Quasi-contiguous approximation for line-shape modeling in plasmas

Stambulchik, E.; Maron, Y.

doi:10.1063/1.4707878

Cited by 3 publications

(4 citation statements)

References 11 publications

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“…Perhaps continued interest in spectroscopic problems within the field of radio astronomy [76,77] will encourage further work along the lines sketched here. For modern developments in Stark broadening and atomic theory intended to overcome numerical difficulties experienced at intermediate to large principal quantum numbers, the reader may consult [88][89][90]105]. Our text develops preliminary ideas presented at conferences [91,92].…”

Section: Discussionmentioning

confidence: 99%

“…The author acknowledges permission of the Department of Physics and Astronomy of the University of Calgary to make use of the library facilities. Thanks are due to Dr Bell and Dr Stambulchik for communicating the results of [79] and [90], respectively, prior to publication. The assistance of Dr C C Chu with the preparation of this paper is gratefully acknowledged.…”

Section: Acknowledgmentsmentioning

confidence: 99%

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On the role of atomic metastability in the production of Balmer line radiation from ‘cold’ atomic hydrogen, deuterium and hydrogenic ion impurities in fusion edge plasmas

Hey¹

2012

J. Phys. B: At. Mol. Opt. Phys.

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Published arguments, which assign an important role to atomic metastability in the production of ‘narrow’ Zeeman component radiation from the boundary region of fusion plasmas, are examined critically in relation to l-redistribution by proton and electron collisions, and mixing of unperturbed atomic states by the ion microfield and microfield gradient. It is concluded that these important processes indeed severely constrain the contribution from ‘metastable’ states to the generation of the hydrogen Balmer spectra, for electron concentrations above 1012 cm−3, as pointed out before by the present author (Hey et al 1999 J. Phys. B: At. Mol. Opt. Phys. 32 3555). The analysis of collision-induced l-redistribution represents an extension of that used previously (Hey et al 1996 Contrib. Plasma Phys. 36 583), applicable up to higher electron densities. For comparison purposes, we also consider the question of metastability of ionized helium in a low-temperature plasma, and that of some common hydrogenic impurities (C5+ and Ne9+) in a hydrogen (deuterium) fusion plasma. While for low nuclear charge Z the metastability of 2s1/2 levels is quenched by the plasma environment, it is much reduced in high-Z ions owing to the rapid increase with Z of the two-photon electric dipole (2E1) and magnetic dipole (M1) spontaneous transition rates to the ground state, whereas the role of the plasma in these cases is less important. The main new principle elaborated in this work is the sensitivity of atomic line strengths, and hence collision strengths, to perturbation by the plasma environment for transitions between fine-structure sublevels of the same principal quantum number. As the plasma microfield strength grows, ‘allowed’ transitions diminish in strength, while ‘forbidden’ transitions grow. However, owing to violation of the parity selection rule, there is an overall loss of collision strength available to transitions, resulting from the appearance of significant ‘self-strength’ contributions, in accord with the sum rules for the line strengths, which remain valid over the range of fields considered. Thus, the relative effectiveness per perturber of both electron and ion collisions, for inducing population transfer between fine-structure sublevels, diminishes as the sublevels evolve from a fine-structure dominated to a Stark-effect-dominated regime. In the concluding discussion, we mention that this finding may have a bearing on discrepancies claimed between Stark broadening theory developed by Griem (1967 Astrophys. J. 148 547) and by Watson (2006 J. Phys.B: At. Mol. Opt. Phys. 39 1889), and the measurements of Bell and co-workers (2000 Publ. Astron. Soc. Pac. 112 1236; 2011 Astrophys. Space Sci. 335 451) for high-n radio recombination lines from galactic H II regions. In the absence of detailed modelling to test this suggestion, however, it would be premature to attempt to draw any firm conclusions along these lines.

