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

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COLLABORATORS

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QUANTUM CHEMISTRY MOLECULAR DYNAMICS COLLISION INTEGRALS ground state excited states Maxwell Distribution (DSMC) Boltzmann Equation for electrons (PIC-MCC) RATE COEFFICIENTS KINETICS LASER-PLASMA Interaction DIVERTOR Plasmas MULTICUSP (Magnetic Plasmas) Filament RF 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 Reentry Problems FLUIDYNAMICS ELECTRON-IMPACT induced PROCESSES (inelastic+reactive) Semiclassical Impact Parameter Method HEAVY PARTICLE COLLISIONS (inelastic+reactive) Quasiclassical Trajectory Method GAS-SURFACE INTERACTION Semiclassical Collisional Model

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OUTLINE - Open problems ( ) in Multipole Magnetic Plasmas a) Validation of Bari code with FOM experiments b) Extension to D 2 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) N 2 and O 2 State-to-State Cross Sections

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OUTLINE - Open problems ( ) in Multipole Magnetic Plasmas a) Validation of Bari code with FOM experiments b) Extension to D 2 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) N 2 and O 2 State-to-State Cross Sections

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VIBRATIONAL EXCITATION and NEGATIVE ION KINETICS Time Evolution (heavy species) 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 Electron source term: MULTIPOLE MAGNETIC PLASMAS: !! Self-consistent non equilibrium vibrational kinetics coupled to the Boltzmann equation for the electron energy distribution function!!

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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 I d

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!!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 N v measured in a H 2 multicusp source (p = mtorr, I d = 0.5 A, V d = 100 V)

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EXTENSION to D 2 PLASMAS theoretical EEDF (a) and N v (b) in H 2 and D 2 sources (p = 4.5 mtorr, I d = 10 A, V d = 115 V, plasma potential V p = 2.9 V) dissociative attachment rates versus vibrational quantum number for H 2 and D 2 molecules

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(a) behavior of electron density ne (b) electron temperature Te (c) atomic concentration [H]/[D] (d) negative ion concentration [H - ]/[D - ] for H 2 and D 2 systems versus pressure p (I d = 10 A, V d = 115 V)

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(a) behavior of electron density ne (b) electron temperature Te (c) atomic concentration [H]/[D] (d) negative ion concentration [H - ]/[D - ] for H 2 and D 2 systems versus current I d (p = 7.5 mtorr, V d = 115 V)

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DISSOCIATIVE ATTACHMENT: H 2 (X 1 g, ) + e H 2 - H - + H E = 4.5 eV

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RESONANT VIBRATIONAL EXCITATION: H 2 (X 1 g, i ) + e H 2 - H 2 (X 1 g, f ) + e E = 5 eV

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PULSED DISCHARGES: MODEL Relaxation of several quantities in the D 2 post-discharge regime (a) EEDF, (b) e-da rate coefficient, (c) N v, (d) D - density

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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, I d = 15 A)

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RYDBERG STATES: HYSTORICAL SCENARIO/1 Pinnaduwage et al. [Phys. Rev. Lett. 70, 754 (1993)] e + H 2 * H + H - K da (Ryd)=10 -6 cm 3 /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 sec + K da (Ryd)=10 -6 cm 3 /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 H 2 * Rydberg states + K da (Ryd)=10 -6 cm 3 /sec Result: lifetime of Rydberg states of the order of sec Consequence: contribution of Rydberg states 1%

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RYDBERG STATES: HYSTORICAL SCENARIO/2 Pinnaduwage et al. [Phys. Rev. A 55, 4131 (1997)] e + H 2 * = H + H - K da (Ryd) = 5 cm 3 /sec Hassouni et al. [Chem. Phys. Lett. 290, 502 (1998)] Model: collisional radiative model for H 2 * Rydberg states + K da (Ryd)= cm 3 /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/ to 1/ cm -3 can be of the same importance as the dissociative attachment from vibrationally excited molecules

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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

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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

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Dissociation Probabilities and Energy Accommodation for H 2 (v,j) Colliding with a Cu(100) Surface as a Function of Vibrational and Rotational Angular Momenta v and j and Initial Kinetic Energy jE kin [eV]P D a) ’ b) j’ b) E int b,c) [eV] 501,00,050,10,016 2,00,70510, ,20,060,10,0024 0,40,060,10,0060 0,60,0610,0095 1,00,62610, ,050,08 (7)00,001 0,21,0 1000,050,95 0,11,0 a) Dissociation probability b) Averaged values for reflected trajectories c) Energy transferred to surface phonons

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FORMATION OF VIBRATIONALLY EXCITED STATES from HETEROGENEOUS ATOM RECOMBINATION H(gas) + H ads H 2 ( ) DIRECT ELEY RIDEAL (E-R) MECHANISM H(gas) H (trapped) H(trapped) + H ads H 2 ( ) HOT ATOM (HA) MECHANISM H ads + H ads H 2 ( ) 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

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semiclassical collisional method H ads equilibrium distance of 1.5 Å in thermal equilibrium with the surface H gas TSTS ( ; ) E kin MD energetic fluxes H 2 vibrational distribution recombination probabilities reaction probabilities for different reaction products surface temperature effect ELEY-RIDEL MECHANISM

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

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VIBRATIONAL DISTRIBUTIONS from CHEMIADSORBED H ATOMS on COPPER (HA-SHALASHILIN et al.) for the REACTION H gas + D ads HD( ) P ( ) vibrational quantum number

