Collisional-Radiative Model For Atomic Hydrogen Plasma L. D. Pietanza, G. Colonna, M. Capitelli Department of Chemistry, University of Bari, Italy IMIP-CNR, Bari section, Italy

T, P or T, NT uniquely defines: internal level populations(Boltzmann) velocity distribution (Maxwell) ionization stage(Saha) LTE Plasma Level populations are obtained by solving a system of rate equations (Master Equations) containg the rate coefficients of the main collisional-radiative elementary processes. Collisional-Radiative Models Non-LTE Plasma Microscopic Kinetic Approach 1)set of energy levels for each species 2)cross sections and radiative transition probabilities we need a)homogeneous, i.e. diffusion processes are neglected b)quasi-neutral (n e = n H + ) c)collision processes induced only by electrons Hydrogen plasma H, H +, e -

Collisional processes 1) Excitation and de-excitation by electron impact 2) Ionization by electron impact and three body recombination

Cross Sections and Detailed Balancing Principle excitation-de-excitation by electron impactgeneric reactive process by electron impact

Radiative Processes 2) Radiative recombination Absorption is inserted by decreasing A ij (s -1 ) by a factor ij, i.e. A ij * = ij A ij Plasma optically thin: ij =1 Plasma optically thick: ij <1 1) Spontaneous emission and absorption

Master Equations of CR ModelRate coefficients f(  ) electron energy distribution function  (  ) cross section v(  ) electron velocity f(  ) LTEMaxwell distribution Non-LTEBoltzmann equation

Coupling of CR Model with Boltzmann Equation for free electrons Master equations Boltzmann equation for free electrons rate coefficients level population plasma composition f(  )

Boltzmann equation J = flux in the energy space due to 1)J E electric field 2)J el elastic collisions with atoms and ions 3)J e-e elastic electron-electron collisions S = electron jumps in the energy space due to 1)S an inelastic and ionization collisions 2)S sup superelastic collisions

only collisional processesP=1 atm, T g =5000 K, T exc =T e =T H =T H+ =20000 K  H =  e eq (T exc )= ,  H+ =  e =  e eq (T exc )= Case 1 H molar fraction vs timeH + -e - molar fraction vs time

Case 1 hydrogen level distribution electron distribution

Case 2 collisional processes + radiative: spontaneous emission ( =1) radiative recombination P=1 atm, T g =5000 K, T exc =T e =T H =T H+ =20000 K  H =  e eq (T exc )= ,  H+ =  e =  e eq (T exc )= hydrogen level distribution electron distribution

Case 2 H + - e - molar fractions

Case 3 collisional processes + radiative: spontaneous emission ( =1) radiative recombination P=1 atm, T g =20000 K, T exc =T e =T H =T H+ =5000 K  H =  e eq (T exc ),  H+ =  e =  e eq (T exc ) hydrogen level distributionelectron distribution

Case 3 molar fractions b(i)=n(i)/n SB (i)

Works in progress Implementation of a collisional-radiative model for N and O Conclusions Collisional-radiative models are foundamental tools to characterize non-LTE plasma. They calculate excited state populations, showing their possible deviation from LTE. Departure from LTE occurs when the effect of radiative processes cannot be neglected respect to electron collisions one, i.e. at lower temperature and electron density.

ionization-three-body recombination Equilibrium constant vs T(K) Equilibrium molar fractions vs T(K) P=1 atm