Home Impact of temperature asymmetry and small fraction of static positive ions on the relaxed states of a relativistic hot pair plasma
Article
Licensed
Unlicensed Requires Authentication

Impact of temperature asymmetry and small fraction of static positive ions on the relaxed states of a relativistic hot pair plasma

  • Usman Shazad ORCID logo EMAIL logo and M. Iqbal ORCID logo
Published/Copyright: August 30, 2023
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 78 Issue 11

Abstract

The relaxed state of a magnetized relativistic hot plasma composed of inertial electrons and positrons having different relativistic temperatures and a fraction of static positive ions is studied. From the steady-state solutions of vortex dynamics equations and the relation for current density, a non-force-free triple Beltrami (TB) relaxed state equation is derived. The TB state is characterized by three scale parameters that consequently provide three different self-organized structures. The analysis of the relaxed state shows that for specific values of generalized helicities, the disparity in relativistic temperature and the existence of a small fraction of static positive ions in pair plasma can transform the nature of scale parameters. Moreover, an analytical solution of the TB state for an axisymmetric cylindrical geometry with an internal conductor configuration demonstrates that due to asymmetries of temperature and density of plasma species, diamagnetic structures can transform into paramagnetic ones and vice versa. The present study will improve our understanding of pair plasmas in trap-based plasma confinement experiments and astrophysical environments.

Keywords: Beltrami field; non-force-free; relativistic plasma; self-organization; vortex dynamics
Corresponding author: Usman Shazad, Department of Physics, University of Engineering and Technology, Lahore 54890, Pakistan, E-mail:

Funding source: Higher Education Commission, Pakistan

Award Identifier / Grant number: 20-9408/Punjab/NRPU/R&D/HEC/2017-18

  1. Research ethics: Not applicable; no experiment has been conducted on humans or animals.

  2. Author contributions: Both authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  3. Conflict of interest statement: Authors state no conflicts of interest.

  4. Research funding: The work of M. Iqbal is funded by Higher Education Commission (HEC) Pakistan under project No.20-9408/Punjab/NRPU/R&D/HEC/2017-18.

  5. Data availability: Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

References

[1] K. A. Holcomb and T. Tajima, “General-relativistic plasma physics in the early universe,” Phys. Rev. D, vol. 40, p. 3809, 1989. https://doi.org/10.1103/physrevd.40.3809.Search in Google Scholar PubMed

[2] V. L. Ginzburg, “Pulsars (theoretical concepts),” Sov. Phys. Usp., vol. 14, p. 83, 1971. https://doi.org/10.1070/pu1971v014n02abeh004446.Search in Google Scholar

[3] P. A. Sturrock, “A model of pulsars,” Astrophys. J., vol. 164, p. 529, 1971. https://doi.org/10.1086/150865.Search in Google Scholar

[4] J. Arons, “Some problems of pulsar physics or I’m madly in love with electricity,” Space Sci. Rev., vol. 24, p. 437, 1979. https://doi.org/10.1007/BF00172212.Search in Google Scholar

[5] R. D. Blandford and A. Levinson, “Pair cascades in extragalactic jets. 1: gamma rays,” Astrophys. J., vol. 441, p. 79, 1995. https://doi.org/10.1086/175338.Search in Google Scholar

[6] J. F. C. Wardle, D. C. Homan, R. Ojha, and D. H. Roberts, “Electron–positron jets associated with the quasar 3C279,” Nature, vol. 395, p. 457, 1998. https://doi.org/10.1038/26675.Search in Google Scholar

[7] I. F. Mirabel and L. F. Rodríguez, “Sources of relativistic jets in the galaxy,” Annu. Rev. Astron. Astrophys., vol. 37, p. 409, 1999. https://doi.org/10.1146/annurev.astro.37.1.409.Search in Google Scholar

[8] P. Mészáros, “Theories of gamma-ray bursts,” Annu. Rev. Astron. Astrophys., vol. 40, p. 137, 2002. https://doi.org/10.1146/annurev.astro.40.060401.093821.Search in Google Scholar

