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Transverse instability of ion acoustic solitons in a magnetized plasma including $q$ -nonextensive electrons and positrons

  • N. Akhtar (a1) (a2), W. F. El-Taibany (a3) (a4), S. Mahmood (a1) (a2) (a5), E. E. Behery (a3), S. A. Khan (a5), S. Ali (a5) and S. Hussain (a1) (a2)...

Abstract

A nonlinear Zakharov–Kuznetsov (ZK) equation for ion acoustic solitary waves (IASWs) is derived using the reductive perturbation method (RPM) for magnetized plasmas in which the inertialess electrons and positrons are nonextensively $q$ -distributed while ions are assumed to be warm and inertial. It is found that both compressive as well as rarefactive solitons coexist in the present model for different regions of non-extensive electron and positron parameters, $q_{e}$ and $q_{p}$ . The magnetic field has no effect on the amplitude of the IASW, whereas the obliqueness angle of the wave propagation, the ion-to-electron temperature ratio  ${\it\sigma}$ and positron-to-ion density concentration ratio $p$ affect both the amplitude and the width of the solitary wave structures. The transverse instability analysis illustrates that the one soliton solution has a constant growth rate, and it suffers from instability in the transverse direction. The relevance of the present study to astrophysical space plasmas is also discussed.

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Corresponding author

Email addresses for correspondence: naseemqau@gmail.com, naseem_qau@yahoo.com

References

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Abe, S. & Okamoto, Y. 2001 Statistical Mechanics and its Applications. Springer.
Akhtar, N., El-Taibany, W. F. & Mahmood, S. 2013 Electrostatic double layers in a warm negative ion plasma with nonextensive electrons. Phys. Lett. A 377, 12821289.
Asbridge, J. R., Bame, S. J. & Strong, I. B. 1968 Outward flow of protons from the Earth’s bow shock. J. Geophys. Res. 73 (17), 57775782.
Bains, A. S., Tribeche, M., Saini, N. S. & Gill, T. S. 2011 A nonlinear Zakharov–Kuznetsov equation in magnetized plasma with $q$ -nonextensive electrons velocity distribution. Phys. Plasmas 18, 104503.1104503.4.
Christon, S. P. et al. 2012 Energy spectra of plasma sheet ions and electrons from ${\sim}50~\text{eV}~\text{e}^{-1}$ to ${\sim}1~\text{MeV}$ during plasma temperature transitions. J. Geophys. Res. 93, 25622572.
Das, K. P. & Verheest, F. 1989 Ion-acoustic solitons in magnetized multi-component plasmas including negative ions. J. Plasma Phys. 41, 139155.
Divine, N. & Garret, H. B. 1983 Charged particle distributions in Jupiter’s magnetosphere. J. Geophys. Res. 88, 68896903.
Dodd, R. K. et al. 1982 Solitons and Nonlinear Waves Equations. Academic.
Du, J. 2004 Nonextensivity in nonequilibrium plasma systems with Coulombian long-range interactions. Phys. Lett. A 329, 262267.
El-Taibany, W. F., El-Bedwehy, N. A. & El-Shamy, E. F. 2011 Three-dimensional stability of dust-ion acoustic solitary waves in a magnetized multicomponent dusty plasma with negative ions. Phys. Plasmas 18, 033703.1033703.8.
El-Taibany, W. F. & Tribeche, M. 2012 Nonlinear ion-acoustic solitary waves in electronegative plasmas with electrons featuring Tsallis distribution. Phys. Plasmas 19, 024507.1024507.4.
Futaana, Y. et al. 2003 Moon-related nonthermal ions observed by Nozomi: species, sources, and generation mechanisms. J. Geophys. Res. 108, 15.115.10.
Ghosh, S. & Chakrabart, N. 2013 Magnetic electron drift solitons in electron magnetohydrodynamic plasmas. Plasma Phys. Control. Fusion 55, 035008.1035008.4.
Ghosh, U. N., Chatterjee, P. & Roychoudhury, R. 2012 The effect of $q$ -distributed electrons on the head-on collision of ion acoustic solitary waves. Phys. Plasmas 19, 012113.1012113.6.
Gosset, W. 1908 The probable error of a mean. Biometrika 6, 125.
Haque, Q., Mahmood, S. & Mushtaq, A. 2008 Nonlinear electrostatic drift waves in dense electron–positron–ion plasmas. Phys. Plasmas 15, 082315.1082315.5.
