Impact Collision Operator for Unbounded Electrons in a Magnetized Plasma Model
DOI:
https://doi.org/10.15407/ujpe68.8.507Keywords:
collision operator for electrons, external magnetic field, plasma spectroscopyAbstract
The shapes of spectral lines in plasmas contain information about plasma parameters and can be used as a diagnostic tool. We have obtained a theoretical expression involving a Meijer function for the plasma collision operator for electrons in the presence of an external magnetic field. We have used the semiclassical theory and the impact approximation which concern the interaction between the emitting systems (hydrogen-like ions in this study) and the plasma electrons. We have calculated the collision operator amplitude for some hydrogen-like ions such as Ar+17, V+22, Cr+23, Fe+25, and Ag+46 for high density intervals between 1018 cm−3 to 1026 cm−3 and at high temperatures between 106 K to 1010 K in a very strong magnetic field between 100 T to 10,000 T. We have applied our results to the Lyman-alpha line, and the comparison with experimental data and some theoretical results gives a good agreement.
References
A. Naam, M. Meftah, S. Douis et al. Spectral line broadening by relativistic electrons in plasmas: Collision operator. Advances in Space Research 54, 1242 (2014).
https://doi.org/10.1016/j.asr.2014.01.010
Sandrine Ferri, Annette Calisti, Caroline MossпїЅ et al. Ion dynamics effect on stark-broadened line shapes: A crosscomparison of various models. Atoms 2 (3), 299 (2014).
https://doi.org/10.3390/atoms2030299
A. Calisti, C. MossпїЅ, S. Ferri et al. Dynamic Stark broadening as the Dicke narrowing effect. Phys. Rev. E 81, 016406 (2010).
https://doi.org/10.1103/PhysRevE.81.016406
A. General, U. Shpenik. Modeling of gas discharge in water vapor. Ukr. J. Phys. 58, 116 (2013).
https://doi.org/10.15407/ujpe58.02.0116
M. Baranger. Simplified quantum-mechanical theory of pressure broadening. Phys. Rev. 111, 481 (1958).
https://doi.org/10.1103/PhysRev.111.481
M. Baranger. Problem of overlapping lines in the theory of pressure broadening. Phys. Rev. 111, 494 (1958).
https://doi.org/10.1103/PhysRev.111.494
S. Alexiou. Collision operator for isolated ion lines in the standard Stark-broadening theory with applications to the Z scaling in the Li isoelectronic series 3P-3S transition. Phys. Rev. A 49, 106 (1994).
https://doi.org/10.1103/PhysRevA.49.106
E. Sadeghzadeh Lari, H. Askari, M. Meftah et al. Calculation of electron density and temperature of plasmas by using new Stark broadening formula of helium lines. High Energy Density Physics 26, 68 (2018).
https://doi.org/10.1016/j.hedp.2018.01.001
K. Arif, M.T. Meftah, K. Chenini et al. Contribution of LiпїЅnard? Wiechert potential to the broadening of spectral lines by electron collisions. Phys. Plasmas 29, 093303 (2022).
https://doi.org/10.1063/5.0085698
P. Zeeman. The effect of magnetisation on the nature of light emitted by a substance. Nature 55, 347 (1897).
https://doi.org/10.1038/055347a0
S. Ferri, O. Peyrusse, A. Calisti. Stark-Zeeman line-shape model for multi-electron radiators in hot dense plasmas subjected to large magnetic fields. Matter Radiat. Extremes 7, 015901 (2022).
https://doi.org/10.1063/5.0058552
A. Raji, R. Rosato, J. Stamm et al. New analysis of Balmer line shapes in magnetic white dwarf atmospheres. Eur. Phys. J. D 75, 1 (2021).
