Home Quadruple Beltrami field structures in electron–positron multi-ion plasma
Article
Licensed
Unlicensed Requires Authentication

Quadruple Beltrami field structures in electron–positron multi-ion plasma

  • Farhat Saleem , Muhammad Iqbal and Usman Shazad ORCID logo EMAIL logo
Published/Copyright: January 12, 2024

Abstract

A quadruple Beltrami (QB) equilibrium state for a four-component plasma that consists of inertial electrons, positrons, lighter positive (H+) ions and heavier negative ions O 2 is derived and investigated. The QB relaxed state is a linear superposition of four distinct single Beltrami fields and provides the possibility of the formation of four self-organized vortices of different length scales. In addition, robust magnetofluid coupling characterizes this non-force-free state. The analysis of the QB state also shows that by adjusting the generalized helicities and densities of plasma species, the formation of multiscale structures as well as the paramagnetic and diamagnetic behavior of the relaxed state can be controlled.


Corresponding author: Usman Shazad, Department of Physics, University of Engineering and Technology, Lahore 54890, Pakistan, E-mail:

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

  1. Research ethics: Not applicable.

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

  3. Competing interests: The authors state no competing interests.

  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: Not applicable.

References

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

[2] L. Woltjer, “A theorem on force-free magnetic fields,” Proc. Natl. Acad. Sci., vol. 44, no. 6, p. 489, 1958. https://doi.org/10.1073/pnas.44.6.489.Search in Google Scholar PubMed PubMed Central

[3] J. B. Taylor, “Relaxation of toroidal plasma and generation of reverse magnetic fields,” Phys. Rev. Lett., vol. 33, no. 19, p. 1139, 1974. https://doi.org/10.1103/physrevlett.33.1139.Search in Google Scholar

[4] L. C. Steinhauer and A. Ishida, “Relaxation of a two-specie magnetofluid,” Phys. Rev. Lett., vol. 79, no. 18, p. 3423, 1997. https://doi.org/10.1103/physrevlett.79.3423.Search in Google Scholar

[5] S. M. Mahajan and Z. Yoshida, “Double curl Beltrami flow: diamagnetic structures,” Phys. Rev. Lett., vol. 81, no. 22, p. 4863, 1998. https://doi.org/10.1103/physrevlett.81.4863.Search in Google Scholar

[6] Z. Yoshida and S. M. Mahajan, “Simultaneous Beltrami conditions in coupled vortex dynamics,” J. Math. Phys., vol. 40, no. 10, p. 5080, 1999. https://doi.org/10.1063/1.533016.Search in Google Scholar

[7] L. C. Steinhauer and A. Ishida, “Relaxation of a two-species magnetofluid and application to finite-β flowing plasmas,” Phys. Plasmas, vol. 5, no. 7, p. 2609, 1998. https://doi.org/10.1063/1.872948.Search in Google Scholar

[8] L. C. Steinhauer, “Double mode condensates of a flowing plasma as possible relaxed states,” Phys. Plasmas, vol. 9, no. 9, p. 3767, 2002. https://doi.org/10.1063/1.1503068.Search in Google Scholar

[9] Z. Yoshida and S. M. Mahajan, “Variational principles and self-organization in two-fluid plasmas,” Phys. Rev. Lett., vol. 88, no. 9, p. 095001, 2002. https://doi.org/10.1103/physrevlett.88.095001.Search in Google Scholar

[10] S. M. Mahajan and M. Lingam, “Multi-fluid systems—multi-Beltrami relaxed states and their implications,” Phys. Plasmas, vol. 22, no. 9, p. 092123, 2015. https://doi.org/10.1063/1.4931069.Search in Google Scholar

[11] S. M. Mahajan and Z. Yoshida, “A collisionless self-organizing model for the high-confinement (H-mode) boundary layer,” Phys. Plasmas, vol. 7, no. 2, p. 635, 2000. https://doi.org/10.1063/1.873850.Search in Google Scholar

[12] 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, no. 5, p. 2125, 2001. https://doi.org/10.1063/1.1354149.Search in Google Scholar

[13] 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, no. 4, p. 1340, 2001. https://doi.org/10.1063/1.1350670.Search in Google Scholar

[14] S. M. Mahajan, K. I. Nikol’skaya, N. L. Shatashvili, and Z. Yoshida, “Generation of flows in the solar atmosphere due to magnetofluid coupling,” Astrophys. J., vol. 576, no. 2, p. L161, 2002. https://doi.org/10.1086/343727.Search in Google Scholar

[15] 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, no. 1, p. 395, 2002. https://doi.org/10.1086/339499.Search in Google Scholar

