Abstract
Collisional-radiative (CR) models of atomic hydrogen have a long history started with two pioneering papers by Bates et al. (1962a,b). The interplay between radiative losses and electron-impact induced processes determines non-equilibrium level distributions of atomic hydrogen. To predict these distributions different approaches have to be considered. The most popular model is the so-called Quasi-Steady State (QSS), assuming slow varying ground state and electron concentrations, while excited states relax very rapidly to a stationary solution determined only by those two quantities. A more detailed model solves the whole set of master equations to determine the evolution of the distribution together with the plasma composition. Maxwellian and self-consistent electron energy distribution functions are used to this end.
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Notes
- 1.
It should be noted that for \( i \rightarrow \infty \) \( \varepsilon _{i} \rightarrow I \) where I is the ionization energy and \( g_{i} \rightarrow \infty \).
- 2.
The coefficient 2 in the equation is the statistical weight of free electrons due to the spin.
- 3.
Obviously this is valid only for an isolated atom, and in presence of electric and magnetic field, as it can happen in a plasma, the degeneracy is broken due to the Stark and Zeeman effects.
- 4.
In some cases (for example, low initial electron density ), atom-atom collisions can be important and must also be considered in the kinetic scheme as also shown in the last examples of the present chapter.
- 5.
The definition given here must be considered an estimation of the relaxation time . Noticing that, if n e is constant, this kind of process results in a linear system of equation, therefore, more rigorously, the eigenvalue of the kinetic matrix must be considered as relaxation times, while Eq. (6.13) consider only the diagonal elements.
References
ALADDIN (2013) Numerical database maintained by the IAEA nuclear data section A + M data unit. https://www-amdis.iaea.org/ALADDIN/
Bates DR, Kingston AE, McWhirter RWP (1962a) Recombination between electrons and atomic ions. I. Optically thin plasmas. Proc R Soc Lond Ser A Math Phys Sci 267(1330):297–312
Bates DR, Kingston AE, McWhirter RWP (1962b) Recombination between electrons and atomic ions. II. Optically thick plasmas. Proc R Soc Lond Ser A Math Phys Sci 270(1341):155–167
Biberman LM, Vorob’ev VS, Yakubov IT (1967) High Temp (Teplofizika Vysokikh Temperatur) 5:177
Biberman LM, Vorob’ev VS, Yakubov IT (1973) Sov Phys Uspekhi 15:375
Biberman LM, Vorob’ev VS, Yakubov IT (1987) Kinetics of nonequilibrium low-temperature plasmas. Springer US
Bruno D, Capitelli M, Catalfamo C, Laricchiuta A (2007) Transport of internal electronic energy in atomic hydrogen thermal plasmas. Phys Plasmas (1994-present) 14(7):072308
Bultel A, Annaloro J (2013) Elaboration of collisional-radiative models for flows related to planetary entries into the Earth and Mars atmospheres. Plasma Sources Sci Technol 22(2):025008
Cacciatore M, Capitelli M (1974) Non L.T.E. populations and related quantities for H-H+-e plasmas as a function of the cut-off level. Zeitschrift für Naturforschung A 29:1507–1509
Cacciatore M, Capitelli M (1975) Population densities and ionization coefficients of fast transient hydrogen plasmas. Zeitschrift für Naturforschung A 30:48–54
Cacciatore M, Capitelli M (1976a) Non L.T.E. properties of quasistationary oxygen plasmas. Zeitschrift für Naturforschung A 31:362–368
Cacciatore M, Capitelli M (1976b) The temporal evolution of population densities of excited states in atomic oxygen thin plasmas. J Quant Spectrosc Radiat Transf 16(4):325–334
Cacciatore M, Capitelli M, Drawin H (1976) Relaxation times for establishing quasi-stationary state populations in non-thermal plasmas. Physica B+C 84(2):267–274
Capitelli M, Colonna G, Gicquel A, Gorse C, Hassouni K, Longo S (1996) Maxwell and non-Maxwell behavior of electron energy distribution function under expanding plasma jet conditions: the role of electron-electron, electron-ion, and superelastic electronic collisions under stationary and time-dependent conditions. Phys Rev E 54(2):1843
Capitelli M, Celiberto R, Gorse C, Laricchiuta A, Pagano D, Traversa P (2004) Transport properties of local thermodynamic equilibrium hydrogen plasmas including electronically excited states. Phys Rev E 69:026412
Capitelli M, Colonna G, D’Angola A (2012) Fundamental aspects of plasma chemical physics: thermodynamics. Springer series on atomic, optical, and plasma physics, vol 66. Springer, New York
Capitelli M, Colonna G, Pietanza LD, D’Ammando G (2013) Coupling of radiation, excited states and electron energy distribution function in non equilibrium hydrogen plasmas. Spectrochim Acta-Part B At Spectrosc 83–84:1–13
Colonna G, Pietanza LD, Capitelli M (2001) Coupled solution of a time-dependent collisional-radiative model and Boltzmann equation for atomic hydrogen plasmas: possible implications with LIBS plasmas. Spectrochim Acta-Part B At Spectrosc 56(6):587–598
