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Modified Zakharov–Kuznetsov equation for a non-uniform electron–positron–ion magnetoplasma with kappa-distributed electrons

Published online by Cambridge University Press:  13 July 2015

Ali Ahmad  and
W. Masood
Ali Ahmad
Affiliation:
National Centre for Physics, Quaid-i-Azam University Campus, Islamabad 44000, Pakistan
W. Masood*
Affiliation:
National Centre for Physics, Quaid-i-Azam University Campus, Islamabad 44000, Pakistan Department of Physics, COMSATS Institute of Information Technology (CIIT), Islamabad 44000, Pakistan
*
†Email address for correspondence: waqasmas@gmail.com
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Abstract

We investigate the low-frequency (by comparison with the ion Larmor frequency) electrostatic solitary structures in a spatially non-uniform electron–positron–ion (e–p–i) magnetoplasma with non-Maxwellian electrons. A linear dispersion relation for the obliquely propagating ion acoustic drift wave is derived and it is shown that the non-Maxwellian electron population modifies the dispersion characteristics of the wave under consideration. We also carry out a nonlinear analysis and derive the modified Zakharov–Kuznetsov (MZK) equation for the coupled drift acoustic wave in a non-uniform magnetized plasma. We highlight the differences between the MZK equation and its homogeneous counterpart. We also find the solution of the MZK equation using the tangent hyperbolic method. It is observed that the electron spectral index ${\it\kappa}$, positron concentration, and propagation angle ${\it\alpha}$ alter the structure of the ion acoustic drift solitary waves. The results obtained in this paper may be beneficial to understanding the propagation characteristics of electrostatic drift solitary structures in the interstellar medium and in laboratory experiments where electron–positron plasmas have recently been created by impinging ultra-intense laser pulses on a solid density target at the Lawrence Livermore National Laboratory (LLNL).

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 5 , October 2015 , 905810505
Copyright
© Cambridge University Press 2015 

