KdV and mKdV Ion-Acoustic Solitary Waves In a Positron-beam Plasma with Kaniadakis Distributed Electrons
Abstract
Theoretical and numerical studies of ion-acoustic solitary waves (IASWs) in an unmagnetized plasma with ions, positron beams under pressure variation, and kaniadakis distributed electrons have been conducted. The potential wave amplitude is calculated by applying the reductive perturbation approach to reduce the controlling set of normalized fluid equations to Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations. In mKdV solutions, only compressive solitons are found, whereas both compressive and rarefactive KdV solitons are found to exist for different values of σ, σb, and ν. The parameter k has no effect on the IASWs of the KdV equation, but have contribution in mKdV solitons. It is also shown that the inclusion of nonthermal electrons drastically changes the basic properties of ion-acoustic solitons and creates a new parametric regime.
Downloads
References
B. Boro, A.N. Dev, B.K. Saikia, and N.C. Adhikary, ”Nonlinear wave interaction with positron beam in a relativistic plasma: evaluation of hypersonic dust ion acoustic waves,” Plasma Physics Reports, 46(6), 641-652 (2020). https://doi.org/10.1134/S1063780X20060021
S.A. El-Tantawy, M.H. Alshehri, F.Z. Duraihem, and L.S. El-Sherif, ”Dark soliton collisions and method of lines approach for modeling freak waves in a positron beam plasma having superthermal electrons,” Results in Physics, 19, 103452 (2020). https://doi.org/10.1016/j.rinp.2020.103452
A.R. Esfandyari, S. Khorram, and A. Rostami, ”Ion-acoustic solitons in a plasma with a relativistic electron beam,” Physics of Plasmas, 8(11), 4753-4761 (2001). https://doi.org/10.1063/1.1399326
M. Vranic, O. Klimo, G. Korn, and S. Weber, ”Multi-GeV electron-positron beam generation from laser-electron scattering,” Scientific reports, 8(1), 4702 (2018). https://doi.org/10.1038/s41598-018-23126-7
J. Warwick, T. Dzelzainis, M.E. Dieckmann, W. Schumaker, D. Doria, L. Romagnani, K. Poder, et al., ”Experimental observation of a current-driven instability in a neutral electron-positron beam,” Physical review letters, 119(18), 185002 (2017). https://doi.org/10.1103/PhysRevLett.119.185002
S. Ali Shan, A. Ur-Rehman, and A. Mushtaq, ”Ion-acoustic solitary waves in a positron beam plasma with electron trapping and nonextensivity effects,” Physics of Plasmas, 24(3), 032104 (2017). https://doi.org/10.1063/1.4978294
R. Khanam, and S.N. Barman, ”The Formation of Ion-Acoustic Solitary Waves in a Plasma Having Nonextensive Electrons and Positrons,” East European Journal of Physics, (4), 518-525 (2024). https://doi.org/10.26565/2312-4334-2024-4-61
G. Sarri, M.E. Dieckmann, I. Kourakis, A. Di Piazza, B. Reville, C.H. Keitel, and M. Zepf, ”Overview of laser-driven generation of electron–positron beams”, Journal of Plasma Physics, 81(4), 455810401 (2015). https://doi.org/10.1017/S002237781500046X
B.C. Kalita, M.K. Kalita, and R.P. Bhatta, ”Solitons in a magnetized ion-beam plasma system,” Journal of plasma physics, 50(3), 349-357 (1993). https://doi.org/10.1017/S0022377800017190
M. Khalid, A. Ullah, A. Kabir, H. Khan, M. Irshad, and S.M. Shah, ”Oblique propagation of ion-acoustic solitary waves in magnetized electron-positron-ion plasma with Cairns distribution,” Europhysics Letters, 138(6), 63001 (2022). https://doi.org/10.1209/0295-5075/ac765c
M.K. Deka, and A.N. Dev, ”Wave propagation with degenerate electron–positron in magnetically quantised ion beam plasma,” Pramana, 95(2), 65 (2021). https://doi.org/10.1007/s12043-021-02081-5
G. Sarri, K. Poder, J.M. Cole,W. Schumaker, A. Di Piazza, B. Reville, T. Dzelzainis, et al., ”Generation of neutral and high-density electron–positron pair plasmas in the laboratory,”Nature communications, 6(1), 6747 (2015). https://doi.org/10.1038/ncomms7747
Y.N. Nejoh, ”Positron-acoustic waves in an electron–positron plasma with an electron beam,” Australian journal of physics, 49(5), 967-976 (1996). https://doi.org/10.1071/PH960967
