The Effects of Superstatistics Properties on Hot Plasma

Authors

  • S. Dilmi Laboratory of Operator Theory and PDE, Faculty of Exact Sciences, University of El Oued, Algeria
  • F. Khalfaoui Laboratory of Operator Theory and PDE, Faculty of Exact Sciences, University of El Oued, Algeria
  • A. Boumali Laboratory of Applied and Theoretical Physics, University Larbi Tébessi, Algeria
Volume: 12 | Issue: 5 | Pages: 9342-9346 | October 2022 | https://doi.org/10.48084/etasr.5223

Abstract

The electron impact ionization is a crucial atomic process in the collisional radiative model and the study of ionization balance. The superstatistics theory, which was originally proposed for the study of non-equilibrium complex systems, has recently been extended to studies of small systems interacting with a finite environment due to their interesting statistical behavior. This paper introduces the superstatistics formalism in the case of ionization rates with different values of the dynamical parameter q and shows how it affects the calculation of the ionization rates for Li+. Moreover, the distribution function for the effective Boltzmann factor of superstatistics was swapped.

Keywords:

ionization rates, Boltzmann factor, superstatistics, code FAC, , cross section

Downloads

Download data is not yet available.

References

A. J. Murray, "(e,2e) ionization studies of alkaline-earth-metal and alkali-earth-metal targets: Na, Mg, K, and Ca, from near threshold to beyond intermediate energies," Physical Review A, vol. 72, no. 6, Dec. 2005, Art. no. 062711. DOI: https://doi.org/10.1103/PhysRevA.72.062711

H. Deutsch and T. D. Märk, "Calculation of absolute electron impact ionization cross-section functions for single ionization of He, Ne, Ar, Kr, Xe, N and F," International Journal of Mass Spectrometry and Ion Processes, vol. 79, no. 3, pp. R1–R8, Nov. 1987. DOI: https://doi.org/10.1016/0168-1176(87)83009-4

X. Llovet, C. J. Powell, F. Salvat, and A. Jablonski, "Cross Sections for Inner-Shell Ionization by Electron Impact," Journal of Physical and Chemical Reference Data, vol. 43, no. 1, Mar. 2014, Art. no. 013102. DOI: https://doi.org/10.1063/1.4832851

V. Jonauskas et al., "Electron-impact ionization of W5+," Physical Review A, vol. 100, no. 6, Dec. 2019, Art. no. 062701.

F. Mehmood, T. Kamal, and U. Ashraf, "Generation and Applications of Plasma (An Academic Review)," Oct. 2018. DOI: https://doi.org/10.20944/preprints201810.0061.v1

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

L. J. Kieffer and G. H. Dunn, "Electron Impact Ionization Cross-Section Data for Atoms, Atomic Ions, and Diatomic Molecules: I. Experimental Data," Reviews of Modern Physics, vol. 38, no. 1, pp. 1–35, Jan. 1966. DOI: https://doi.org/10.1103/RevModPhys.38.1

M. Alhamdany and A. H. K. Albayati, "Statistical Modeling of Time Headway on Urban Roads: A Case Study in Baghdad," Engineering, Technology & Applied Science Research, vol. 12, no. 3, pp. 8584–8591, Jun. 2022. DOI: https://doi.org/10.48084/etasr.4878

A. Chachereau and S. Pancheshnyi, "Calculation of the Effective Ionization Rate in Air by Considering Electron Detachment From Negative Ions," IEEE Transactions on Plasma Science, vol. 42, no. 10, pp. 3328–3338, Jul. 2014. DOI: https://doi.org/10.1109/TPS.2014.2354676

C. Beck and E. G. D. Cohen, "Superstatistics," Physica A: Statistical Mechanics and its Applications, vol. 322, pp. 267–275, May 2003. DOI: https://doi.org/10.1016/S0378-4371(03)00019-0

A. F. Tseluyko, V. T. Lazurik, D. L. Ryabchikov, V. I. Maslov, and I. N. Sereda, "Experimental study of radiation in the wavelength range 12.2–15.8 nm from a pulsed high-current plasma diode," Plasma Physics Reports, vol. 34, no. 11, pp. 963–968, Nov. 2008. DOI: https://doi.org/10.1134/S1063780X0811010X

A. F. Tseluyko et al., "Influence of plasma nucleus form on radiation orientation in high-current pulse plasma diode," Problems of Atomic Science and Technology, no. 6, pp. 176–178, 2010.

C. Beck, E. G. D. Cohen, and H. L. Swinney, "From time series to superstatistics," Physical Review E, vol. 72, no. 5, Nov. 2005, Art. no. 056133. DOI: https://doi.org/10.1103/PhysRevE.72.056133

H. Touchette and C. Beck, "Asymptotics of superstatistics," Physical Review E, vol. 71, no. 1, Jan. 2005, Art. no. 016131.

C. Mark, C. Metzner, and B. Fabry, "Bayesian inference of time varying parameters in autoregressive processes." Oct. 2009, 2014.