[9] G. Weidenspointner, G. Skinner, P. Jean, et al.., “An asymmetric distribution of positrons in the galactic disk revealed by γ-rays,” Nature, vol. 451, p. 159, 2008. https://doi.org/10.1038/nature06490.Search in Google Scholar PubMed

[10] R. D. Blandford and R. L. Znajek, “Electromagnetic extraction of energy from Kerr black holes,” Mon. Not. R. Astron. Soc., vol. 179, p. 433, 1977. https://doi.org/10.1093/mnras/179.3.433.Search in Google Scholar

[11] A. Spitkovsky, “Time-dependent force-free pulsar magnetospheres: axisymmetric and oblique rotators,” Astrophys. J., vol. 648, p. L51, 2006. https://doi.org/10.1086/507518.Search in Google Scholar

[12] G. Brambilla, C. Kalapotharakos, A. N. Timokhin, A. K. Harding, and D. Kazanas, “Electron–positron pair flow and current composition in the pulsar magnetosphere,” Astrophys. J., vol. 858, p. 81, 2018. https://doi.org/10.3847/1538-4357/aab3e1.Search in Google Scholar

[13] J. J. Geng, X. F. Wu, Y. F. Huang, L. Li, and Z. G. Dai, “Imprints of electron–positron winds on the multiwavelength afterglows of gamma-ray bursts,” Astrophys. J., vol. 825, p. 107, 2016. https://doi.org/10.3847/0004-637x/825/2/107.Search in Google Scholar

[14] M. Boettcher, H. Mause, and R. Schlickeiser, “γ-ray emission and spectral evolution of pair plasmas in AGN jets. I. General theory and a prediction for the GeV - TeV emission from ultrarelativistic jets,” Astron. Astrophys., vol. 324, p. 395, 1996. https://doi.org/10.48550/arXiv.astro-ph/9604003.Search in Google Scholar

[15] R. Blandford, D. Meier, and A. Readhead, “Relativistic jets from active galactic nuclei,” Annu. Rev. Astron. Astrophys., vol. 57, p. 467, 2019. https://doi.org/10.1146/annurev-astro-081817-051948.Search in Google Scholar

[16] V. I. Berezhiani and S. M. Mahajan, “Large amplitude localized structures in a relativistic electron-positron ion plasma,” Phys. Rev. Lett., vol. 73, p. 1110, 1994. https://doi.org/10.1103/physrevlett.73.1110.Search in Google Scholar PubMed

[17] G. Sarri, K. Poder, J. M. Cole, et al.., “Generation of neutral and high-density electron–positron pair plasmas in the laboratory,” Nat. Commun., vol. 6, p. 6747, 2015. https://doi.org/10.1038/ncomms7747.Search in Google Scholar PubMed PubMed Central

[18] V. I. Berezhiani and S. M. Mahajan, “Large relativistic density pulses in electron-positron-ion plasmas,” Phys. Rev. E, vol. 52, p. 1968, 1995. https://doi.org/10.1103/physreve.52.1968.Search in Google Scholar PubMed

[19] O. A. Pokhotelov, O. G. Onishchenko, V. P. Pavlenko, et al., “Nonlinear drift-Alfvén waves in relativistically hot multicomponent plasmas and their relevance to the fine structure of pulsar radioemissions,” Astrophys. Space Sci., vol. 277, p. 497, 2001. https://doi.org/10.1023/a:1012579613890.10.1023/A:1012579613890Search in Google Scholar

[20] R. A. López, F. A. Asenjo, V. Muñoz, and J. A. Valdivia, “Parametric decays in relativistic magnetized electron-positron plasmas with relativistic temperatures,” Phys. Plasmas, vol. 19, p. 082104, 2012. https://doi.org/10.1063/1.4742315.Search in Google Scholar

