Magnetic Plasmas
a) Validation of Bari code with FOM experiments
b) Extension to D2 plasmas
c) Pulsed discharges
d) Rydberg states
e) Wall effects
- Cross Section Improvements ( )
a) Electron-molecule cross sections
b) Heavy particle collision cross sections
c) Gas surface interaction
- Kinetic models Improvements( )
a) New multipole zerodimensional code
b) Parallel-plate 1D code
c) RF and MW quasi 1D code
- Air Plasmas
a) N2 and O2 State-to-State Cross Sections

6. VIBRATIONAL EXCITATION and NEGATIVE ION KINETICS
MULTIPOLE MAGNETIC PLASMAS:
!! Self-consistent non equilibrium vibrational kinetics coupled to the Boltzmann equation for the electron energy distribution function!!
Time Evolution
(heavy species)
Electron source term:
Term due to inelastic collisions
Term due to ionization collisions
Term due to superelastic collisions
Electron loss term
Flux of electrons along energy axis due to elastic collisions
Flux of electrons along energy axis due to electron-electron collisions

7. VALIDATION of BARI CODE with the FOM EXPERIMENTS (GORSE ET AL. 1992)
comparison between experimental (a) and theoretical (b) vdfs at several pressures
comparison between experimental (a) and theoretical (b) vdfs at several discharge currents Id

8. !!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!!
vibrational distribution Nv measured in a H2 multicusp source (p = mtorr, Id = 0.5 A, Vd = 100 V)

9. EXTENSION to D2 PLASMAS
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)
dissociative attachment rates versus vibrational quantum number
for H2 and D2 molecules

10. (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)

11. (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)

12. DISSOCIATIVE ATTACHMENT: H2 (X 1g,) + e  H2-  H- + H
E = 4.5 eV

13. RESONANT VIBRATIONAL EXCITATION:
H2 (X 1g,  i) + e  H2-  H2 (X 1g,  f) + e
E = 5 eV

14. PULSED DISCHARGES: MODEL
Relaxation of several quantities in the D2 post-discharge regime
(a) EEDF, (b) e-da rate coefficient, (c) Nv, (d) D- density

15. PULSED DISCHARGES: EXPERIMENT
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)

16. 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 plasmas
Result: 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/sec
Result: lifetime of Rydberg states of the order of 10-8sec
Consequence: contribution of Rydberg states 1%

17. RYDBERG STATES: HYSTORICAL SCENARIO/2
Pinnaduwage et al. [Phys. Rev. A 55, 4131 (1997)]
e + H2* = H + H Kda(Ryd) = 510-5 cm3/sec
Hassouni et al. [Chem. Phys. Lett. 290, 502 (1998)]
Model: collisional radiative model for H2* Rydberg states + Kda(Ryd)= cm3/sec
Result: enhancement by factor 2.7
Problem: Rydberg state from n>3
Pinnaduwage et al. [J.Appl.Phys. 85, 7064 (1999)]
scaling law for Rydberg states
which corresponds to n=12
An estimation
For a plateau between cm-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

18. 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

19. WALL EFFECTS: HYSTORICAL SCENARIO
Hiskes & Karo
Model: trajectory calculations
Results: strong deactivation of vibrationally excited molecules on iron surfaces - widely used in multicusp modelling
Billing & Cacciatore
Model: 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 metal
Results : small deactivation of vibrationally excited molecules on copper surfaces

20. 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
1,0
0,0
0,1
0,016
2,0
0,70 1
0,026 6
0,2
0,0024
0,4
0,0060
0,6
0,0095
0,62
0,014 8
0,05
8 (7)
0,001 10
0,95
a) Dissociation probability
b) Averaged values for reflected trajectories
c) Energy transferred to surface phonons

21. H(gas) + Hads  H2() DIRECT ELEY RIDEAL (E-R) MECHANISM
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

22. semiclassical collisional method
Hads
equilibrium distance of 1.5 Å
in thermal equilibrium with the surface
Hgas
(;)
Ekin TS
ELEY-RIDEL MECHANISM MD
energetic fluxes
surface temperature effect
recombination
probabilities
H2 vibrational
distribution
reaction probabilities
for different reaction products