R. Hanel, S. Thurner, and M. Gell-Mann, "Generalized entropies and the transformation group of superstatistics," Proceedings of the National Academy of Sciences, vol. 108, no. 16, pp. 6390–6394, Apr. 2011. DOI: https://doi.org/10.1073/pnas.1103539108

A. M. Reynolds, "Superstatistical Mechanics of Tracer-Particle Motions in Turbulence," Physical Review Letters, vol. 91, no. 8, Aug. 2003, Art. no. 084503. DOI: https://doi.org/10.1103/PhysRevLett.91.084503

M. Ausloos and K. Ivanova, "Dynamical model and nonextensive statistical mechanics of a market index on large time windows," Physical Review E, vol. 68, no. 4, Oct. 2003, Art. no. 046122. DOI: https://doi.org/10.1103/PhysRevE.68.046122

C. Beck, "Statistics of Three-Dimensional Lagrangian Turbulence," Physical Review Letters, vol. 98, no. 6, Feb. 2007, Art. no. 064502. DOI: https://doi.org/10.1103/PhysRevLett.98.064502

C. Beck and S. Miah, "Statistics of Lagrangian quantum turbulence," Physical Review E, vol. 87, no. 3, Mar. 2013, Art. no. 031002. DOI: https://doi.org/10.1103/PhysRevE.87.031002

P. Jizba and F. Scardigli, "Special relativity induced by granular space," The European Physical Journal C, vol. 73, no. 7, Jul. 2013, Art. no. 2491. DOI: https://doi.org/10.1140/epjc/s10052-013-2491-x

S. Rizzo and A. Rapisarda, "Environmental Atmospheric Turbulence at Florence Airport," AIP Conference Proceedings, vol. 742, no. 1, pp. 176–181, Dec. 2004. DOI: https://doi.org/10.1063/1.1846475

P. Rabassa and C. Beck, "Superstatistical analysis of sea-level fluctuations," Physica A: Statistical Mechanics and its Applications, vol. 417, pp. 18–28, Jan. 2015. DOI: https://doi.org/10.1016/j.physa.2014.08.068

Y. Itto, "Heterogeneous anomalous diffusion in view of superstatistics," Physics Letters A, vol. 378, no. 41, pp. 3037–3040, Aug. 2014. DOI: https://doi.org/10.1016/j.physleta.2014.08.022

K. Briggs and C. Beck, "Modelling train delays with q-exponential functions," Physica A: Statistical Mechanics and its Applications, vol. 378, no. 2, pp. 498–504, May 2007. DOI: https://doi.org/10.1016/j.physa.2006.11.084

L. Leon Chen and C. Beck, "A superstatistical model of metastasis and cancer survival," Physica A: Statistical Mechanics and its Applications, vol. 387, no. 13, pp. 3162–3172, May 2008. DOI: https://doi.org/10.1016/j.physa.2008.01.116

D. N. Sob’yanin, "Hierarchical maximum entropy principle for generalized superstatistical systems and Bose-Einstein condensation of light," Physical Review E, vol. 85, no. 6, Jun. 2012, Art. No. 061120. DOI: https://doi.org/10.1103/PhysRevE.85.061120

G. C. Yalcin and C. Beck, "Environmental superstatistics," Physica A: Statistical Mechanics and its Applications, vol. 392, no. 21, pp. 5431–5452, Nov. 2013. DOI: https://doi.org/10.1016/j.physa.2013.06.057

K. Ourabah and M. Tribeche, "Fractional superstatistics from a kinetic approach," Physical Review E, vol. 97, no. 3, Mar. 2018, Art. no. 032126. DOI: https://doi.org/10.1103/PhysRevE.97.032126

M. Baus and C. F. Tejero, Eds., Equilibrium Statistical Physics. Berlin, Heidelberg: Springer, 2008. DOI: https://doi.org/10.1007/978-3-540-74632-4

T. D. Märk, "Cluster ions: Production, detection and stability," International Journal of Mass Spectrometry and Ion Processes, vol. 79, no. 1, pp. 1–59, Oct. 1987. DOI: https://doi.org/10.1016/0168-1176(87)80022-8

G. C. Yalcin and C. Beck, "Currents in complex polymers: An example of superstatistics for short time series," Physics Letters A, vol. 376, no. 35, pp. 2344–2347, Jul. 2012. DOI: https://doi.org/10.1016/j.physleta.2012.05.057

H. Touchette and C. Beck, "Asymptotics of superstatistics," Physical Review E, vol. 71, no. 1, Jan. 2005, Art. no. 016131. DOI: https://doi.org/10.1103/PhysRevE.71.016131

A. Boumali, F. Serdouk, and S. Dilmi, "Superstatistical properties of the one-dimensional Dirac oscillator," Physica A: Statistical Mechanics and its Applications, vol. 553, Sep. 2020, Art. no. 124207. DOI: https://doi.org/10.1016/j.physa.2020.124207

S. Sargolzaeipor, H. Hassanabadi, and W. S. Chung, "q-deformed superstatistics of the Schrödinger equation in commutative and noncommutative spaces with magnetic field," The European Physical Journal Plus, vol. 133, no. 1, Jan. 2018, Art. no. 5. DOI: https://doi.org/10.1140/epjp/i2018-11827-1

C. Tsallis and A. M. C. Souza, "Constructing a statistical mechanics for Beck-Cohen superstatistics," Physical Review E, vol. 67, no. 2, Feb. 2003, Art. no. 026106. DOI: https://doi.org/10.1103/PhysRevE.67.026106

F. Sattin, "Bayesian approach to superstatistics," The European Physical Journal B - Condensed Matter and Complex Systems, vol. 49, no. 2, pp. 219–224, Jan. 2006. DOI: https://doi.org/10.1140/epjb/e2006-00038-8

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

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

Flexible Atomic Code (FAC). https://www-amdis.iaea.org/FAC/.

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, May 1967. DOI: https://doi.org/10.1086/190154

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

Downloads

How to Cite

[1]
S. Dilmi, F. Khalfaoui, and A. Boumali, “The Effects of Superstatistics Properties on Hot Plasma”, Eng. Technol. Appl. Sci. Res., vol. 12, no. 5, pp. 9342–9346, Oct. 2022.

Metrics

Abstract Views: 361
PDF Downloads: 189

Metrics Information
Bookmark and Share