[21] F. A. Asenjo, F. A. Borotto, A. C. L. Chian, V. Muñoz, J. A. Valdivia, and E. L. Rempel, “Self-modulation of nonlinear waves in a weakly magnetized relativistic electron-positron plasma with temperature,” Phys. Rev. E, vol. 85, p. 046406, 2012. https://doi.org/10.1103/physreve.85.046406.Search in Google Scholar PubMed

[22] L. Comisso and F. A. Asenjo, “Thermal-inertial effects on magnetic reconnection in relativistic pair plasmas,” Phys. Rev. Lett., vol. 113, p. 045001, 2014. https://doi.org/10.1103/physrevlett.113.045001.Search in Google Scholar PubMed

[23] S. Mahajan and M. Lingam, “Relativistic-amplitude electromagnetic waves—Beating the “magnetic” barrier,” Phys. Plasmas, vol. 25, p. 072112, 2018. https://doi.org/10.1063/1.5033907.Search in Google Scholar

[24] A. Saha and S. Banerjee, Dynamical Systems and Nonlinear Waves in Plasmas, 1st ed. US, CRC Press Taylor and Francis Group, 2021.10.1201/9781003042549-1Search in Google Scholar

[25] P. Chatterjee, R. Kaushik, and U. N. Ghosh, Waves and Wave Interaction in Plasmas, 1st ed. Singapore, World Scientific, 2023.10.1142/13114Search in Google Scholar

[26] S. Ortolani and D. D. Schnack, Magnetohydrodynamics of Plasma Relaxation, 1st ed. Singapore, World Scientific, 1993.10.1142/1564Search in Google Scholar

[27] L. Woltjer, “A theorem on force-free magnetic fields,” Proc. Natl. Acad. Sci., vol. 44, p. 489, 1958. https://doi.org/10.1073/pnas.44.6.489.Search in Google Scholar PubMed PubMed Central

[28] J. B. Taylor, “Relaxation of toroidal plasma and generation of reverse magnetic fields,” Phys. Rev. Lett., vol. 33, p. 1139, 1974. https://doi.org/10.1103/physrevlett.33.1139.Search in Google Scholar

[29] S. M. Mahajan and Z. Yoshida, “Double curl Beltrami flow: diamagnetic structures,” Phys. Rev. Lett., vol. 81, p. 4863, 1998. https://doi.org/10.1103/physrevlett.81.4863.Search in Google Scholar

[30] L. C. Steinhauer, “Double mode condensates of a flowing plasma as possible relaxed states,” Phys. Plasmas, vol. 9, p. 3767, 2002. https://doi.org/10.1063/1.1503068.Search in Google Scholar

[31] R. Bhattacharyya, M. S. Janaki, and B. Dasgupta, “Relaxation in electron–positron plasma: a possibility,” Phys. Lett. A, vol. 315, p. 120, 2003. https://doi.org/10.1016/s0375-9601(03)00977-0.Search in Google Scholar

[32] M. Iqbal, “Beltrami fields at nanoscales in a quantum electron-hole plasma,” Appl. Phys. Lett., vol. 103, p. 034109, 2013.10.1063/1.4816159Search in Google Scholar

[33] N. L. Shatashvili, S. M. Mahajan, and V. I. Berezhiani, “Mechanisms for multi-scale structures in dense degenerate astrophysical plasmas,” Astrophys. Space Sci., vol. 361, p. 70, 2016. https://doi.org/10.1007/s10509-016-2663-x.Search in Google Scholar

[34] V. I. Berezhiani, N. L. Shatashvili, and S. M. Mahajan, “Beltrami-Bernoulli equilibria in plasmas with degenerate electrons,” Phys. Plasmas, vol. 22, p. 022902, 2015.10.1063/1.4913356Search in Google Scholar

[35] N. L. Shatashvili, S. M. Mahajan, and V. I. Berezhiani, “On the relaxed states in the mixture of degenerate and non-degenerate hot plasmas of astrophysical objects,” Astrophys. Space Sci., vol. 364, p. 148, 2019. https://doi.org/10.1007/s10509-019-3596-y.Search in Google Scholar