Hellberg, M. A. et al. 2009 Comment on ‘Mathematical and physical aspects of Kappa velocity distribution’ [Phys. Plasmas 14, 110702 2007]. Phys. Plasmas 16, 094701.1094701.5.
Hirotani, K. et al. 1999 Pair plasma dominance in the 3c 279 jet on parsec scales. Publ. Astron. Soc. Japan 51 (2), 263267.
Hussain, S., Akhtar, N. & Mahmood, S. 2013 Propagation of ion acoustic shock waves in negative ion plasmas with nonextensive electrons. Phys. Plasmas 20, 092303.1092303.7.
Iwamoto, N. 1993 Collective modes in nonrelativistic electron–positron plasmas. Phys. Rev. E 47, 604611.
Jain, S. L., Tiwari, R. S. & Sharma, S. R. 1990 Large-amplitude ion-acoustic double layers in multispecies plasma. Can. J. Phys. 68, 474478.
Kourakis, I. et al. 2009 Nonlinear dynamics of rotating multi-component pair plasmas and epi plasmas. Plasma Fusion Res. 4, 018.1018.11.
Latora, V., Rapisarda, A. & Tsallis, C. 2001 Non-Gaussian equilibrium in a long-range Hamiltonian system. Phys. Rev. E 64, 056134.1056134.5.
Lazarus, I. J. et al. 2012a Arbitrary amplitude Langmuir solitons in a relativistic electron–positron plasma. J. Plasma Phys. 78 (2), 175180.
Lazarus, I. J. et al. 2012b Linear electrostatic waves in two-temperature electron–positron plasmas. J. Plasma Phys. 78 (6), 621628.
Leubner, M. P. 2004 Fundamental issues on kappa-distributions in space plasmas and interplanetary proton distributions. Phys. Plasmas 11, 13081316.
Lima, J. A. S., Silva, J. R. & Santos, J. 2000 Plasma oscillations and nonextensive statistics. Phys. Rev. E 61, 32603263.
Liu, J. M. et al. 1994 Measurements of inverse bremsstrahlung absorption and non-Maxwellian electron velocity distributions. Phys. Rev. Lett. 72 (17), 27172720.
Liyan, L. & Jiulin, D. 2008 Ion acoustic waves in the plasma with the power-law $q$ -distribution in nonextensive statistics. Physica A 387, 48214827.
Lonngren, K. E. 1998 Ion acoustic soliton experiments in a plasma. Opt. Quant. Electron. 30, 615630.
Mace, R. L. & Hellberg, M. A. 2001 The Korteweg–de Vries–Zakharov–Kuznetsov equation for electron-acoustic waves. Phys. Plasmas 8, 26492656.
Mahajan, S. M., Berezhiani, V. I. & Mikilaszewski, R. 1998 On the robustness of the localized spatiotemporal structures in electron–positron–ion plasmas. Phys. Plasmas 5, 32643269.
Mahmood, S. & Akhtar, N. 2008 Ion acoustic solitary waves with adiabatic ions in magnetized electron–positron–ion plasmas. Eur. Phys. J. D 49, 217222.
Mahmood, S., Akhtar, N. & Ur-Rehman, H. 2011 Acoustic solitons in magnetized quantum electron–positron plasmas. Phys. Scr. 83, 035505035510.
Mahmood, S., Mushtaq, A. & Saleem, H. 2003 Ion acoustic solitary wave in homogeneous magnetized electron–positron–ion plasmas. New J. Phys. 5, 28.128.10.
Mahmood, S. & Ur-Rehman, H. 2009 Electrostatic solitons in unmagnetized hot electron–positron–ion plasmas. Phys. Lett. A 373, 22552259.
Maksimovic, M., Pierrard, V. & Riley, P. 1997 Ulysses electron distributions fitted with kappa functions. Geophys. Res. Lett. 24, 15111519.
Miller, H. R. & Wiita, P. J. 1987 Active Galactic Nuclei. Springer.
Moslem, W. M. et al. 2007 Solitary, explosive, and periodic solutions of the quantum Zakharov–Kuznetsov equation and its transverse instability. Phys. Plasmas 14, 082308.1082308.5.
Munoz, V. 2006 A nonextensive statistics approach for Langmuir waves in relativistic plasmas. Nonlinear Process. Geophys. 13, 237241.
Mushtaq, A., Saeed, R. & Haque, Q. 2009 Ion acoustic solitary waves in magnetized pair-ion electron plasmas. Phys. Plasmas 16, 084501.1084501.4.
Nakamura, Y. 1982 Experiments on ion-acoustic solitons in plasmas invited review article. IEEE Trans. Plasma Sci. 10, 180195.
Nsengiyumva, F. et al. 2014 Stopbands in the existence domains of acoustic solitons. Phys. Plasmas 21 (10), 102301.1102301.8.
Pakzad, H. R. & Tribeche, M. 2011 Electron acoustic double layers in a plasma with a $q$ -nonextensive electron velocity distribution. Astrophys. Space Sci. 334, 4553.
