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
Funding source: Higher Education Commission, Pakistan
Award Identifier / Grant number: 20-9408/Punjab/NRPU/R&D/HEC/2017-18
-
Research ethics: Not applicable.
-
Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.
-
Competing interests: The authors state no competing interests.
-
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.
-
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
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Atomic, Molecular & Chemical Physics
- Extended calculations of energy levels and transition rates for Yb LVII
- Two curvature sensors based on no-core–seven-core fiber interference
- Environmentally friendly reduction of graphene oxide using the plant extract of novel Chromolaena odorata and evaluation of adsorption capacity on methylene blue dye
- Dynamical Systems & Nonlinear Phenomena
- Novel compound multistable stochastic resonance weak signal detection
- The absorbing boundary conditions of Newtonian fluid flowing across a semi-infinite plate with different velocities and pressures
- Three-to-one internal resonances of stepped nanobeam of nonlinearity
- Evaluation of weak discontinuity in rotating medium with magnetic field, characteristic shock and weak discontinuity interaction
- Robust inverse scattering analysis of discrete high-order nonlinear Schrödinger equation
- Hydrodynamics
- Quadruple Beltrami field structures in electron–positron multi-ion plasma
- Quantum Theory
- New expressions for the Aharonov–Bohm phase and consequences for the fundamentals of quantum mechanics
Articles in the same Issue
- Frontmatter
- Atomic, Molecular & Chemical Physics
- Extended calculations of energy levels and transition rates for Yb LVII
- Two curvature sensors based on no-core–seven-core fiber interference
- Environmentally friendly reduction of graphene oxide using the plant extract of novel Chromolaena odorata and evaluation of adsorption capacity on methylene blue dye
- Dynamical Systems & Nonlinear Phenomena
- Novel compound multistable stochastic resonance weak signal detection
- The absorbing boundary conditions of Newtonian fluid flowing across a semi-infinite plate with different velocities and pressures
- Three-to-one internal resonances of stepped nanobeam of nonlinearity
- Evaluation of weak discontinuity in rotating medium with magnetic field, characteristic shock and weak discontinuity interaction
- Robust inverse scattering analysis of discrete high-order nonlinear Schrödinger equation
- Hydrodynamics
- Quadruple Beltrami field structures in electron–positron multi-ion plasma
- Quantum Theory
- New expressions for the Aharonov–Bohm phase and consequences for the fundamentals of quantum mechanics