[36] M. Iqbal, V. I. Berezhiani, and Z. Yoshida, “Multiscale structures in relativistic pair plasmas,” Phys. Plasmas, vol. 15, p. 032905, 2008.10.1063/1.2896991Search in Google Scholar

[37] J. Pino, H. Li, and S. M. Mahajan, “Relaxed states in relativistic multifluid plasmas,” Phys. Plasmas, vol. 17, p. 112112, 2010.10.1063/1.3505326Search in Google Scholar

[38] M. Iqbal and P. K. Shukla, “Multiscale structures in a two-temperature relativistic electron-positron-ion plasma,” J. Plasma Phys., vol. 79, p. 715, 2013. https://doi.org/10.1017/s0022377813000342.Search in Google Scholar

[39] U. Shazad, M. Iqbal, and S. Ullah, “Self-organized multiscale structures in thermally relativistic electron-positron-ion plasmas,” Phys. Scr., vol. 96, p. 125627, 2021. https://doi.org/10.1088/1402-4896/ac38d5.Search in Google Scholar

[40] U. Shazad and M. Iqbal, “On the quadruple Beltrami fields in thermally relativistic electron-positron-ion plasma,” Phys. Scr., vol. 98, p. 055605, 2023. https://doi.org/10.1088/1402-4896/acc7d6.Search in Google Scholar

[41] F. A. Asenjo and S. M. Mahajan, “Diamagnetic field states in cosmological plasmas,” Phys. Rev. E, vol. 99, p. 053204, 2019. https://doi.org/10.1103/physreve.99.053204.Search in Google Scholar PubMed

[42] C. Bhattacharjee and J. C. Feng, “On Beltrami states near black hole event horizon,” Phys. Plasmas, vol. 27, p. 072901, 2020.10.1063/5.0010050Search in Google Scholar

[43] S. Ullah, U. Shazad, and M. Iqbal, “Multiscale structures in three species magnetoplasmas with two positive ions,” Phys. Scr., vol. 97, p. 065605, 2022. https://doi.org/10.1088/1402-4896/ac7109.Search in Google Scholar

[44] F. Ahmed, M. Iqbal, and U. Shazad, “Beltrami fields in partially ionized magnetized dusty plasma,” AIP Adv., vol. 13, p. 055305, 2023.10.1063/5.0147223Search in Google Scholar

[45] C. Bhattacharjee, “Beltrami–Bernoulli equilibria in weakly rotating self-gravitating fluid,” J. Plasma Phys., vol. 88, p. 175880101, 2022. https://doi.org/10.1017/s0022377822000101.Search in Google Scholar

[46] C. Bhattacharjee, “Implications of nonzero photon mass on plasma equilibria,” Phys. Rev. E, vol. 107, p. 035207, 2023. https://doi.org/10.1103/physreve.107.035207.Search in Google Scholar PubMed

[47] Z. Yoshida, S. M. Mahajan, S. Ohsaki, M. Iqbal, and N. Shatashvili, “Beltrami fields in plasmas: high-confinement mode boundary layers and high beta equilibria,” Phys. Plasmas, vol. 8, p. 2125, 2001. https://doi.org/10.1063/1.1354149.Search in Google Scholar

[48] R. Bhattacharyya, M. S. Janaki, and B. Dasgupta, “Field-reversed configuration (FRC) as a minimum-dissipative relaxed state,” Phys. Lett. A, vol. 291, p. 291, 2001. https://doi.org/10.1016/s0375-9601(01)00723-x.Search in Google Scholar

[49] S. M. Mahajan, R. Miklaszewski, K. I. Nikol’skaya, and N. L. Shatashvili, “Formation and primary heating of the solar corona: theory and simulation,” Phys. Plasmas, vol. 8, p. 1340, 2001. https://doi.org/10.1063/1.1350670.Search in Google Scholar