B.C. Kalita, R. Das, and H.K. Sarmah, ”Weakly relativistic solitons in a magnetized ion-beam plasma in presence of electron inertia,” Physics of Plasmas, 18(1), 012304 (2011). https://doi.org/10.1063/1.3536428
E.F. El-Shamy, W.F. El-Taibany, E.K. El-Shewy, and K.H. El-Shorbagy, ”Positron acoustic solitary waves interaction in a four component space plasma,” Astrophysics and Space Science, 338, 279-285 (2012). https://doi.org/10.1007/s10509-011-0930-4
E. Saberian, A. Esfandyari-Kalejahi, and M. Akbari-Moghanjoughi, ”Propagation of ion-acoustic solitary waves in a relativistic electron-positron-ion plasma,” Canadian Journal of Physics, 89(3), 299-309 (2011). https://doi.org/10.1139/P11-024
H.A. Alyousef, S.N. Naeem, M. Irshad, A.U.R. Ata-ur-Rahman, S.M. Ismaeel, and S.A. El-Tantawy, ”On the dynamics of large amplitude ion-acoustic waves in a non-Maxwellian plasma with nonthermal electrons and an electron beam,” Physics of Fluids, 36(3), 035151 (2024). https://doi.org/10.1063/5.0189713
K. Javidan, and D. Saadatmand, ”Effect of high relativistic ions on ion acoustic solitons in electron-ion-positron plasmas with nonthermal electrons and thermal positrons,” Astrophysics and Space Science, 333, 471-475 (2011). https://doi.org/10.1007/s10509-011-0645-6
E.I. El-Awady, S.A. El-Tantawy, W.M. Moslem, and P.K. Shukla, ”Electron–positron–ion plasma with kappa distribution: Ion acoustic soliton propagation,” Physics Letters A, 374(31-32), 3216-3219 (2010). https://doi.org/10.1016/j.physleta.2010.05.053
N.S. Saini, and I. Kourakis, ”Electron beam–plasma interaction and ion-acoustic solitary waves in plasmas with a superthermal electron component,” Plasma Physics and Controlled Fusion, 52(7), 075009 (2010). https://doi.org/10.1088/0741-3335/52/7/075009
A. Esfandyari-Kalejahi, M. Mehdipoor, and M. Akbari-Moghanjoughi, ”Effects of positron density and temperature on ionacoustic solitary waves in a magnetized electron-positron-ion plasma: Oblique propagation,” Physics of Plasmas, 16(5), 052309 (2009). https://doi.org/10.1063/1.3142465
J.N. Han, S.C. Li, X.X. Yang, and W.S. Duan, ”Head-on collision of ion-acoustic solitary waves in an unmagnetized electronpositron-ion plasma,” The European Physical Journal D, 47, 197-201 (2008). https://doi.org/10.1140/epjd/e2008-00033-3
R.G. Greaves, and C.M. Surko, ”An electron-positron beam-plasma experiment,” Physical review letters, 75(21), 3846 (1995). https://doi.org/10.1103/PhysRevLett.75.3846
P.G.Coleman, Positron beams and their applications, World Scientific, 9789810233945, 9810233949 (2000).
R. Sarma, A.P. Misra, andN.C.Adhikary, ”Nonlinear ion-acoustic solitarywaves in an electron-positron-ion plasma with relativistic positron beam,” Chinese Physics B, 27(10), 105207 (2018). 10.1088/1674-1056/27/10/105207
P.J. Schultz, and K.G. Lynn, ”Interaction of positron beams with surfaces, thin films, and interfaces,” Reviews of Modern Physics, 60(3), 701 (1988). https://doi.org/10.1103/RevModPhys.60.701
S. Ali Shan, S.A. El-Tantawy, and W.M. Moslem, ”On the fully nonlinear acoustic waves in a plasma with positrons beam impact and superthermal electrons,” Physics of Plasmas, 20(8), 082104 (2013). https://doi.org/10.1063/1.4817280
A. Shah, S. Mahmood, and Q. Haque, ”Ion acoustic shock waves in presence of superthermal electrons and interaction of classical positron beam,” Physics of Plasmas, 19(3), 032302 (2012). https://doi.org/10.1063/1.3684659
A. Shah, Q. Haque, and S. Mahmood, ”Astrophysical naturally moderated classical positron beam interaction with nonlinear waves in nonextensive astrophysical plasmas,” Astrophysics and Space Science, 344, 119-126 (2013). https://doi.org/10.1007/s10509-012-1305-1
M.J. Hogan, ”Electron and positron beam–driven plasma acceleration,” Reviews of Accelerator Science and Technology, 9, 63-83 (2016). https://doi.org/10.1142/S1793626816300036
S.N. Barman, and K. Talukdar, ”Nonlinear Ion-Acoustic Solitary Waves in a Weakly Relativistic Electron-Positron-Ion Plasma with Relativistic Electron and Positron Beams,” East European Journal of Physics, (4), 79-85 (2024). https://doi.org/