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References

Asenjo, F. A., Borotto, F. A., Chian, A. C.-L., Munoz, V., Valdivia, J. A. & Rempel, E. L. 2012 Self-modulation of nonlinear waves in a weakly magnetized relativistic electron–positron plasma with temperature. Phys. Rev. E 85, 046406, 1–6.Google Scholar
Baluku, T. K. & Hellberg, M. A. 2008 Dust acoustic solitons in plasmas with kappa-distributed electrons and/or ions. Phys. Plasmas 15, 123705, 1–11.CrossRefGoogle Scholar
Bell, A. R. & Kingham, R. J. 2003 Resistive collimation of electron beams in laser-produced plasmas. Phys. Rev. Lett. 91, 035003, 1–4.Google Scholar
Berezhiani, V. I. & Mahajan, S. M. 1994 Large amplitude localized structures in a relativistic electron–positron ion plasma. Phys. Rev. Lett. 73, 1110–1113.CrossRefGoogle Scholar
Cheng, L. H., Tang, R. A., Zhang, A. X. & Xue, J. K. 2013 Nonlinear interaction of intense laser pulses and an inhomogeneous electron–positron–ion plasma. Phys. Rev. E 87, 025101, 1–5.Google Scholar
Cowan, T. E., Perry, M. D., Key, M. H., Ditmire, T. R., Hatchett, S. P., Henry, E. A., Moody, J. D., Moran, M. J., Pennington, D. M., Phillips, T. W., Sangster, T. C., Sefcik, J. A., Singh, M. S., Snavely, R. A., Stoyer, M. A., Wilks, S. C., Young, P. E., Takahashi, Y., Dong, B., Fountain, W., Parnell, T., Johnson, J., Hunt, A. W. & Kühl, T. 1999 High energy electrons, nuclear phenomena and heating in petawatt laser-solid experiments. Laser Part. Beams 17, 773–783.Google Scholar
El-Shamy, E. F. 2014 Multi-dimensional instability of obliquely propagating ion acoustic solitary waves in electron–positron–ion superthermal magnetoplasmas. Phys. Plasmas 21, 082110, 1–9.Google Scholar
Esarey, E., Schroeder, C. B. & Leemans, W. P. 2009 Physics of laser-driven plasma-based electron accelerators. Rev. Mod. Phys. 81, 1229–1285.Google Scholar
Gell, Y. 1977 Drift solitons and their two-dimensional stability. Phys. Rev. A 16, 402–405.Google Scholar
Godyak, V. A., Piejak, R. B. & Alexandrovich, B. M. 1993 Probe diagnostics of non-Maxwellian plasmas. J. Appl. Phys. 73, 3657–3663.Google Scholar
Goldreich, P. & Julian, W. H. 1969 Pulsar electrodynamics. Astrophys. J. 157, 869–880.Google Scholar
Haque, Q. & Saleem, H. 2003 Ion acoustic and drift wave vortices in electron–positron–ion plasmas. Phys. Plasmas 10, 3793–3795.CrossRefGoogle Scholar
Hellberg, M. A., Mace, R. L., Baluku, T. K., Kourakis, I. & Saini, N. S. 2009 Comment on ‘Mathematical and physical aspects of Kappa velocity distribution’ [Phys. Plasmas 14, 110702 (2007)]. Phys. Plasmas 16, 094701, 1–5.Google Scholar
Infeld, E. & Rowlands, G. 1990 Nonlinear Waves, Solitons and Chaos. Cambridge University Press.Google Scholar
Iwasaki, H., Toh, S. & Kawahara, T. 1990 Cylindrical quasi-solitons of the Zakharov–Kuznetsov equation. Physica D 43, 293–303.CrossRefGoogle Scholar
Kadomtsev, B. B. & Petviashvilli, V. I. 1970 On the stability of solitary waves in weakly dispersing media. Sov. Phys. Dokl. 15 (6), 539–541.Google Scholar
Klein, U. & Kerp, J. 2008 Physics of the Interstellar Medium. Argelander, Institut für Astronomie.Google Scholar
Kourakis, I., Sultana, S. & Hellberg, M. A. 2012 Dynamical characteristics of solitary waves, shocks and envelope modes in kappa-distributed non-thermal plasmas. Plasma Phys. Control. Fusion 54, 124001, 1–7.Google Scholar
Lee, M.-J. 2007 Landau damping of dust acoustic waves in a Lorentzian plasma. Phys. Plasmas 14, 032112, 1–5.Google Scholar
Liang, E. P., Wilks, S. C. & Tabak, M. 1998 Pair production by ultraintense lasers. Phys. Rev. Lett. 81, 4887–4890.Google Scholar
Livadiotis, G. & McComas, D. J. 2013 Understanding kappa distributions: a toolbox for space science and astrophysics. Space Sci. Rev. 175, 183–214.CrossRefGoogle Scholar
Mace, R. L. & Hellberg, M. A. 2001 The Korteweg–de Vries–Zakharov–Kuznetsov equation for electron-acoustic waves. Phys. Plasmas 8, 2649–2656.Google Scholar
Malfliet, W. 1992 Solitary wave solutions of nonlinear wave equations. Am. J. Phys. 60 (7), 650–654.CrossRefGoogle Scholar
Malfliet, W. 2004 The tanh method: a tool for solving certain classes of nonlinear evolution and wave equations. J. Comput. Appl. Maths 164–165, 529–541.CrossRefGoogle Scholar
Mandal, P. K., Ghorui, M. K., Saha, A. & Chatterjee, P. 2015 Nonplanar ion-acoustic two-soliton systems in quantum electron–positron–ion plasmas. Astrophys. Space Sci. 355, 89–94.Google Scholar
Masood, W., Hassan, S., Batool, N. & Siddiq, M. 2013 Formation of solitary structures in uniform and nonuniform magnetoplasmas with superthermal electrons: a non-reductive perturbative approach. Astrophys. Space Sci. 348, 107–114.CrossRefGoogle Scholar
Masood, W., Jahangir, R., Eliasson, B. & Siddiq, M. 2014 A nonlinear model for magnetoacoustic waves in dense dissipative plasmas with degenerate electrons. Phys. Plasmas 21, 102311, 1–4.Google Scholar
Masood, W. & Schwartz, S. J. 2008 Observations of the development of electron temperature anisotropies in Earth’s magnetosheath. J. Geophys. Res. 113, A01216, 1–12.Google Scholar