[50] S. Ohsaki, N. L. Shatashvili, Z. Yoshida, and S. M. Mahajan, “Energy transformation mechanism in the solar atmosphere associated with magnetofluid coupling: explosive and eruptive events,” Astrophys. J., vol. 570, p. 395, 2002. https://doi.org/10.1086/339499.Search in Google Scholar

[51] D. Kagan and S. M. Mahajan, “Application of double beltrami states to solar eruptions,” Mon. Not. R. Astron. Soc., vol. 406, p. 1140, 2010.10.1111/j.1365-2966.2010.16741.xSearch in Google Scholar

[52] R. Bhattacharyya, M. S. Janaki, B. Dasgupta, and G. P. Zank, “Solar arcades as possible minimum dissipative relaxed states,” Sol. Phys., vol. 240, p. 63, 2007. https://doi.org/10.1007/s11207-006-0280-5.Search in Google Scholar

[53] S. M. Mahajan, N. L. Shatashvili, S. V. Mikeladze, and K. I. Sigua, “Acceleration of plasma flows due to reverse dynamo mechanism,” Astrophys. J., vol. 634, p. 419, 2005. https://doi.org/10.1086/432867.Search in Google Scholar

[54] K. Kotorashvili, N. Revazashvili, and N. L. Shatashvili, “Dynamical fast flow generation/acceleration in dense degenerate two-fluid plasmas of astrophysical objects,” Astrophys. Space Sci., vol. 365, p. 175, 2020. https://doi.org/10.1007/s10509-020-03871-w.Search in Google Scholar

[55] K. Kotorashvili and N. L. Shatashvili, “Macroscale fast flow and magnetic-field generation in two-temperature relativistic electron–ion plasmas of astrophysical objects,” Astrophys. Space Sci., vol. 367, p. 2, 2022. https://doi.org/10.1007/s10509-021-04034-1.Search in Google Scholar

[56] S. M. Gondal and M. Iqbal, “Formation of self-organized structures in internal conductor plasma,” Phys. Scr., vol. 96, p. 75602, 2021.10.1088/1402-4896/abf8e9Search in Google Scholar

[57] S. M. Gondal, “Relaxation of multi-ion plasmas in an internal conductor,” AIP Adv., vol. 12, p. 025202, 2022.10.1063/5.0081284Search in Google Scholar

[58] H. Chen, S. C. Wilks, J. D. Bonlie, et al.., “Making relativistic positrons using ultraintense short pulse lasers,” Phys. Plasmas, vol. 16, p. 122702, 2009. https://doi.org/10.1063/1.3271355.Search in Google Scholar

[59] H. Chen, S. C. Wilks, D. D. Meyerhofer, et al.., “Relativistic quasimonoenergetic positron jets from intense laser-solid interactions,” Phys. Rev. Lett., vol. 105, p. 015003, 2010. https://doi.org/10.1103/physrevlett.105.015003.Search in Google Scholar PubMed

[60] H. Chen, D. D. Meyerhofer, S. C. Wilks, et al.., “Towards laboratory produced relativistic electron–positron pair plasmas,” High Energy Density Phys., vol. 7, p. 225, 2011. https://doi.org/10.1016/j.hedp.2011.05.006.Search in Google Scholar

[61] S. M. Mahajan, N. L. Shatashvili, and V. I. Berezhiani, “Asymmetry-driven structure formation in pair plasmas,” Phys. Rev. E, vol. 80, p. 066404, 2009. https://doi.org/10.1103/physreve.80.066404.Search in Google Scholar

[62] V. I. Berezhiani, S. M. Mahajan, and N. L. Shatashvili, “Stable localized electromagnetic pulses in asymmetric pair plasmas,” J. Plasma Phys., vol. 76, p. 467, 2010. https://doi.org/10.1017/s0022377809990699.Search in Google Scholar