23. VIBRATIONAL DISTRIBUTIONS from PHYSIADSORBED H and D ATOMS on COPPER
(E-R mechanism, BILLING&CACCIATORE)

24. P () VIBRATIONAL DISTRIBUTIONS from CHEMIADSORBED H ATOMS on COPPER
(HA-SHALASHILIN et al.) for the REACTION Hgas + Dads  HD()
P ()
vibrational quantum number

25. (v, j) distribution of the H2 product
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

26. VIBRATIONAL DISTRIBUTIONS from PHYSIADSORBED H ATOMS on GRAPHITE
(E-R mechanism, BILLING&CACCIATORE)
0.00
0.10
0.20
0.30
0.40
0.50 2 4 6 8 10 12
VIBRATIONAL QUANTUM NUMBER
TS = 500K

27. OUTLINE - Open problems (1985-1995) in Multipole Magnetic Plasmas
a) Validation of Bari code with FOM experiments
b) Extension to D2 plasmas
c) Pulsed discharges
d) Rydberg states
e) Wall effects
- Cross Section Improvements ( )
a) Electron-molecule cross sections
b) Heavy particle collision cross sections
c) Gas surface interaction
- Kinetic models Improvements( )
a) New multipole zerodimensional code
b) Parallel-plate 1D code
c) RF and MW quasi 1D code
- Air Plasmas
a) N2 and O2 State-to-State Cross Sections

28. ELECTRONIC EXCITATION to the lowest SINGLETS
CROSS SECTIONS IMPROVEMENTS
ELECTRONIC EXCITATION to the lowest SINGLETS
X 1g (i)  B 1  u
X 1  g ( i)  C 1u

29. IMPACT PARAMETER METHOD DISSOCIATIVE EXCITATION
THEORETICAL APPROACH
IMPACT PARAMETER METHOD
SEMICLASSICAL Method (quantal target - classical projectile)
ALLOWED Transitions (selection rules)
degenerate rotational levels
TOTAL
CROSS SECTION
VIBRONIC EXCITATION
DISSOCIATIVE EXCITATION
STRUCTURAL FACTOR
DYNAMICAL FACTOR
TRANSITION DIPOLE MOMENT
IMPACT PARAMETER
(BORN cross section)

30. CROSS SECTIONS for H2 ISOTOPIC VARIANTS
E = 40 eV
X 1g (i)  B 1  u

31. RESONANT VIBRATIONAL EXCITATION
H2 (X 1g, ni) + e  H2-  H2 (X 1g, nf) + e
E = 5 eV

32. EXCITATION of low-lying RYDBERG STATES
X 1g (i)  B’ 1  u
X 1  g ( i)  D 1u
X 1g (i)  B” 1  u
X 1  g ( i)  D’ 1u

33. s  n-4

34. DIRECT DISSOCIATION through EXCITED STATES
excited bound state ’
DISSOCIATION
B 1  u and C 1  u + low-lying RYDBERG STATES B’, B” 1  u , D, D’ 1  u 
DISSOCIATION
pure repulsive state i

35. months on fast processor
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
good
months on fast processor

36. RATE COEFFICIENTS for the PROCESS: H+H2(,Trot)  3H
Trot=500 K H2 D2

37. HYDROGEN VIBRATIONAL EXCITATION RATE COEFFICIENTS
as a FUNCTION of FINAL VIBRATIONAL QUANTUM NUMBER

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

39. HYDROGEN VIBRATIONAL MONOQUANTUM DEACTIVATION RATE COEFFICIENTS

40. HYDROGEN RECOMBINATION RATE COEFFICIENTS
as a FUNCTION of FINAL VIBRATIONAL QUANTUM NUMBER
!! normalized to total recombination, at different temperatures !!