Masood, W., Schwartz, S. J., Maksimovic, M. & Fazakerley, A. N. 2006 Electron velocity distribution and lion roars in the magnetosheath. Ann. Geophys. 24, 1725–1735.CrossRefGoogle Scholar
Michel, F. C. 1982 Theory of pulsar magnetospheres. Rev. Mod. Phys. 54, 1–66.Google Scholar
Mikhailovskii, A. B. 1974 Theory of Plasma Instabilities, vol. 2. Consultants Bureau.Google Scholar
Miller, H. R. & Witta, P. J. 1987 Active Galactic Nuclei. Springer.Google Scholar
Misner, W., Thorne, K. S. & Wheeler, J. I. 1973 Gravitation. Freeman.Google Scholar
Modena, A., Najmudin, Z., Dangor, A. E., Clayton, C. E., Marsh, K. A., Joshi, C., Malka, V., Darrow, C. B., Danson, C., Neely, D. & Walsh, F. N. 1995 Electron acceleration from the breaking of relativistic plasma waves. Nature 377, 606–608.CrossRefGoogle Scholar
Mushtaq, A. 2008 Spatially limited ion acoustic drift soliton in electron–positron–ion magnetoplasma. Phys. Plasmas 15, 082313, 1–6.CrossRefGoogle Scholar
Mushtaq, A. & Shah, H. A. 2005 Nonlinear Zakharov–Kuznetsov equation for obliquely propagating two-dimensional ion-acoustic solitary waves in a relativistic, rotating magnetized electron–positron–ion plasma. Phys. Plasmas 12, 072306, 1–8.CrossRefGoogle Scholar
Palastro, J. P., Divol, L., Michel, P., Williams, E. A. & Strozzi, D. 2008 Kinetic dispersion of the Langmuir decay instability and its relevance for ignition plasmas. Bull. Am. Phys. Soc. 53 (14).Google Scholar
Pierrard, V. & Lazar, M. 2010 Kappa distributions: theory and applications in space plasmas. Solar Phys. 267, 153–174.Google Scholar
Popel, S. I., Vladimirov, S. V. & Shukla, P. K. 1995 Ion-acoustic solitons in electron–positron–ion plasmas. Phys. Plasmas 2, 716–719.Google Scholar
Pukhov, A. 2003 Strong field interaction of laser radiation. Rep. Prog. Phys. 66, 47–101.Google Scholar
Rees, M. J. 1983 What the astrophysicist wants from the very early universe. In The Very Early Universe (ed. Gibbson, G. W., Hawking, S. W. & Siklas, S.), p. 29. Cambridge University Press.Google Scholar
Ridgers, C. P., Brady, C. S., Duclous, R., Kirk, J. G., Bennett, K., Arber, T. D., Robinson, A. P. L. & Bell, A. R. 2012 Dense electron–positron plasmas and ultraintense ${\it\gamma}$ rays from laser-irradiated solids. Phys. Rev. Lett. 108, 165006, 1–5.Google Scholar
Rizzato, F. B. 1988 Weak nonlinear electromagnetic waves and low-frequency magnetic-field generation in electron–positron–ion plasmas. J. Plasma Phys. 40, 289–298.Google Scholar
Saha, A. & Chatterjee, P. 2014 Bifurcations of ion acoustic solitary and periodic waves in an electron–positron–ion plasma through non-perturbative approach. J. Plasma Phys. 80, 553–563.Google Scholar
Saha, A., Pal, N. & Chatterjee, P. 2014 Dynamic behavior of ion acoustic waves in electron–positron–ion magnetoplasmas with superthermal electrons and positrons. Phys. Plasmas 21, 102101, 1–10.Google Scholar
Sahu, B. & Roychoudhury, R. 2012 Zakharov–Kuznetsov equation for ion acoustic waves with superthermal electrons in cylindrical geometry. Eur. Phys. Lett. 100, 15001, p1–p6.CrossRefGoogle Scholar
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, 1–5.Google Scholar
Scudder, J. D. & Olbert, S. 1979 A theory of local and global processes which affect solar wind electrons. I – The origin of typical 1 AU velocity distribution functions – Steady state theory. J. Geophys. Res. 84, 2755–2772.Google Scholar
Shukla, P. K., Marklund, M. & Eliasson, B. 2004 Nonlinear dynamics of intense laser pulses in a pair plasma. Phys. Lett. A 324, 193–197.Google Scholar
Summers, D. & Thorne, R. M. 1991 The modified plasma dispersion function. Phys. Fluids B 3, 1835–1847.CrossRefGoogle Scholar
Surko, C. M., Leventhal, M., Crane, W. S., Passner, A., Wysocki, F., Murphy, T. J., Strachan, J. & Rowan, W. L. 1986 Use of positrons to study transport in tokamak plasmas. Rev. Sci. Instrum. 57, 1862–1867.CrossRefGoogle Scholar
Surko, C. M. & Murphy, T. 1990 Use of the positron as a plasma particle. Phys. Fluids B 2, 1372–1375.Google Scholar
Tabak, M., Hammer, J., Glinsky, M. E., Kruer, W. L., Wilks, S. C., Woodworth, J., Campbell, E. M., Perry, M. D. & Mason, R. J. 1994 Ignition and high gain with ultrapowerful lasers. Phys. Plasmas 1, 1626–1634.CrossRefGoogle Scholar
Tandberg-Hansen, E. & Emslie, A. G. 1988 The Physics of Solar Flares. Cambridge University Press.Google Scholar
Vasyliunas, V. 1968 A survey of low-energy electrons in the evening sector of the magnetosphere with OGO 1 and OGO 3. J. Geophys. Res. 73, 2839–2884.Google Scholar
Weinberg, S. 1972 Gravitation and Cosmology. Wiley.Google Scholar
Yoon, P. H. 2012 Electron kappa distribution and steady-state Langmuir turbulence. Phys. Plasmas 19, 052301, 1–6.Google Scholar
Yoon, P. H., Ziebell, L. F., Gaelzer, R., Lin, R. P. & Wang, L. 2012 Langmuir turbulence and suprathermal electrons. Space Sci. Rev. 173, 459–489.Google Scholar
Zakharov, V. E. & Kuznetsov, E. A. 1974 Three-dimensional solitons. Sov. Phys. JETP 39 (2), 285–286.Google Scholar