A. Roy, T. Sarkar, S. Roy, and S. Raut, ”Impact of relativistic positron beam on ion-acoustic solitary, periodic and breather waves in Earths’ ionospheric region through the framework of KdV and modified KdV equation,” Physica Scripta, 99(12), 125603 (2024). https://doi.org/10.1088/1402-4896/ad8d36
A. R´enyi, ”On a new axiomatic theory of probability,” Acta Mathematica Academiae Scientiarum Hungaricae, 6, 285–335 (1955). https://doi.org/10.1007/BF02024393
C. Tsallis, ”Possible generalization of Boltzmann-Gibbs statistics,” Journal of Statistical Physics, 52, 479–487 (1988). https://doi.org/10.1007/BF01016429
C. Tsallis, and L.J. Cirto, ”Black hole thermodynamical entropy,” The European Physical Journal C, 73, 2487 (2013). https://doi.org/10.1140/epjc/s10052-013-2487-6
G. Kaniadakis, ”Non-linear kinetics underlying generalized statistics,” Journal of Physics A: Mathematical and Theoretical, 296, 405–425 (2001). https://doi.org/10.1016/S0378-4371(01)00184-4
G. Kaniadakis, ”Statistical mechanics in the context of special relativity,” Physical Review E, 66, 056125 (2002). https://doi.org/10.1103/PhysRevE.66.056125
A.M. Teweldeberhan, H.G. Miller, R. Tegen, ”k-deformed statistics and the formation of a quark-gluon plasma,” International Journal of Modern Physics E, 12, 669–673 (2003). https://doi.org/10.1142/S021830130300148X
A. Rossani, and A.M. Scarfone, ”Generalized kinetic equations for a system of interacting atoms and photons: theory and simulations,” Journal of Physics A: Mathematical and Theoretical, 37, 4955 (2004). https://doi.org/10.1088/0305-4470/37/18/004
T.S. Biro, and G. Kaniadakis, ”Two generalizations of the Boltzmann equation,” European Physical Journal B, 50, 3–6 (2006). https://doi.org/10.1140/epjb/e2006-00112-3
K. Ourabah, A.H. Hamici-Bendimerad, and M. Tribeche, ”Quantum entanglement and Kaniadakis entropy,” Physica Scripta, 90, 045101 (2015). https://doi.org/10.1088/0031-8949/90/4/045101
K. Ourabah, and M. Tribeche, ”Planck radiation law and Einstein coefficients reexamined in Kaniadakis k-statistics,” Physical Review E, 89, 062130 (2014). https://doi.org/10.1103/PhysRevE.89.062130
J. Kalita, R. Das, K. Hosseini, S. Salahshour, and D. Baleanu: ”Some Models in Unmagnetized Plasma involving Kaniadakis Distributed Electrons and Temperature Ratio: Dust Ion Acoustic Solitary Waves,” Journal of Applied and Computational Mechanics, 10(4), 792-800 (2024). https://doi.org/10.22055/jacm.2024.46197.4476
M. Khalid, A. Khan, M. Khan, and F. Hadi, ”Dust Ion Acoustic Solitary Waves in Unmagnetized Plasma with Kaniadakis Distributed Electrons,” Brazilian Journal of Physics, 51, 60-65 (2021). https://doi.org/10.1007/s13538-020-00807-1
M. Das, and R. Das, ”High Relativistic Impact on Dust-Ion-Acoustic Solitary Waves in Unmagnetised Plasma with Kaniadakis Distributed Electrons,” Brazilian Journal of Physics, 54, 161 (2024). https://doi.org/10.1007/s13538-024-01532-9
S. Raut, K.K. Mondal, P. Chatterjee, and S. Roy, ”Dust ion acoustic bi-soliton, soliton, and shock waves in unmagnetized plasma with Kaniadakis-distributed electrons in planar and nonplanar geometry,” The European Physical Journal D, 77, 100 (2023). https://doi.org/10.1140/epjd/s10053-023-00676-8
I. Lourek, and M. Tribeche, ”On the role of the k-deformed Kaniadakis distribution in nonlinear plasma waves,” Physica A: Statistical Mechanics and its Applications, 441, 215–220 (2016). https://doi.org/10.1016/j.physa.2015.08.055
M. Irshad, A.R. Ata-ur-Rahman, M. Khalid, S. Khan, B.M. Alotaibi, S.A. El-Sherif, and S.A. El-Tantawy, ”Effect of k-deformed Kaniadakis distribution on the modulational instability of electron-acoustic waves in a non-Maxwellian plasma,” Physics of Fluids, 35, 105116 (2023). https://doi.org/10.1063/5.0171327
Copyright (c) 2025 Rafia Khanam, Satyendra Nath Barman
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 copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment 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 acknowledgment 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) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