Colonna G, Pietanza LD, D’Ammando G (2012) Self-consistent collisional-radiative model for hydrogen atoms: atom-atom interaction and radiation transport. Chem Phys 398:37–45
Colonna G, D’Ammando G, Pietanza LD, Capitelli M (2015) Excited-state kinetics and radiation transport in low-temperature plasmas. Plasma Phys Control Fusion 57:014009
D’Ammando G, Capitelli M, Esposito F, Laricchiuta A, Pietanza LD, Colonna G (2014) The role of radiative reabsorption on the electron energy distribution functions in H2/He plasma expansion through a tapered nozzle. Phys Plasmas 21(9):093508
Drawin HW (1969) Collisional-radiative ionization and recombination coefficients for quasi-stationary homogeneous hydrogen and hydrogenic ion plasmas. Zeitschrift für Physik 225(5):470–482
Drawin HW (1970) Thermodynamic properties of the equilibrium and non equilibrium states of plasmas. In: Venugopalan M (ed) Reactions under plasma conditions, Chapter 3. Wiley Interscience, New York/London
Drawin H, Emard F (1971) Collisional-radiative volume recombination and ionization coefficients for quasi-stationary helium plasmas. Zeitschrift für Physik 243(4):326–340
Fujimoto T (1973) Validity criteria for local thermodynamic equilibrium and coronal equilibrium. J Phys Soc Jpn 34(1):216–224
Fujimoto T (2004) Plasma spectroscopy. Clarendon Press, Oxford
Fujimoto T, Ogata Y, Sugiyama I, Tachibana K, Fukuda K (1972) Population density and LTE of excited atoms in a positive-column plasma I. Calculation on hydrogen. Jpn J Appl Phys 11(5):718–725
Gordiets BF, Gudzenko LI, Shelepin LA (1968) J Quant Spectrosc Radiat Transf (in Russian) 8(2):791–804
Gorse C, Cacciatore M, Capitelli M (1978) Some aspects in recombining transient nitrogen plasmas. Zeitschrift für Naturforschung A 33:895–902
Gudzenko LI, Shelepin LA (1964) Negative absorption in a nonequilibrium hydrogen plasma. JETP 18(4):998. (Russian original - (1964) ZhETF 45:1445)
Hassouni K, Gicquel A, Capitelli M (1999a) Self-consistent relaxation of the electron energy distribution function in excited H2 postdischarges. Phys Rev E 59:3741–3744
Hassouni K, Gicquel A, Capitelli M, Loureiro J (1999b) Chemical kinetics and energy transfer in moderate pressure H2 plasmas used in diamond MPACVD processes. Plasma Sources Sci Technol 8(3):494
Hassouni K, Lombardi G, Duten X, Haagelar G, Silva F, Gicquel A, Grotjohn TA, Capitelli M, Röpcke J (2006) Overview of the different aspects in modelling moderate pressure H2 and H2 CH4 microwave discharges. Plasma Sources Sci Technol 15(1):117–125
Janev RK, Smith J (1993) Cross sections for collision processes of hydrogen atoms with electrons, protons and multiply charge ions. International Atomic Energy Agency (ed) Atomic and plasma-material interaction data for fusion, vol 4. IAEA, Vienna
Johnson LC (1972) Approximations for collisional and radiative transition rates in atomic hydrogen. Astrophys J 174:227–236
Limbaugh CC, Mason AA (1971) Validity of the quasisteady state and collisional-radiative recombination for helium plasmas. I. Pure afterglows. Phys Rev A 4(6):2368
Longo S, Capitelli M, Hassouni K (1998) Nonequilibrium vibrational distributions of N2 in radio-frequency parallel-plate reactors. J Thermophys Heat Transf 12(4):473–477
Munafò A, Lani A, Bultel A, Panesi M (2013) Modeling of non-equilibrium phenomena in expanding flows by means of a collisional-radiative model. Phys Plasmas 20(7):073501
Pietanza LD (2000) Coupling of a collisional-radiative model with the electron Boltzmann equations for the study of hydrogen plasma in transient regime. Degree Thesis, Department of Physics, University of Bari
Pietanza LD, Colonna G, De Giacomo A, Capitelli M (2010) Kinetic processes for laser induced plasma diagnostic: a collisional-radiative model approach. Spectrochim Acta Part B: At Spectrosc 65(8):616–626
Seaton MJ (1959) Radiative recombination in hydrogenic ions. Mon Not R Astron Soc 119:81
Tallents GJ (1977) Population inversions of soft X-ray transitions computed for rapidly cooling plasmas. J Phys B: At Mol Phys 10(9):1769
van der Mullen JAM (1990) Excitation equilibria in plasmas; a classification. Phys Rep 191(2–3):109–220
Van Sijde BD, van der Mullen JJAM, Schram DC (1984) Collisional radiative models in plasmas. Beiträge aus der Plasmaphysik 24(5):447–473
Vlcek J, Pelikan V (1985) Electron energy distribution function in the collisional-radiative model of an argon plasma. J Phys D: Appl Phys 18(3):347
Zel’dovich YB, Raizer YP (1967) Physics of shock waves and high-temperature hydrodynamic phenomena. Academic Press, New York and London
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Capitelli, M. et al. (2016). Collisional-Radiative Models for Atomic Hydrogen Plasmas. In: Fundamental Aspects of Plasma Chemical Physics. Springer Series on Atomic, Optical, and Plasma Physics, vol 85. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8185-1_6
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