41. OUTLINE - Open problems (1985-1995) in Multipole Magnetic Plasmas
a) Validation of Bari code with FOM experiments
b) Extension to D2 plasmas
c) Pulsed discharges
d) Rydberg states
e) Wall effects
- Cross Section Improvements ( )
a) Electron-molecule cross sections
b) Heavy particle collision cross sections
c) Gas surface interaction
- Kinetic models Improvements( )
a) New multipole zerodimensional code
b) Parallel-plate 1D code
c) RF and MW quasi 1D code
- Air Plasmas
a) N2 and O2 State-to-State Cross Sections

42. KINETIC MODELS IMPROVEMENTS
MULTIPOLE H2 DISCHARGES
!! Time dependent electron kinetics and vibrational kinetics treated at the same level!! i
ELECTRON ENERGY DISCRETIZATION
for
each electron energy sub-interval
a “different electron” characterized by a representative energy
i (sub-interval mean energy)
ELECTRONS STATE-TO-STATE KINETICS
(electrons with different energies
as molecular energy levels)
discretized electron rate coefficients:

43. VDF and EEDF as a function of PRESSURE
TG =500 K
DISCHARGE CURRENT=10 A
DISCHARGE VOLTAGE=100 V

44. VDF and EEDF as a function of CURRENT
TG =500 K
PRESSURE=7.5 mtorr
DISCHARGE VOLTAGE=100 V

45. RF DISCHARGES: PARALLEL PLATES
1D(r)2D(v) self-consistent particle/continuum model
BOUNDARY
CONDITIONS
POISSON EQUATION
REACTION/DIFFUSION
EQUATIONS
CHARGED PARTICLE
KINETICS
SPACE
CHARGE
EEDF
ELECTR./ION
DENSITY
ELECTRIC
FIELD
GAS COMPOSITION
SURFACE
REACTIONS
 (WALL)
ABSORPTION,
SEC.EMISSION
PIC/MCC
applied to ELECTRONS and IONIC SPECIES
GRID-DISCRETIZED RELAXATION technique
for REACTION-DIFFUSION part
Cs: Boltzmann collision integral for charged/neutral collisions

46. p = 10 mtorr d = 36 cm Vrf = 300 V mean kinetic energy(eV)
number density (m-3)
position (m)
position (m)
EEDF (eV-3/2)
VDF (m-3)
vibrational quantum number
energy (eV)

47. 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

48.  HARPOON REACTION INVOLVING CESIUM ATOM AND HYDROGEN MOLECULE
Asymptotic Approach

49. OUTLINE - Open problems (1985-1995) in Multipole Magnetic Plasmas
a) Validation of Bari code with FOM experiments
b) Extension to D2 plasmas
c) Pulsed discharges
d) Rydberg states
e) Wall effects
- Cross Section Improvements ( )
a) Electron-molecule cross sections
b) Heavy particle collision cross sections
c) Gas surface interaction
- Kinetic models Improvements( )
a) New multipole zerodimensional code
b) Parallel-plate 1D code
c) RF and MW quasi 1D code
- Air Plasmas
a) N2 and O2 State-to-State Cross Sections

50. AIR PLASMAS ELECTRON IMPACT induced PROCESSES
in HOMONUCLEAR DIATOMIC MOLECULES
NON-DISSOCIATIVE IONIZATION of N2
VIBRONIC EXCITATION and (PRE)DISSOCIATION of O2 and N2
ATOM-DIATOM COLLISION PROCESSES
DISSOCIATION/RECOMBINATION of O2 and N2
ENERGY EXCHANGE (VT Processes) of O2 and N2

51. N2-N2+ system POTENTIAL ENERGY CURVES
IONIZATION
N2-N2+ system POTENTIAL ENERGY CURVES
F.R. Gilmore, J.Q.R.S.T. 5, 369 (1965)

52. ELECTRON-IMPACT IONIZATION: THEORETICAL APPROACH
IONIZATION CROSS SECTION
of atoms by electron impact
CLASSICAL METHODS (THOMSON)
ƒ universal function
IONIZATION CROSS SECTION
of vibrationally excited molecules
by electron impact
Franck-Condon factor
SIMPLIFIED APPROACH
ionization potential