[16] R. Bhattacharyya, M. S. Janaki, B. Dasgupta, and G. P. Zank, “Solar arcades as possible minimum dissipative relaxed states,” Sol. Phys., vol. 240, no. 1, p. 63, 2007. https://doi.org/10.1007/s11207-006-0280-5.Search in Google Scholar

[17] D. Kumar and R. Bhattacharyya, “Solar coronal loops as non force-free minimum energy relaxed states,” Phys. Plasmas, vol. 18, no. 8, p. 084506, 2011. https://doi.org/10.1063/1.3623743.Search in Google Scholar

[18] 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, no. 1, p. 419, 2005. https://doi.org/10.1086/432867.Search in Google Scholar

[19] M. Lingam and S. M. Mahajan, “Modelling astrophysical outflows via the unified dynamo–reverse dynamo mechanism,” Mon. Not. R. Astron. Soc.: Lett., vol. 449, no. 1, p. L36, 2015. https://doi.org/10.1093/mnrasl/slv017.Search in Google Scholar

[20] H. M. Abdelhamid and Z. Yoshida, “Nonlinear Alfvén waves in extended magnetohydrodynamics,” Phys. Plasmas, vol. 23, no. 2, p. 022105, 2016. https://doi.org/10.1063/1.4941596.Search in Google Scholar

[21] H. M. Abdelhamid and Z. Yoshida, “Nonlinear helicons bearing multi-scale structures,” Phys. Plasmas, vol. 24, no. 2, p. 022107, 2017. https://doi.org/10.1063/1.4975184.Search in Google Scholar

[22] H. M. Abdelhamid, M. Lingam, and S. M. Mahajan, “Extended MHD turbulence and its applications to the solar wind,” Astrophys. J., vol. 829, no. 2, p. 87, 2016. https://doi.org/10.3847/0004-637x/829/2/87.Search in Google Scholar

[23] S. M. Mahajan and M. Lingam, “Constraining Alfvénic turbulence with helicity invariants,” Mon. Not. R. Astron. Soc., vol. 495, no. 3, p. 2771, 2020. https://doi.org/10.1093/mnras/staa1318.Search in Google Scholar

[24] V. I. Berezhiani, N. L. Shatashvili, and S. M. Mahajan, “Beltrami–Bernoulli equilibria in plasmas with degenerate electrons,” Phys. Plasmas, vol. 22, no. 2, p. 022902, 2015. https://doi.org/10.1063/1.4913356.Search in Google Scholar

[25] 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, no. 2, p. 70, 2016. https://doi.org/10.1007/s10509-016-2663-x.Search in Google Scholar

[26] 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, no. 9, p. 148, 2019. https://doi.org/10.1007/s10509-019-3596-y.Search in Google Scholar

[27] U. Shazad, M. Iqbal, and S. Ullah, “Self-organized multiscale structures in thermally relativistic electron-positron-ion plasmas,” Phys. Scr., vol. 96, no. 12, p. 125627, 2021. https://doi.org/10.1088/1402-4896/ac38d5.Search in Google Scholar

[28] U. Shazad and M. Iqbal, “On the quadruple Beltrami fields in thermally relativistic electron-positron-ion plasma,” Phys. Scr., vol. 98, no. 5, p. 055605, 2023. https://doi.org/10.1088/1402-4896/acc7d6.Search in Google Scholar

[29] U. Shazad and M. Iqbal, “Impact of temperature asymmetry and small fraction of static positive ions on the relaxed states of a relativistic hot pair plasma,” Z. Naturforsch. A, vol. 78, no. 11, p. 983, 2023. https://doi.org/10.1515/zna-2023-0112.Search in Google Scholar

[30] U. Shazad and M. Iqbal, “Relaxation of a two electron-temperature relativistic hot electron-positron-ion plasma,” Braz. J. Phys., vol. 54, no. 1, p. 22, 2024. https://doi.org/10.1007/s13538-023-01393-8.Search in Google Scholar

[31] C. Bhattacharjee, J. C. Feng, and D. J. Stark, “Surveying the implications of generalized vortical dynamics in curved space–time,” Mon. Not. R. Astron. Soc., vol. 481, no. 1, p. 206, 2018. https://doi.org/10.1093/mnras/sty2277.Search in Google Scholar

[32] F. A. Asenjo and S. M. Mahajan, “Diamagnetic field states in cosmological plasmas,” Phys. Rev. E, vol. 99, no. 5, p. 053204, 2019. https://doi.org/10.1103/physreve.99.053204.Search in Google Scholar PubMed

