Lenka Dosoudilová Lenka Dosoudilová 1 / 14
Motivation Equations Approximative models Emission coefficient Particles J ij = 1 4π n j A ij hν ij, atoms in ground state atoms in excited states resonance metastable i < j ions in ground and excited states molecules in ground and excited states electrons s r -1 ) -3 E m is s io n c o e ffic ie n t (W m 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 8 0 6 0 0 6 2 0 6 4 0 6 6 0 6 8 0 7 0 0 7 2 0 7 4 0 W a v e le n g th (n m ) Lenka Dosoudilová 2 / 14
Continuity equation Plasma modelling n i t + (n i v) = Motivation Equations Approximative models ( ) ni t coll,rad collisional and radiative processes much faster than transport processes ( ) ni 0 = particles with long lifetimes t coll,rad balance equation ( ) ni (n i v) = D 2 n i t coll,rad Equation for ground state n gs = p kt g = R prod R loss Lenka Dosoudilová 3 / 14
Motivation Equations Approximative models Approximative models weakly ionized plasma: n g > n e, n + excitation of atoms primarily by electrons deexcitation of atoms primarily by spontaneous emission Lenka Dosoudilová 4 / 14
Motivation Equations Approximative models Approximative models weakly ionized plasma: n g > n e, n + excitation of atoms primarily by electrons deexcitation of atoms primarily by spontaneous emission simple corona model applicable at very low ne excitation solely through electron impact excitation of gs deexcitation solely through spontaneous emission no radiation trapping for lowest lying energy levels with short radiative lifetimes Lenka Dosoudilová 4 / 14
Motivation Equations Approximative models Approximative models weakly ionized plasma: n g > n e, n + excitation of atoms primarily by electrons deexcitation of atoms primarily by spontaneous emission simple corona model applicable at very low ne excitation solely through electron impact excitation of gs deexcitation solely through spontaneous emission no radiation trapping for lowest lying energy levels with short radiative lifetimes Saha/thermodynamic equilibrium applicable at high ne (de)excitation by electron collisions for levels close Eion with long radiative lifetimes recombination ionization excitation Lenka Dosoudilová 4 / 14
Energy level diagram Elementary processes Lenka Dosoudilová 5 / 14
Elementary processes Plasma modelling Energy level diagram Elementary processes electron-impact excitation and de-excitation e + Xe(i) e + Xe(j), i < j Lenka Dosoudilová 6 / 14
Elementary processes Plasma modelling Energy level diagram Elementary processes electron-impact excitation and de-excitation e + Xe(i) e + Xe(j), i < j electron-impact/atom-collision population transfer e/xe + Xe(i) e/xe + Xe(j), i < j Lenka Dosoudilová 6 / 14
Elementary processes Plasma modelling Energy level diagram Elementary processes electron-impact excitation and de-excitation e + Xe(i) e + Xe(j), i < j electron-impact/atom-collision population transfer electron-impact ionization e/xe + Xe(i) e/xe + Xe(j), e + Xe(i) e + e + Xe + i < j Lenka Dosoudilová 6 / 14
Elementary processes Plasma modelling Energy level diagram Elementary processes electron-impact excitation and de-excitation e + Xe(i) e + Xe(j), i < j electron-impact/atom-collision population transfer electron-impact ionization e/xe + Xe(i) e/xe + Xe(j), e + Xe(i) e + e + Xe + Penning ionization of excited particles Xe(i) + Xe m e + Xe + Xe + Xe 2 + Xe 2 e + Xe + Xe + Xe+ 2 i < j Lenka Dosoudilová 6 / 14
Elementary processes Plasma modelling Energy level diagram Elementary processes electron-impact excitation and de-excitation e + Xe(i) e + Xe(j), i < j electron-impact/atom-collision population transfer e/xe + Xe(i) e/xe + Xe(j), i < j electron-impact ionization e + Xe(i) e + e + Xe + Penning ionization of excited particles Xe(i) + Xe m e + Xe + Xe + Xe2 + Xe 2 e + Xe + Xe + Xe+ 2 electron collisional recombination for atomic and molecular ions e + e/xe + Xe + e/xe + Xe(j) e + Xe + 2 Xe(j) + Xe gs Lenka Dosoudilová 6 / 14
Energy level diagram Elementary processes three-body collisional association Xe m + Xe + Xe Xe 2 + Xe Xe + + Xe + Xe Xe + 2 + Xe Lenka Dosoudilová 7 / 14
Energy level diagram Elementary processes three-body collisional association Xe m + Xe + Xe Xe 2 + Xe Xe + + Xe + Xe Xe + 2 + Xe electron-impact/atom-collision dissociation of excimers and molecular ions e/xe + Xe 2 e/xe + Xe gs + Xe m e/xe + Xe + 2 e/xe + Xe + Xe+ Lenka Dosoudilová 7 / 14