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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 H 2 product

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VIBRATIONAL DISTRIBUTIONS from PHYSIADSORBED H ATOMS on GRAPHITE (E-R mechanism, BILLING&CACCIATORE) T S = 500K VIBRATIONAL QUANTUM NUMBER

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OUTLINE - Open problems ( ) in Multipole Magnetic Plasmas a) Validation of Bari code with FOM experiments b) Extension to D 2 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) N 2 and O 2 State-to-State Cross Sections

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ELECTRONIC EXCITATION to the lowest SINGLETS X 1 g ( i ) C 1 u X 1 g ( i ) B 1 u CROSS SECTIONS IMPROVEMENTS

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

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CROSS SECTIONS for H 2 ISOTOPIC VARIANTS E = 40 eV X 1 g ( i ) B 1 u

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RESONANT VIBRATIONAL EXCITATION H 2 (X 1 g, n i ) + e H 2 - H 2 (X 1 g, n f ) + e E = 5 eV

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EXCITATION of low-lying RYDBERG STATES X 1 g ( i ) D 1 u X 1 g ( i ) B’ 1 u X 1 g ( i ) D’ 1 u X 1 g ( i ) B” 1 u

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n -4

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DISSOCIATION DIRECT DISSOCIATION through EXCITED STATES 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 ’’

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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 LOADRELIABILITY of METHOD good months on fast processor

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RATE COEFFICIENTS for the PROCESS: H+H 2 (,T rot ) 3H T rot =500 K H2H2 D2D2

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

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

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HYDROGEN VIBRATIONAL MONOQUANTUM DEACTIVATION RATE COEFFICIENTS

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

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OUTLINE - Open problems ( ) in Multipole Magnetic Plasmas a) Validation of Bari code with FOM experiments b) Extension to D 2 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) N 2 and O 2 State-to-State Cross Sections

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KINETIC MODELS IMPROVEMENTS MULTIPOLE H 2 DISCHARGES !! Time dependent electron kinetics and vibrational kinetics treated at the same level!! for ii ELECTRON ENERGY DISCRETIZATION each electron energy sub-intervala “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:

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

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

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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 C s : Boltzmann collision integral for charged/neutral collisions 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

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

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FUTURE STEPS CONSTRUCTION OF A DATA BASE OF CROSS SECTIONS FOR H 2 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

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HARPOON REACTION INVOLVING CESIUM ATOM AND HYDROGEN MOLECULE Asymptotic Approach

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OUTLINE - Open problems ( ) in Multipole Magnetic Plasmas a) Validation of Bari code with FOM experiments b) Extension to D 2 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) N 2 and O 2 State-to-State Cross Sections

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ELECTRON IMPACT induced PROCESSES in HOMONUCLEAR DIATOMIC MOLECULES VIBRONIC EXCITATION and (PRE)DISSOCIATION of O 2 and N 2 NON-DISSOCIATIVE IONIZATION of N 2 AIR PLASMAS ATOM-DIATOM COLLISION PROCESSES DISSOCIATION/RECOMBINATION of O 2 and N 2 ENERGY EXCHANGE (VT Processes) of O 2 and N 2

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F.R. Gilmore, J.Q.R.S.T. 5, 369 (1965) N 2 -N 2 + system POTENTIAL ENERGY CURVES IONIZATION

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

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ELECTRON-IMPACT IONIZATION from GROUND STATE cross section [ cm 2 ] [ J.Geophys.Res. 100, (1995) ] ionic stateVan Zylthis work E=100eV

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ELECTRON-IMPACT IONIZATION from EXCITED STATE

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O 2 system POTENTIAL ENERGY CURVES: Schumann-Runge transition

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DISSOCIATIVE O 2 CHANNELS

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Direct Dissociation through the excited state Vibronic Excitation D.Spelsberg, W.Meyer, Journal of Chemical Physics 115 (2001) 6438 The N 2 Birge-Hopfield system Dissociation through Predissociative Channels

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X 1 g ( i ) b 1 u X 1 g ( i ) b 1 u (continuum) E=40eV

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CROSS SECTION DEPENDENCE on the INITIAL VIBRATIONAL QUANTUM NUMBER

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DISSOCIATION CROSS SECTIONS FOR NITROGEN rotationally averaged cross sections from =40, T rot = 50, 1000, 3000 K rotationally averaged cross sections from =40,50,60,65, T rot = 3000 K

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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)

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

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

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

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

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

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

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

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

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DISSOCIATION CROSS SECTIONS FOR OXYGEN rotationally averaged cross sections from =30, T rot = 50,1000,3000,10000 K rotationally averaged cross sections from =20,25,30,35,40, T rot = 1000 K

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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

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

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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 The system of equations is linear in X 1 X j (j>1) can be calculated when X 1, n e, T e are given

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CR for Atomic Nitrogen Plasma: Energy-level Model

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CR for Atomic Nitrogen Plasma with QSS X i vs level energy T e =5800 KT e =11600 K T e =17400 K

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

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ATOMIC HYDROGEN PLASMA P=100 Torr, T g =30000 K, T e (t=0)=1000 K H + = e - =10 -8, H =1, H (1)=1, H (i)=0 i>1 density (cm -3 ) vs time(s) X i = n i /n i SB vs time(s) T e vs time(s)

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

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