[33] C. Bhattacharjee and J. C. Feng, “On Beltrami states near black hole event horizon,” Phys. Plasmas, vol. 27, no. 7, p. 072901, 2020. https://doi.org/10.1063/5.0010050.Search in Google Scholar

[34] C. Bhattacharjee, “Classifying diamagnetic states of plasma near Schwarzschild event horizon: local approximation,” Phys. Lett. A, vol. 384, no. 27, p. 126698, 2020. https://doi.org/10.1016/j.physleta.2020.126698.Search in Google Scholar

[35] S. Ullah, U. Shazad, and M. Iqbal, “Multiscale structures in three species magnetoplasmas with two positive ions,” Phys. Scr., vol. 97, no. 6, p. 065605, 2022. https://doi.org/10.1088/1402-4896/ac7109.Search in Google Scholar

[36] F. Ahmed, M. Iqbal, and U. Shazad, “Beltrami fields in partially ionized magnetized dusty plasma,” AIP Adv., vol. 13, no. 5, p. 055305, 2023. https://doi.org/10.1063/5.0147223.Search in Google Scholar

[37] C. Bhattacharjee, “Implications of nonzero photon mass on plasma equilibria,” Phys. Rev. E, vol. 107, no. 3, p. 035207, 2023. https://doi.org/10.1103/physreve.107.035207.Search in Google Scholar PubMed

[38] U. Shazad and M. Iqbal, “Relaxation of relativistic pair plasma in a massive photon field,” J. Plasma Phys., vol. 89, no. 5, p. 905890512, 2023. https://doi.org/10.1017/s0022377823001071.Search in Google Scholar

[39] S. V. Vladimirov, K. Ostrikov, M. Y. Yu, and G. E. Morfill, “Ion-acoustic waves in a complex plasma with negative ions,” Phys. Rev. E, vol. 67, no. 3, p. 036406, 2003. https://doi.org/10.1103/physreve.67.036406.Search in Google Scholar

[40] O. Adriani, et al.., “An anomalous positron abundance in cosmic rays with energies 1.5–100 GeV,” Nature, vol. 458, no. 7238, p. 607, 2009. https://doi.org/10.1038/nature07942.Search in Google Scholar PubMed

[41] I. Kourakis, A. Esfandyari-Khalejahi, M. Mehdipoor, and P. K. Shukla, “Modulated electrostatic modes in pair plasmas: modulational stability profile and envelope excitations,” Phys. Plasmas, vol. 13, no. 5, p. 052117, 2006. https://doi.org/10.1063/1.2203951.Search in Google Scholar

[42] H. Massey, Negative Ions, 3rd ed. Cambridge, Cambridge University Press, 1976.Search in Google Scholar

[43] P. Chaizy, et al.., “Negative ions in the coma of comet Halley,” Nature, vol. 349, no. 6308, p. 393, 1991. https://doi.org/10.1038/349393a0.Search in Google Scholar

[44] A. J. Coates, F. J. Crary, G. R. Lewis, D. T. Young, J. H. WaiteJr., and E. C. SittlerJr., “Discovery of heavy negative ions in Titan’s ionosphere,” Geophys. Res. Lett., vol. 34, no. 22, p. L22103, 2007. https://doi.org/10.1029/2007gl030978.Search in Google Scholar

[45] R. Ichiki, S. Yoshimura, T. Watanabe, Y. Nakamura, and Y. Kawai, “Experimental observation of dominant propagation of the ion-acoustic slow mode in a negative ion plasma and its application,” Phys. Plasmas, vol. 9, no. 11, p. 4481, 2002. https://doi.org/10.1063/1.1515770.Search in Google Scholar

[46] M. Bacal and G. W. Hamilton, “H−and D−Production in plasmas,” Phys. Rev. Lett., vol. 42, no. 23, p. 1538, 1979. https://doi.org/10.1103/physrevlett.42.1538.Search in Google Scholar

[47] D. P. Sheehan and N. Rynn, “Negative-ion plasma sources,” Rev. Sci. Instrum., vol. 59, no. 8, p. 1369, 1988. https://doi.org/10.1063/1.1139671.Search in Google Scholar

[48] R. A. Gottscho and C. E. Gaebe, “Negative ion kinetics in RF glow discharges,” IEEE Trans. Plasma Sci., vol. 14, no. 2, p. 92, 1986. https://doi.org/10.1109/tps.1986.4316511.Search in Google Scholar

[49] S. Sultana and A. A. Mamun, “Linear and nonlinear propagation of ion-acoustic waves in a multi-ion plasma with positrons and two-temperature superthermal electrons,” Astrophys. Space Sci., vol. 349, no. 1, p. 229, 2014. https://doi.org/10.1007/s10509-013-1634-8.Search in Google Scholar

