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.
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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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