[63] V. I. Berezhiani, S. M. Mahajan, and N. L. Shatashvili, “Stable optical vortex solitons in pair plasmas,” Phys. Rev. A, vol. 81, p. 053812, 2010. https://doi.org/10.1103/physreva.81.053812.Search in Google Scholar

[64] V. I. Berezhiani, N. L. Shatashvili, S. M. Mahajan, and B. N. Aleksić, “Vortex bubble formation in pair plasmas,” Phys. Rev. E, vol. 88, p. 015101, 2013. https://doi.org/10.1103/physreve.88.015101.Search in Google Scholar PubMed

[65] M. R. Stoneking, T. S. Pedersen, P. Helander, et al.., “A new Frontier in laboratory physics: magnetized electron–positron plasmas,” J. Plasma Phys., vol. 86, p. 155860601, 2020. https://doi.org/10.1017/s0022377820001385.Search in Google Scholar

[66] J. Fajans and C. M. Surko, “Plasma and trap-based techniques for science with antimatter,” Phys. Plasmas, vol. 27, p. 030601, 2020.10.1063/1.5131273Search in Google Scholar

[67] J. von der Linden, G. Fiksel, J. Peebles, et al.., “Confinement of relativistic electrons in a magnetic mirror en route to a magnetized relativistic pair plasma,” Phys. Plasmas, vol. 28, p. 092508, 2021.10.1063/5.0057582Search in Google Scholar

[68] H. Chen and F. Fiuza, “Perspectives on relativistic electron-positron pair plasma experiments of astrophysical relevance using high-power lasers,” Phys. Plasmas, vol. 30, p. 020601, 2023.10.1063/5.0134819Search in Google Scholar

[69] Z. Yoshida, Y. Ogawa, J. Morikawa, et al.., “First plasma in the RT-1 device,” Plasma Fusion Res., vol. 1, p. 008, 2006. https://doi.org/10.1585/pfr.1.008.Search in Google Scholar

[70] Z. Yoshida, S. M. Mahajan, T. Mizushima, Y. Yano, H. Saitoh, and J. Morikawa, “Generalized two-fluid equilibria: Understanding RT-1 experiments and beyond,” Phys. Plasmas, vol. 17, p. 112507, 2010.10.1063/1.3505821Search in Google Scholar

[71] N. Sato, “Maximum entropy states of collisionless positron–electron plasma in a dipole magnetic field,” Phys. Plasmas, vol. 30, p. 042503, 2023. https://doi.org/10.1063/5.0135659.Search in Google Scholar

[72] M. Yamada, H. Ji, S. Hsu, et al.., “Study of driven magnetic reconnection in a laboratory plasma,” Phys. Plasmas, vol. 4, p. 1936, 1997. https://doi.org/10.1063/1.872336.Search in Google Scholar

[73] A. I. Morozov, A. I. Bugrova, A. M. Bishaev, A. S. Lipatov, and M. V. Kozintseva, “Plasma parameters in the upgraded trimyx-M galathea,” Tech. Phys., vol. 52, p. 1546, 2007. https://doi.org/10.1134/s1063784207120031.Search in Google Scholar

[74] V. I. Berezhiani, S. M. Mahajan, Z. Yoshida, and M. Ohhashi, “Self-trapping of strong electromagnetic beams in relativistic plasmas,” Phys. Rev. E, vol. 65, p. 047402, 2002. https://doi.org/10.1103/physreve.65.047402.Search in Google Scholar PubMed

[75] T. Tajima and T. Taniuti, “Nonlinear interaction of photons and phonons in electron-positron plasmas,” Phys. Rev. A, vol. 42, p. 3587, 1990. https://doi.org/10.1103/physreva.42.3587.Search in Google Scholar PubMed

[76] L. C. Steinhauer and A. Ishida, “Relaxation of a two-specie magnetofluid,” Phys. Rev. Lett., vol. 79, p. 3423, 1997. https://doi.org/10.1103/physrevlett.79.3423.Search in Google Scholar

