# Influence of Helical Trajectories of Perturbers on Stark Line Shapes in Magnetized Plasmas

^{*}

## Abstract

**:**

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Külebi, B.; Jordan, S.; Euchner, F.; Gänsicke, B.T.; Hirsch, H. Analysis of hydrogen-rich magnetic white dwarfs detected in the Sloan Digital Sky Survey. Astron. Astrophys.
**2009**, 506, 1341–1350. [Google Scholar] [CrossRef] - Kepler, S.O.; Pelisoli, I.; Jordan, S.; Kleinman, S.J.; Koester, D.; Külebi, B.; Peçanha, V.; Castanheira, B.G.; Nitta, A.; da Silveira Costa, J.E.; et al. Magnetic white dwarf stars in the Sloan Digital Sky Survey. Mon. Not. R. Astron. Soc.
**2013**, 429, 2934–2944. [Google Scholar] [CrossRef] - Maschke, E.K.; Voslamber, D. Stark-Broadening of Hydrogen Lines in Strong Magnetic Fields; Report EUR-CEA-FC-354; The European Insurance and Reinsurance Federation (CEA): Fontenay-aux-Roses, France, 1966. [Google Scholar]
- Nguyen-Hoe; Drawin, H.-W.; Herman, L. Effet d’un champ magnétique uniforme sur les profils des raies de l’hydrogène. J. Quant. Spectrosc. Radiat. Transf.
**1967**, 7, 429–474. [Google Scholar] [CrossRef] - Drawin, H.-W.; Henning, H.; Herman, L. Nguyen-Hoe Stark-broadening of hydrogen Balmer lines in the presence of strong magnetic fields in plasmas. J. Quant. Spectrosc. Radiat. Transf.
**1969**, 9, 317–331. [Google Scholar] [CrossRef] - Oks, E. Influence of magnetic-field-caused modifications of trajectories of plasma electrons on spectral line shapes: Applications to magnetic fusion and white dwarfs. J. Quant. Spectrosc. Radiat. Transf.
**2016**, 171, 15–27. [Google Scholar] [CrossRef] - Stambulchik, E. Review of the 1st Spectral Line Shapes in Plasmas code comparison workshop. High Energy Density Phys.
**2013**, 9, 528–534. [Google Scholar] [CrossRef] - Rosato, J. Report on the third SLSP code comparison workshop. High Energy Density Phys.
**2017**, 22, 60–63. [Google Scholar] [CrossRef] - Derevianko, A.; Oks, E. Generalized theory of ion impact broadening in magnetized plasmas and its applications for tokamaks. Phys. Rev. Lett.
**1994**, 73, 2059–2062. [Google Scholar] [CrossRef] [PubMed] - Rosato, J.; Marandet, Y.; Capes, H.; Ferri, S.; Mossé, C.; Godbert-Mouret, L.; Koubiti, M.; Stamm, R. Stark broadening of hydrogen lines in low-density magnetized plasmas. Phys. Rev. E
**2009**, 79, 046408. [Google Scholar] [CrossRef] [PubMed] - Rosato, J.; Capes, H.; Godbert-Mouret, L.; Koubiti, M.; Marandet, Y.; Stamm, R. Accuracy of impact broadening models in low-density magnetized hydrogen plasmas. J. Phys. B Atomic Mol. Opt. Phys.
**2012**, 45, 165701. [Google Scholar] [CrossRef] - Griem, H.R.; Kolb, A.C.; Shen, K.Y. Stark broadening of hydrogen lines in a plasma. Phys. Rev.
**1959**, 116, 4–16. [Google Scholar] [CrossRef] - Hegerfeldt, G.C.; Kesting, V. Collision time simulation technique for pressure-broadened spectral lines with applications to Ly-α. Phys. Rev. A
**1988**, 37, 1488–1496. [Google Scholar] [CrossRef] - Alexiou, S. Implementation of the Frequency Separation Technique in general lineshape codes. High Energy Density Phys.
**2013**, 9, 375–384. [Google Scholar] [CrossRef] - Kieu, N.; Rosato, J.; Stamm, R.; Kovačević-Dojcinović, J.; Dimitrijević, M.S.; Popović, L.C.; Simić, Z.S. A New analysis of Stark and Zeeman effects on hydrogen lines in magnetized DA white dwarfs. Atoms
**2017**, 5, 44. [Google Scholar] [CrossRef] - Rosato, J.; Marandet, Y.; Stamm, R. Stark broadening by Lorentz fields in magnetically confined plasmas. J. Phys. B Atomic Mol. Opt. Phys.
**2014**, 47, 105702. [Google Scholar] [CrossRef]

**Figure 1.**An example of electron helical trajectory is shown in (

**a**) and the resulting electric field at an atom’s location is shown in (

**b**). Conditions relevant to magnetized white dwarf atmospheres have been assumed: given an atomic emitter placed at the origin, the helix axis has been placed at ${x}_{0}={N}_{e}^{-1/3}$ with ${N}_{e}={10}^{17}$ cm${}^{-3}$, the velocities ${v}_{\perp}$ and ${v}_{//}$ have both been set equal to $\sqrt{{T}_{e}/{m}_{e}}$ with ${T}_{e}=1$ eV, and a value of 2 kT has been assumed for the magnetic field. The Debye length ${\lambda}_{D}\simeq 2.4\times {10}^{-8}$ m is much larger than the Larmor radius ${b}_{L}\simeq 1.2\times {10}^{-9}$ m and, accordingly, the electric field exhibits oscillations.

**Figure 2.**Plot of (

**a**) the atomic dipole autocorrelation function and (

**b**) the corresponding line shape obtained from a numerical simulation accounting for the helical motion of the electrons. The Lyman $\alpha $ line in magnetized white dwarf atmosphere conditions is considered with focus on the central Zeeman component. The decrease is slower than in the absence of a magnetic field. This trend is also expected from analytical estimates based on collision operators.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rosato, J.; Ferri, S.; Stamm, R.
Influence of Helical Trajectories of Perturbers on Stark Line Shapes in Magnetized Plasmas. *Atoms* **2018**, *6*, 12.
https://doi.org/10.3390/atoms6010012

**AMA Style**

Rosato J, Ferri S, Stamm R.
Influence of Helical Trajectories of Perturbers on Stark Line Shapes in Magnetized Plasmas. *Atoms*. 2018; 6(1):12.
https://doi.org/10.3390/atoms6010012

**Chicago/Turabian Style**

Rosato, J., S. Ferri, and R. Stamm.
2018. "Influence of Helical Trajectories of Perturbers on Stark Line Shapes in Magnetized Plasmas" *Atoms* 6, no. 1: 12.
https://doi.org/10.3390/atoms6010012