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

COLLABORATORS

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

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 (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 code b) Parallel-plate 1D code c) RF and MW quasi 1D code - Air Plasmas a) N2 and O2 State-to-State Cross Sections

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 (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 code b) Parallel-plate 1D code c) RF and MW quasi 1D code - Air Plasmas a) N2 and O2 State-to-State Cross Sections

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

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

!!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 = 11.25 mtorr, Id = 0.5 A, Vd = 100 V)

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

(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)

(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 1g,) + e  H2-  H- + H E = 4.5 eV

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

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

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)

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%

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)=5 10-5 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 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

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 & 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

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

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

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

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

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

(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

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

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 (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 code b) Parallel-plate 1D code c) RF and MW quasi 1D code - Air Plasmas a) N2 and O2 State-to-State Cross Sections

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

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)

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

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

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

s  n-4

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

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

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

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

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

HYDROGEN VIBRATIONAL MONOQUANTUM DEACTIVATION RATE COEFFICIENTS

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

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 (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 code b) Parallel-plate 1D code c) RF and MW quasi 1D code - Air Plasmas a) N2 and O2 State-to-State Cross Sections

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:

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

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

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

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)

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 Asymptotic Approach

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 (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 code b) Parallel-plate 1D code c) RF and MW quasi 1D code - Air Plasmas a) N2 and O2 State-to-State Cross Sections

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

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

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

ELECTRON-IMPACT IONIZATION from GROUND STATE cross section [10-17 cm2] ionic state Van Zyl this work 0.320 0.30 0.535 0.50 0.145 0.20 E=100eV [J.Geophys.Res. 100, 23755 (1995)]

ELECTRON-IMPACT IONIZATION from EXCITED STATE

O2 system POTENTIAL ENERGY CURVES: Schumann-Runge transition

DISSOCIATIVE O2 CHANNELS

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

X 1g (i)  b 1u (continuum) E=40eV

CROSS SECTION DEPENDENCE on the INITIAL VIBRATIONAL QUANTUM NUMBER

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

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)

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!!

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

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

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

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

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

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

-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)

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

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

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

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

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

CR for Atomic Nitrogen Plasma: Energy-level Model

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

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

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)

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