The Influence of Hot Electrons on the Calculation of Ionization Rates
Received: 28 August 2022 | Revised: 12 September 2022 | Accepted: 21 September 2022 | Online: 1 October 2022
Corresponding author: S. Dilmi
Abstract
Electron-Impact Ionization (EII) is considered one of the most important ionization methods in dynamic systems, in which elements and ions are suddenly exposed to energetic electrons. In many plasma types, it has been observed that some electrons (hot) are governed by a non-Maxwellian energy distribution. This study illustrates the effects of a non-Maxwellian distribution on beryllium and Be+2 emission lines and their effective ionization rate coefficients. The focus on beryllium as an impacted material by electron flux aimed to evaluate the EII rates for Be and generate the corresponding datasets needed for Be+2 data analysis. An interaction cross-section was generated using the Flexible Atomic Code (FAC) and used in the estimation of the EII distribution energy functions to estimate the ionization rates for a non-Maxwellian distribution. The use of non-Maxwellian energy distributions for different fractions of hot electrons showed the sensitivity of these rates to the fraction of hot electrons and the forms of the electron energy distribution. The results were in good agreement with those found in the literature.
Keywords:
distribution function, non- Maxwellian distribution, cross-sections, Electron-Impact Ionization (EII), FACDownloads
References
D. Salzmann, Atomic Physics in Hot Plasmas. Oxford, UK: Oxford University Press, 1998.
A. S. Shlyaptseva et al., "Advanced spectroscopic analysis of 0.8-1.0-MA Mo x pinches and the influence of plasma electron beams on L-shell spectra of Mo ions," Physical Review E, vol. 67, no. 2, Feb. 2003, Art. no. 026409. DOI: https://doi.org/10.1103/PhysRevE.67.026409
J. Colgan, H. L. Zhang, and C. J. Fontes, "Electron-impact excitation and ionization cross sections for the Si, Cl, and Ar isonuclear sequences," Physical Review A, vol. 77, no. 6, Jun. 2008, Art. no. 062704. DOI: https://doi.org/10.1103/PhysRevA.77.062704
M. Davoudabadi, J. S. Shrimpton, and F. Mashayek, "On accuracy and performance of high-order finite volume methods in local mean energy model of non-thermal plasmas," Journal of Computational Physics, vol. 228, no. 7, pp. 2468–2479, Apr. 2009. DOI: https://doi.org/10.1016/j.jcp.2008.12.015
R. Bartiromo, F. Bombarda, and R. Giannella, "Spectroscopic study of nonthermal plasmas," Physical Review A, vol. 32, no. 1, pp. 531–537, Jul. 1985. DOI: https://doi.org/10.1103/PhysRevA.32.531
A. Alogla, M. a. H. Eleiwa, and H. Alshortan, "Design and Evaluation of Transmitting Antennas for Solar Power Satellite Systems," Engineering, Technology & Applied Science Research, vol. 11, no. 6, pp. 7950–7956, Dec. 2021. DOI: https://doi.org/10.48084/etasr.4607
D. Mihalas and M. E. Stone, "Statistical Equilibrium Model Atmospheres for Early-Type Stars. III. Hydrogen and Helium Continua," The Astrophysical Journal, vol. 151, pp. 293–310, Jan. 1968. DOI: https://doi.org/10.1086/149437
M. A. Mahmoud and K. A. Hamam, "Studies of Electron Energy Distribution Function (EEDF) in Lithium Vapor Excitation at 2S→3D Two-Photon Resonance," Optics and Photonics Journal, vol. 04, no. 08, pp. 195–212, 2014. DOI: https://doi.org/10.4236/opj.2014.48020
S. Dilmi and A. Boumali, "Influence of the Electron Energy Distribution Function on the Calculation of Ionization Rate in Hot Plasma," UPB Scientific Bulletin, Series A: Applied Mathematics, vol. 79, no. 1, pp. 249–260.
T. Kato, K. Masai, and M. Arnaud, "NIFS Data 014 - Comparison of Ionization Rate Coefficients of Ions from Hydrogen Through Nickel," National Institute for Fusion Science, Nagoya, Japan, Sep. 1991.