[77] S. M. Mahajan and M. Lingam, “Multi-fluid systems – multi-Beltrami relaxed states and their implications,” Phys. Plasmas, vol. 22, p. 092123, 2015.10.1063/1.4931069Search in Google Scholar

[78] Z. Yoshida and Y. Giga, “Remarks on spectra of operator rot,” Math. Z., vol. 204, p. 235, 1990. https://doi.org/10.1007/bf02570870.Search in Google Scholar

[79] S. M. Mahajan, “Classical perfect diamagnetism: expulsion of current from the plasma interior,” Phys. Rev. Lett., vol. 100, p. 075001, 2008. https://doi.org/10.1103/physrevlett.100.075001.Search in Google Scholar

[80] M. Iqbal, A. M. Mirza, G. Murtaza, and Z. Yoshida, “High β relaxed states with internal conductor plasma configuration,” Phys. Plasmas, vol. 8, p. 1559, 2001. https://doi.org/10.1063/1.1364672.Search in Google Scholar

[81] J. Pétri, “Theory of pulsar magnetosphere and wind,” J. Plasma Phys., vol. 82, p. 635820502, 2016.10.1017/S0022377816000763Search in Google Scholar
Received: 2023-05-07
Accepted: 2023-08-08
Published Online: 2023-08-30
Published in Print: 2023-11-27

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. General
  3. Impact of temperature asymmetry and small fraction of static positive ions on the relaxed states of a relativistic hot pair plasma
  4. Dynamical Systems & Nonlinear Phenomena
  5. Similarity solutions for cylindrical shock wave in a self-gravitating and rotating gas under the influence of monochromatic radiation and azimuthal or axial magnetic field by using Lie invariance method
  6. Chaotic dynamics of an extended Duffing-van der Pol system with a non-smooth perturbation and parametric excitation
  7. Hydrodynamics
  8. On the limitations of the complex wave velocity for the heterogeneous swirling flows
  9. Solid State Physics & Materials Science
  10. Photocatalytic decomposition of Congo red dye by black paste@TiO2 as an efficient recyclable photocatalyst
  11. Theoretical investigation on the elastic and mechanical properties of high-entropy alloys with partial replacement of Sc in Hf0.25Ti0.25Zr0.25Sc0.25−xAl x (x ≤ 15 %)
  12. Synthesis, structure, and luminescence properties of double perovskites Ba2.9Sr0.1WO6: Eu3+ red emitting phosphor
  13. Unveiling transport properties in rare-earth-substituted nanostructured bismuth telluride for thermoelectric application
https://doi.org/10.1515/zna-2023-0112
Keywords for this article
Beltrami field; non-force-free; relativistic plasma; self-organization; vortex dynamics

Articles in the same Issue

  1. Frontmatter
  2. General
  3. Impact of temperature asymmetry and small fraction of static positive ions on the relaxed states of a relativistic hot pair plasma
  4. Dynamical Systems & Nonlinear Phenomena
  5. Similarity solutions for cylindrical shock wave in a self-gravitating and rotating gas under the influence of monochromatic radiation and azimuthal or axial magnetic field by using Lie invariance method
  6. Chaotic dynamics of an extended Duffing-van der Pol system with a non-smooth perturbation and parametric excitation
  7. Hydrodynamics
  8. On the limitations of the complex wave velocity for the heterogeneous swirling flows
  9. Solid State Physics & Materials Science
  10. Photocatalytic decomposition of Congo red dye by black paste@TiO2 as an efficient recyclable photocatalyst
  11. Theoretical investigation on the elastic and mechanical properties of high-entropy alloys with partial replacement of Sc in Hf0.25Ti0.25Zr0.25Sc0.25−xAl x (x ≤ 15 %)
  12. Synthesis, structure, and luminescence properties of double perovskites Ba2.9Sr0.1WO6: Eu3+ red emitting phosphor
  13. Unveiling transport properties in rare-earth-substituted nanostructured bismuth telluride for thermoelectric application
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 28.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/zna-2023-0112/html
Scroll to top button