53. ELECTRON-IMPACT IONIZATION from GROUND STATE
cross section [10-17 cm2]
ionic state Van Zyl this work
E=100eV
[J.Geophys.Res. 100, (1995)]

54. ELECTRON-IMPACT IONIZATION from EXCITED STATE

55. O2 system POTENTIAL ENERGY CURVES: Schumann-Runge transition

56. DISSOCIATIVE O2 CHANNELS

57. The N2 Birge-Hopfield system
Direct Dissociation through the excited state
Vibronic Excitation
Dissociation through
Predissociative Channels
D.Spelsberg, W.Meyer, Journal of Chemical Physics 115 (2001) 6438

58. X 1g (i)  b 1u (continuum)
E=40eV

59. CROSS SECTION DEPENDENCE on the INITIAL VIBRATIONAL QUANTUM NUMBER

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

61. T = 300, 1000, 3000 K DISSOCIATION RATE COEFFICIENTS FOR NITROGEN
!!interpolated with polynomials of order 3-4!!
comparison of total dissociation
rate coefficient with experimental results
Appleton (1968)
Roth&Thielen (1986)

62. VIBRATIONAL DE-EXCITATION RATE COEFFICIENTS FOR NITROGEN
-1, -5, -15, -25, -35 T=1000 K
comparison with theoretical results of
Laganà&Garcia (1996) (T=1000 K)
!!lines without points are reactive rates!!

63. DISSOCIATION RATE COEFFICIENTS FOR OXYGEN
T = 300, 1000, 3000 K

64. VIBRATIONAL DE-EXCITATION RATE COEFFICIENTS FOR OXYGEN
-1 T=1000 K

65. VIBRATIONAL DE-EXCITATION RATE COEFFICIENTS FOR OXYGEN
-5 T=1000 K

66. VIBRATIONAL DE-EXCITATION RATE COEFFICIENTS FOR OXYGEN
-15 T=1000 K

67. VIBRATIONAL DE-EXCITATION RATE COEFFICIENTS FOR OXYGEN
-25 T=1000 K

68. VIBRATIONAL DE-EXCITATION RATE COEFFICIENTS FOR OXYGEN
-35 T=1000 K

69. -1(yellow) -5(black)
VIBRATIONAL DE-EXCITATION RATE COEFFICIENTS FOR OXYGEN
comparison of rate coefficients
with Laganà&Garcia results on the same PES
-1(yellow) -5(black)

70. rotationally averaged cross sections
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

71. 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 K
NF: no correction factor
VF: variable factor

72. Collisional-Radiative Model for Atomic Plasma
Excitation and de-excitation by electron impact
Ionization by electron impact and three body recombination
Spontaneous emission and absorption
Radiative recombination

73. Rate Equations Stationary solution Quasi-Stationary Solution(QSS)
Time-dependent solution

74. QSS approximation
The ground state density changes like the density of the charged particles and
the 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
Xj (j>1) can be calculated when
X1, ne, Te are given
The system of equations is linear in X1

75. CR for Atomic Nitrogen Plasma: Energy-level Model

76. CR for Atomic Nitrogen Plasma with QSS
Xi vs level energy
Te=5800 K
Te=11600 K
Te=17400 K

77. Time-dependent solution
Rate coefficients for electron impact processes
f(e) electron energy distribution function
s(e) cross section
v(e) electron velocity
rate coefficients
f(e)
CR rate equations
Boltzmann equation
level population
plasma composition

78. ATOMIC HYDROGEN PLASMA
P=100 Torr, Tg=30000 K, Te(t=0)=1000 K c H+ =c e- =10-8 ,
cH=1, cH(1)=1, cH(i)=0 i>1
density (cm-3) vs time(s)
Xi = ni/niSB vs time(s)
Te vs time(s)

79. cH(i)/g(i) vs Ei
eedf(eV-3/2) vs E