[50] N. Jannat, M. Ferdousi, and A. A. Mamun, “Nonplanar ion-acoustic shock waves in a multi-ion plasma with nonextensive electrons and positrons,” J. Korean Phys. Soc., vol. 67, no. 3, p. 496, 2015. https://doi.org/10.3938/jkps.67.496.Search in Google Scholar

[51] N. Jannat, M. Ferdousi, and A. A. Mamun, “Ion-acoustic Gardner solitons in a four-component nonextensive multi-ion plasma,” Plasma Phys. Rep., vol. 42, no. 7, p. 678, 2016. https://doi.org/10.1134/s1063780x16070059.Search in Google Scholar

[52] N. A. Chowdhury, A. Mannan, M. M. Hasan, and A. A. Mamun, “Heavy ion-acoustic rogue waves in electron-positron multi-ion plasmas,” Chaos, vol. 27, no. 9, p. 093105, 2017. https://doi.org/10.1063/1.4985113.Search in Google Scholar PubMed

[53] N. Ahmed, A. Mannan, N. A. Chowdhury, and A. A. Mamun, “Electrostatic rogue waves in double pair plasmas,” Chaos, vol. 28, no. 12, p. 123107, 2018. https://doi.org/10.1063/1.5061800.Search in Google Scholar PubMed

[54] S. Khondaker, A. Mannan, N. A. Chowdhury, and A. A. Mamun, “Rogue waves in multi‐pair plasma medium,” Contrib. Plasma Phys., vol. 59, no. 7, p. e201800125, 2019. https://doi.org/10.1002/ctpp.201800125.Search in Google Scholar

[55] H. G. Abdelwahed, R. Sabry, and A. A. El-Rahman, “On the positron superthermality and ionic masses contributions on the wave behaviour in collisional space plasma,” Adv. Space Res., vol. 66, no. 2, p. 259, 2020. https://doi.org/10.1016/j.asr.2020.03.046.Search in Google Scholar

[56] D. V. Douanla, D. V. Alim, C. G. L. Tiofack, and A. Mohamadou, “Heavy ion–acoustic rogue waves in magnetized electron–positron multi‐ion plasmas,” Contrib. Plasma Phys., vol. 60, no. 9, p. e202000036, 2020. https://doi.org/10.1002/ctpp.202000036.Search in Google Scholar

[57] S. Jahan, M. N. Haque, N. A. Chowdhury, A. Mannan, and A. Al Mamun, “Ion-Acoustic rogue waves in double pair plasma having non-extensive particles,” Universe, vol. 7, no. 3, p. 63, 2021. https://doi.org/10.3390/universe7030063.Search in Google Scholar

[58] W. F. El-Taibany, N. A. El-Bedwehy, N. A. El-Shafeay, and S. K. El-Labany, “Three-dimensional rogue waves in earth’s ionosphere,” Galaxies, vol. 9, no. 3, p. 48, 2021. https://doi.org/10.3390/galaxies9030048.Search in Google Scholar

[59] N. M. Heera, et al.., “Ion-acoustic shock waves in a magnetized plasma featuring super-thermal distribution,” AIP Adv., vol. 11, no. 5, p. 055117, 2021. https://doi.org/10.1063/5.0050519.Search in Google Scholar

[60] T. Tajima and T. Taniuti, “Nonlinear interaction of photons and phonons in electron-positron plasmas,” Phys. Rev. A, vol. 42, no. 6, p. 3587, 1990. https://doi.org/10.1103/physreva.42.3587.Search in Google Scholar PubMed

[61] A. L. Petrakis and L. A. Petrakis, “The type of the roots of the complete quartic equation,” J. Interdiscip. Math., vol. 11, no. 6, p. 815, 2008. https://doi.org/10.1080/09720502.2008.10700603.Search in Google Scholar

[62] Z. Yoshida and Y. Giga, “Remarks on spectra of operator rot,” Math. Z., vol. 204, no. 1, p. 235, 1990. https://doi.org/10.1007/bf02570870.Search in Google Scholar

[63] S. M. Mahajan, “Classical perfect diamagnetism: expulsion of current from the plasma interior,” Phys. Rev. Lett., vol. 100, no. 7, p. 075001, 2008. https://doi.org/10.1103/physrevlett.100.075001.Search in Google Scholar

Received: 2023-09-29
Accepted: 2023-12-27
Published Online: 2024-01-12
Published in Print: 2024-04-25

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 18.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/zna-2023-0265/html
Scroll to top button