W. Lotz, "Electron-impact ionization cross-sections and ionization rate coefficients for atoms and ions from hydrogen to calcium," Zeitschrift für Physik, vol. 216, no. 3, pp. 241–247, Jun. 1968. DOI: https://doi.org/10.1007/BF01392963
W. Lotz, "Electron-impact ionization cross-sections and ionization rate coefficients for atoms and ions from scandium to zinc," Zeitschrift für Physik A Hadrons and nuclei, vol. 220, no. 5, pp. 466–472, Oct. 1969. DOI: https://doi.org/10.1007/BF01394789
M. Arnaud and R. Rothenflug, "An Updated Evaluation of Recombination and Ionization Rates," Astronomy and Astrophysics Supplement Series, vol. 60, pp. 425–457, Jun. 1985.
S. M. Younger, "Electron impact ionization rate coefficients and cross sections for highly ionized iron," Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 27, no. 5, pp. 541–544, May 1982. DOI: https://doi.org/10.1016/0022-4073(82)90106-6
S. M. Younger, "Electron-impact ionization cross sections for highly ionized hydrogen- and lithium-like atoms," Physical Review A, vol. 22, no. 1, pp. 111–117, Jul. 1980. DOI: https://doi.org/10.1103/PhysRevA.22.111
International Atomic Energy Agency, "Flexible Atomic Code (FAC)." https://www-amdis.iaea.org/FAC/ (accessed Sep. 26, 2022).
M. F. Gu, "The flexible atomic code," Canadian Journal of Physics, vol. 86, no. 5, pp. 675–689, May 2008. DOI: https://doi.org/10.1139/p07-197
W. Lotz, "Electron-Impact Ionization Cross-Sections and Ionization Rate Coefficients for Atoms and Ions," The Astrophysical Journal Supplement Series, vol. 14, pp. 207–238, May 1967. DOI: https://doi.org/10.1086/190154
A. Escarguel, F. B. Rosmej, C. Brault, T. Pierre, R. Stamm, and K. Quotb, "Influence of hot electrons on radiative properties of a helium plasma," Plasma Physics and Controlled Fusion, vol. 49, no. 1, pp. 85–93, Sep. 2006. DOI: https://doi.org/10.1088/0741-3335/49/1/006
S. B. Hansen and A. S. Shlyaptseva, "Effects of the electron energy distribution function on modeled x-ray spectra," Physical Review E, vol. 70, no. 3, Sep. 2004, Art. no. 036402. DOI: https://doi.org/10.1103/PhysRevE.70.036402
T. D. Märk and G. H. Dunn, Eds., Electron Impact Ionization, Softcover reprint of the original 1st ed. 1985 edition. New York, NY, US: Springer, 2013. DOI: https://doi.org/10.1007/978-3-7091-4028-4
N. B. Serradj, A. D. K. Ali, and M. E. A. Ghernaout, "A Contribution to the Thermal Field Evaluation at the Tool-Part Interface for the Optimization of Machining Conditions," Engineering, Technology & Applied Science Research, vol. 11, no. 6, pp. 7750–7756, Dec. 2021. DOI: https://doi.org/10.48084/etasr.4235
R. S. Freund, "Electron Impact Ionization Cross-Sections for Atoms, Radicals, and Metastables," in Swarm Studies and Inelastic Electron-Molecule Collisions, New York, NY, 1987, pp. 329–346. DOI: https://doi.org/10.1007/978-1-4612-4662-6_41
J. L. S. Lino, "Cross sections for electron-impact excitation of neutral atoms," Revista mexicana de física, vol. 63, no. 2, pp. 190–193, Apr. 2017.
S. Dilmi and A. Boumali, "Estimation of Electron Impact Ionization Rates of Li Using a Non-Maxwellian Distribution Function," Ukrainian Journal of Physics, vol. 66, no. 8, pp. 691–697, Sep. 2021. DOI: https://doi.org/10.15407/ujpe66.8.691
S. Saxena and L. B. Roy, "The Effect of Geometric Parameters on the Strength of Stone Columns," Engineering, Technology & Applied Science Research, vol. 12, no. 4, pp. 9028–9033, Aug. 2022. DOI: https://doi.org/10.48084/etasr.5138
Downloads
How to Cite
License
Copyright (c) 2022 S. Dilmi, A. Lifa, S. E. Bentridi
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.