Energy level diagram Elementary processes three-body collisional association Xe m + Xe + Xe Xe 2 + Xe Xe + + Xe + Xe Xe + 2 + Xe electron-impact/atom-collision dissociation of excimers and molecular ions e/xe + Xe 2 e/xe + Xe gs + Xe m e/xe + Xe + 2 e/xe + Xe + Xe+ radiative transitions and radiation trapping Xe(i) Xe(j) + hν, j < i Lenka Dosoudilová 7 / 14
Energy level diagram Elementary processes three-body collisional association Xe m + Xe + Xe Xe 2 + Xe Xe + + Xe + Xe Xe + 2 + Xe electron-impact/atom-collision dissociation of excimers and molecular ions e/xe + Xe 2 e/xe + Xe gs + Xe m e/xe + Xe + 2 e/xe + Xe + Xe+ radiative transitions and radiation trapping Xe(i) Xe(j) + hν, j < i radiation of excimer molecules Xe2 Xe(i) + Xe + hν Lenka Dosoudilová 7 / 14
Energy level diagram Elementary processes three-body collisional association Xe m + Xe + Xe Xe 2 + Xe Xe + + Xe + Xe Xe + 2 + Xe electron-impact/atom-collision dissociation of excimers and molecular ions e/xe + Xe 2 e/xe + Xe gs + Xe m e/xe + Xe + 2 e/xe + Xe + Xe+ radiative transitions and radiation trapping Xe(i) Xe(j) + hν, j < i radiation of excimer molecules Xe2 Xe(i) + Xe + hν quenching: diffusion-controlled at the wall, collisions with neutral species and metastables Lenka Dosoudilová 7 / 14
Rate coefficient Types of cross sections Determination of cross sections Measurements vs theoretical calculations Rate coefficient e.g. excitation from ground state calculation k = σ(v) v = ( ) ni 0 t coll,rad = k 1i n e n gs 2 σ(v)v f (v)dv = m e 0 distribution function ( ) 3/2 me f (v) = 4π v 2 exp( m ev 2 ) 2πkT e 2kT e 2 ( E f (E) = π(kte ) exp E ) 3 kt e measurements: cross sections σ(e)e f (E)dE Lenka Dosoudilová 8 / 14
Types of cross sections σ optical emission Plasma modelling σ opt i j Φobs i j Rate coefficient Types of cross sections Determination of cross sections Measurements vs theoretical calculations Lenka Dosoudilová 9 / 14
Types of cross sections σ optical emission Plasma modelling σ opt i j Φobs i j Rate coefficient Types of cross sections Determination of cross sections Measurements vs theoretical calculations Lenka Dosoudilová 9 / 14
Types of cross sections σ optical emission apparent Plasma modelling σ opt i j Φobs i j Rate coefficient Types of cross sections Determination of cross sections Measurements vs theoretical calculations σ app i σ opt i j = = σ opt i j j<i A ij σ app A i il l<i Lenka Dosoudilová 9 / 14
Types of cross sections σ optical emission apparent Plasma modelling σ opt i j Φobs i j Rate coefficient Types of cross sections Determination of cross sections Measurements vs theoretical calculations cascade σ app i σ opt i j = σ cas i = σ opt i j j<i A ij σ app A i il l<i = σ opt k i k>i Lenka Dosoudilová 9 / 14
Types of cross sections σ optical emission apparent Plasma modelling σ opt i j Φobs i j Rate coefficient Types of cross sections Determination of cross sections Measurements vs theoretical calculations cascade σ app i σ opt i j = σ cas i = σ opt i j j<i A ij σ app A i il l<i = σ opt k i k>i Lenka Dosoudilová 9 / 14
Types of cross sections σ optical emission apparent Plasma modelling σ opt i j Φobs i j Rate coefficient Types of cross sections Determination of cross sections Measurements vs theoretical calculations cascade direct σ app i σ opt i j = σ cas i σ dir i = σ opt i j j<i A ij σ app A i il l<i = σ opt k i k>i = σ app i σ cas i Lenka Dosoudilová 9 / 14
Rate coefficient Types of cross sections Determination of cross sections Measurements vs theoretical calculations Measurements of cross section optical emission cross section vacuum chamber, ultrahigh purity gas, monoenergetic beam of e measuring electron current and photon emission rate direct excitation cross sections σ opt i j = Φ ij n 0 (I/e) electron energy loss as function of scattering angle differential cross section Theoretical calculations Born approximation R-matrix distorted-wave approximation Lenka Dosoudilová 10 / 14
Rate coefficient Types of cross sections Determination of cross sections Measurements vs theoretical calculations Cross section (10 20 cm 2 ) Pressure (mtorr) Incident electron energy 30 ev J. T. Fons, C. C. Lin, Phys. Rev. A 58, 4603 (1998) K. Bartschat et al., Phys. Rev. A 69, 062706 (2004) Lenka Dosoudilová 11 / 14
Computation of spectrum Results Lenka Dosoudilová 12 / 14
Computation of spectrum Results Emission coefficient (W m -3 sr -1 ) 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 Measurement: pos. 4 mm, power 50 W Fit with CR model 600 620 640 660 680 700 720 740 Wavelength (nm) Z. Navrátil et al., Journal of Physics D: Applied Physics, 43 (50), 505203 (2010) Lenka Dosoudilová 13 / 14
Thank you for your attention! Lenka Dosoudilová 14 / 14