Popel, S. I., Vladimirov, S. V. & Shukla, P. K. 1995 Ion-acoustic solitons in electron–positron–ion plasmas. Phys. Plasmas 2 (3), 716719.
Renyi, A. 1955 On a new axiomatic theory of probability. Acta Math. Acad. Sci. Hung. 6, 285335.
Reynolds, C. S. et al. 1996 The matter content of the jet in M87: evidence for an electron–positron jet. Mon. Not. R. Astron. Soc. 283, 873880.
Sahu, B. 2011 Ion acoustic solitary waves and double layers with nonextensive electrons and thermal positrons. Phys. Plasmas 18, 082302.1082302.6.
Saini, N. S. & Kholi, R. 2014 Electrostatic envelope excitations under transverse perturbations in a plasma with nonextensive hot electrons. Astrophys. Space Sci. 349, 293303.
Saini, N. S. & Shalini 2013 Ion acoustic solitons in a nonextensive plasma with multi-temperature electrons. Astrophys. Space Sci. 346, 155163.
Saitou, Y. & Nakamura, Y. 2005 Ion-acoustic soliton-like waves undergoing Landau damping. Phys. Lett. A 343, 397402.
Samanta, U. K., Saha, A. & Chatterjee, P. 2013 Bifurcations of nonlinear ion acoustic travelling waves in the frame of a Zakharov–Kuznetsov equation in magnetized plasma with a kappa distributed electron. Phys. Plasmas 20, 052111.1052111.5.
Shan, S. A. & Akhtar, N. 2013 Korteweg–de Vries equation for ion acoustic soliton with negative ions in the presence of nonextensive electrons. Astrophys. Space Sci. 346, 367374.
Silva, R. Jr., Plastino, A. R. & Lima, J. A. S. 1998 A Maxwellian path to the $q$ -nonextensive velocity distribution function. Phys. Lett. A 249 (5), 401408.
Singh, S. V. et al. 2013 Effect of ion temperature on ion-acoustic solitary waves in a magnetized plasma in presence of superthermal electrons. Phys. Plasmas 20, 012306.1012306.6.
Stenflo, L., Shukla, P. K. & Yu, M. Y. 1985 Nonlinear propagation of electromagnetic waves in magnetized electron–positron plasmas. Astrophys. Space Sci. 117 (2), 303308.
Sultana, S. et al. 2010 Oblique electrostatic excitations in a magnetized plasma in the presence of excess superthermal electrons. Phys. Plasmas 17, 032310.1032310.10.
Taruya, A. & Sakagami, M. A. 2003 Long-term evolution of stellar self-gravitating systems away from thermal equilibrium: connection with nonextensive statistics. Phys. Rev. Lett. 90, 181101.1181101.4.
Tiwari, R. S., Jain, S. L. & Chawla, J. K. 2007 Ion acoustic cnoidal waves and associated nonlinear ion flux in a warm ion plasma. Phys. Plasmas 14, 022106.1022106.9.
Tran, M. Q. 1979 Ion acoustic solitons in a plasma: a review of their experimental properties and related theories. Phys. Scr. 20, 317327.
Tribeche, M., Djebarni, L. & Amour, R. 2010 Ion-acoustic solitary waves in a plasma with a $q$ -nonextensive electron velocity distribution. Phys. Plasmas 17, 042114.1042114.6.
Tsallis, C. 1988 Possible generalization of Boltzmann–Gibbs statistics. J. Stat. Phys. 52, 479487.
Tsallis, C. 1995 Non-extensive thermostatistics: brief review and comments. Physica A 221, 277290.
Vasyliunas, V. M. 1968 A survey of low energy electrons in the evening sector of the magnetosphere with OGO-1 and OGO-3. J. Geophys. Res. 73, 28392884.
Verheest, F. et al. 2006 On the existence of ion-acoustic double layers in two-electron temperature plasmas. Phys. Plasmas 13, 042301.1042301.9.
Verheest, F. 2013 Ambiguities in the Tsallis description of non-thermal plasma species. J. Plasma Phys. 79 (6), 10311034.
Washimi, H. & Taniuti, T. 1966 Propagation of ion-acoustic solitary waves of small amplitude. Phys. Rev. Lett. 17, 996997.
Yu, M. Y., Shukla, P. K. & Stenflo, L. 1986 Alfven vortices in a strongly magnetized electron-position plasma. Astrophys. J. 309, L63L66.
Zakharov, V. E. & Kuznetsov, E. A. 1974 Three-dimensional solitons. Sov. Phys. JETP 39, 285286.
Zank, G. P. & Greaves, R. G. 1995 Linear and nonlinear modes in nonrelativistic electron–positron plasmas. Phys. Rev. E 51, 60796090.
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