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Section: Discussionmentioning

confidence: 99%

Section: Acknowledgmentsmentioning

confidence: 99%

On the role of atomic metastability in the production of Balmer line radiation from ‘cold’ atomic hydrogen, deuterium and hydrogenic ion impurities in fusion edge plasmas

Hey¹

2012

J. Phys. B: At. Mol. Opt. Phys.

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“…We give below the main steps of two different ways to obtain the new formula. The first one consists in using inverse Fourier transform of exp(−|τ | 3/2 ) [13][14][15]:…”

Section: Analytical Expressions Of S(β) and H(β)mentioning

confidence: 99%

Expression of the Holtsmark function in terms of hypergeometric $$_{2}F_2$$ and Airy Bi functions

Pain

2020

Eur. Phys. J. Plus

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The Holtsmark distribution has applications in plasma physics, for the electric-microfield distribution involved in spectral line shapes for instance, as well as in astrophysics for the distribution of gravitating bodies. It is one of the few examples of a stable distribution for which a closed-form expression of the probability density function is known. However, the latter is not expressible in terms of elementary functions. In the present work, we mention that the Holtsmark probability density function can be expressed in terms of hypergeometric function 2F2 and of Airy function of the second kind Bi and its derivative. The new formula is simpler than the one proposed by Lee involving 2F3 and 3F4 hypergeometric functions.

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“…It is interesting to note (see the analogous analysis for the stellar case [74]) that the perturber charge Q f does not enter in (C.5). For the evaluation of the two characteristic functions of the Holtsmark distribution in (C.7), [17,75,76] may be consulted and [77] for a modern application in line broadening theory. For small and large values of the reduced field-strength parameter, respectively, we have the expansions: The three functions of β in equation (C.7) are plotted in figure C2, which may be compared with the original diagram in [74].…”

Section: Appendix C Time-scales For Collective Effects During Ion Col...mentioning

confidence: 99%

Does atomic polarizability play a role in hydrogen radio recombination spectra from Galactic H II regions?

Hey

2013

J. Phys. B: At. Mol. Opt. Phys.

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Since highly excited atoms, which contribute to the radio recombination spectra from Galactic H II regions, possess large polarizabilities, their lifetimes are influenced by ion (proton)–induced dipole collisions. It is shown that, while these ion–radiator collisional processes, if acting alone, would effectively limit the upper principal quantum number attainable for given plasma parameters, their influence is small relative to that of electron impacts within the framework of line broadening theory. The present work suggests that ion–permanent dipole interactions (Hey et al 2004 J. Phys. B: At. Mol. Opt. Phys. 37 2543) would also be of minor importance in limiting the occupation of highly excited states. On the other hand, the ion–induced dipole collisions are essential for ensuring equipartition of energy between atomic and electron kinetic distributions (Hey et al 1999 J. Phys. B: At. Mol. Opt. Phys. 32 3555; 2005 J. Phys. B: At. Mol. Opt. Phys. 38 3517), without which Voigt profile analysis to extract impact broadening widths would not be possible. Electron densities deduced from electron impact broadening of individual lines (Griem 1967 Astrophys. J. 148 547; Watson 2006 J. Phys. B: At. Mol. Opt. Phys. 39 1889) may be used to check the significance of the constraints arising from the present analysis. The spectra of Bell et al (2000 Publ. Astron. Soc. Pac. 112 1236; 2011 Astrophys. Space Sci. 333 377; 2011 Astrophys. Space Sci. 335 451) for Orion A and W51 in the vicinity of 6.0 and 17.6 GHz are examined in this context, and also in terms of a possible role of the background ion microfield in reducing the near-elastic contributions to the electron impact broadening below the predictions of theory (Hey 2012 J. Phys. B: At. Mol. Opt. Phys. 45 065701). These spectra are analysed, subject to the constraint that calculated relative intensities of lines, arising from upper states in collisional–radiative equilibrium, should be consistent with those obtained from Voigt profile analysis. It is shown that the experimental technique yields an excellent temperature diagnostic for the H II regions. On the other hand, strong evidence is not obtained, from those spectra which satisfy the above constraint on intensity, to indicate that the electron impact broadening theory requires substantial correction. The main grounds for attempting a revision of theory to allow for the influence of the ion microfield during the scattering processes on the upper and lower states of each line thus still appear to have a stronger theoretical (Hey 2007 J. Phys. B: At. Mol. Opt. Phys. 40 4077) than experimental basis.

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Quasi-contiguous approximation for line-shape modeling in plasmas

Cited by 3 publications

References 11 publications

On the role of atomic metastability in the production of Balmer line radiation from ‘cold’ atomic hydrogen, deuterium and hydrogenic ion impurities in fusion edge plasmas

On the role of atomic metastability in the production of Balmer line radiation from ‘cold’ atomic hydrogen, deuterium and hydrogenic ion impurities in fusion edge plasmas

Expression of the Holtsmark function in terms of hypergeometric $$_{2}F_2$$ and Airy Bi functions

Does atomic polarizability play a role in hydrogen radio recombination spectra from Galactic H II regions?

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