https://doi.org/10.1140/epjd/s10053-021-00067-x
E. Oks. 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. 171, 15 (2016).
https://doi.org/10.1016/j.jqsrt.2015.10.026
E. Oks. Corrigendum to: ?Influence of magnetic-fieldcaused modifications of trajectories of plasma electrons on spectral line shapes: Applications to magnetic fusion and white dwarfs? J. Quant. Spectrosc. Radiat. Transf. 175, 107 (2016).
https://doi.org/10.1016/j.jqsrt.2016.01.036
Ny Kieu, JoпїЅl Rosato, Roland Stamm et al. A new analysis of stark and zeeman effects on hydrogen lines in magnetized da white dwarfs. Atoms 5, 44 (2017).
https://doi.org/10.3390/atoms5040044
S.O. Kepler, I. Pelisoli, S. Jordan et al. Magnetic white dwarf stars in the sloan digital sky survey. Mon. Not. R. Astron. Soc. 429, 2934 (2013).
https://doi.org/10.1093/mnras/sts522
J.D. Landstreet, S. Bagnulo, G.G. Valyavin et al. On the incidence of weak magnetic fields in DA white dwarfs. Astron. Astrophys. 545, 1 (2012).
https://doi.org/10.1051/0004-6361/201219829
J. Rosato, N. Kieu, I. Hannachi et al. Stark-Zeeman line shape modeling for magnetic white dwarf and tokamak edge plasmas: Common challenges. Atoms 5 (4), 36 (2017).
https://doi.org/10.3390/atoms5040036
R. Brauer, S. Wolf, S. Reissl, F. Ober. Magnetic fields in molecular clouds: Limitations of the analysis of Zeeman observations. Astron. Astrophys. 601, 1 (2017).
https://doi.org/10.1051/0004-6361/201629001
L. Godbert-Mouret, M. Koubitia, R. Stamm et al. Spectroscopy of magnetized plasmas. Q. R. S. T. 71, 365 (2001).
https://doi.org/10.1016/S0022-4073(01)00082-6
E. Stambulchik, Y. Maron. Zeeman effect induced by intense laser light. Phys. Rev. Lett. E 113, 083002 (2014).
https://doi.org/10.1103/PhysRevLett.113.083002
S. Fadhel, M.T. Meftah, K. Chenini. Quantum dynamics of hydrogen-like ions in a spatially nonuniform magnetic field: A possible application to fusion plasma. Atoms 6, 1 (2022).
https://doi.org/10.3390/atoms10010020
O. Loginov, O. Cheremnykh, V. Krivodubskij et al. Kinematic dynamo model of a solar magnetic cycle. Ukr. J. Phys. 67, 796 (2022).
https://doi.org/10.15407/ujpe67.11.796
S. Nasrin, M. Bose. Effect of two different electron temperatures in auroral ionosphere. Ukr. J. Phys. 67, 136 (2022).
https://doi.org/10.15407/ujpe67.2.136
J. Rosato, S. Ferri, R. Stamm. Influence of helical trajectories of perturbers on Stark Line shapes in magnetized plasmas. Atoms 6 (1), 12 (2018).
https://doi.org/10.3390/atoms6010012
S. Alexiou. Line shapes in a magnetic field: Trajectory modifications I: Electrons. Atoms 7 (2), 52 (2019).
https://doi.org/10.3390/atoms7020052
S. Alexiou. Line Shapes in a magnetic field: Trajectory modifictions II: Full collision-time statistics. Atoms 7 (4), 94 (2019).
https://doi.org/10.3390/atoms7040094
M.G. Haines, P.D. LePell, C.A. Coverdale et al. Ion viscous heating in a magnetohydrodynamically unstable Z pinch at over 2 × 10^9 Kelvin. Phys. Rev. Lett. 96, 075003 (2006).
https://doi.org/10.1103/PhysRevLett.96.075003
D. Zenkhri, M. Meftah, F. Khelfaoui. Relativistic calculation of spectral line broadening by electron collisions in plasmas: Case of hydrogenic ions. Advances in Space Research 69, 3553 (2022).
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
