Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-29T15:06:08.080Z Has data issue: false hasContentIssue false
  • English
  • Français

Semiclassical relativistic fluid theory for electrostatic envelope modes in dense electron–positron–ion plasmas: Modulational instability and rogue waves

Published online by Cambridge University Press:  22 November 2013

IOANNIS KOURAKIS ,
MICHAEL MC KERR  and
ATA UR-RAHMAN
IOANNIS KOURAKIS
Affiliation:
Centre for Plasma Physics, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, Northern Ireland, UK ([email protected])
MICHAEL MC KERR
Affiliation:
Centre for Plasma Physics, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, Northern Ireland, UK ([email protected])
ATA UR-RAHMAN
Affiliation:
Institute of Physics and Electronics, University of Peshawar, Peshawar 25000, Pakistan National Centre for Physics, Shahdrah Valley Road, Islamabad 44000, Pakistan
Get access Rights & Permissions [Opens in a new window]

Abstract

A fluid model is used to describe the propagation of envelope structures in an ion plasma under the influence of the action of weakly relativistic electrons and positrons. A multiscale perturbative method is used to derive a nonlinear Schrödinger equation for the envelope amplitude. Criteria for modulational instability, which occurs for small values of the carrier wavenumber (long carrier wavelengths), are derived. The occurrence of rogue waves is briefly discussed.

Type
Papers
Information
Journal of Plasma Physics , Volume 79 , Special Issue 6: Special issue in memory of Professor Padma Kant Shukla 1950-2013 , December 2013 , pp. 1089 - 1094
Copyright
Copyright © Cambridge University Press 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akbari-Moghanjoughi, M. 2010 Effects of ion-temperature on propagation of the large-amplitude ion-acoustic solitons in degenerate electron–positron–ion plasmas. Phys. Plasmas 17, 082315/1–8.CrossRefGoogle Scholar
Akbari-Moghanjoughi, M. 2011 Propagation of arbitrary-amplitude ion waves in relativistically degenerate electron-ion plasmas. Astrophys. Space Sci. 332, 187–192.CrossRefGoogle Scholar
Akhmediev, N., Soto-Crespo, J. M. and Ankiewicz, A. 2009 Extreme waves that appear from nowhere: on the nature of rogue waves. Phys. Lett. A 373, 2137–2145.CrossRefGoogle Scholar
Asano, N., Taniuti, T. and Yajima, N. 1969 Perturbation method for a nonlinear wave modulation. II. J. Math. Phys. 10, 2020–2024.CrossRefGoogle Scholar
Chandrasekhar, S. 1935 Mon. Not. R. Astron. Soc. 170, 405.Google Scholar
Chandrasekhar, S. 1939 An Introduction to the Study of Stellar Structure. Chicago, IL: University of Chicago Press.Google Scholar
Dauxois, T. and Peyrard, M. 2005 Physics of Solitons. Cambridge, UK: Cambridge University Press.Google Scholar
Dysthe, K. and Trulsen, K. 1999 Note on breather type solutions of the NLS as models for freak waves. Phys. Scripta T82, 48–52.CrossRefGoogle Scholar
Fortov, V. E. 2009 Extreme states of matter on earth and in space. Phys. Usp. 52, 615–647.CrossRefGoogle Scholar
Haider, M. M., Akhter, S., Duha, S. S. and Mamun, A. A. 2012 Multi-dimensional instability of electrostatic solitary waves in ultra-relativistic degenerate electron-positron-ion plasmas. Cent. Eur. J. Phys. 10 (5), 1168–1177.Google Scholar
Hansen, C. J., Kawaler, S. D. and Trimble, V. 2004 Stellar Interiors – Physical Principles, Structure, and Evolution. New York, NY: Springer.CrossRefGoogle Scholar
Khan, S. A. 2013 Low frequency shear electromagnetic modes in strongly coupled, relativistic-degenerate, astrophysical electron-positron-ion plasmas. Astrophys Space Sci. 343, 683–688.CrossRefGoogle Scholar
Kibler, B., Fatome, J., Finot, C., Millot, G., Dias, F., Genty, G., Akhmediev, N. and Dudley, J. M. 2010 The Peregrine soliton in nonlinear fibre optics. Nat. Phys. A 6, 790–795.CrossRefGoogle Scholar
Koester, D. and Chanmugam, G. 1990 Physics of white dwarf stars. Rep. Prog. Phys. 53, 837–915.CrossRefGoogle Scholar
Kourakis, I. and Shukla, P. K. 2004 Finite ion temperature effects on oblique modulational stability and envelope excitations of dust-ion acoustic waves. Eur. Phys. J. D 28, 109–117.CrossRefGoogle Scholar
Kourakis, I. and Shukla, P. K. 2005 Exact theory for localized envelope modulated electrostatic wave packets in space and dusty plasmas. Nonlin. Proc. Geophys. 12, 407–423.CrossRefGoogle Scholar
Lai, D. 2001 Matter in strong magnetic fields. Rev. Mod. Phys. 73, 629–661.CrossRefGoogle Scholar
Lallement, R., Welsh, B. Y., Barstow, M. A. and Casewell, S. L. 2011 High ions towards white dwarfs: circumstellar line shifts and stellar temperature. Astron. Astrophys. 533, A140/1–13.CrossRefGoogle Scholar
Peregrine, D. H. 1983 Water waves, nonlinear Schrdinger equations and their solutions. J. Austral. Math. Soc. Ser. B 25, 16–43.CrossRefGoogle Scholar
Popel, S. I., Tsytovich, V. N. and Vladimirov, S. V. 1995a Modulational interactions in plasmas. Dordrecht, Netherlands, Kluwer.Google Scholar
Popel, S. I., Vladimirov, S. V. and Tsytovich, V. N. 1995b Theory of modulational interactions in plasmas in the presence of an external magnetic field. Phys. Rep. 259, 327–404.CrossRefGoogle Scholar
Rahman, A., Ali, S., Mirza, A. M. and Qamar, A. 2013a Planar and non-planar ion acoustic shock waves in relativistic degenerate astrophysical electron–positron–ion plasmas. Phys. Plasmas 20, 042305.CrossRefGoogle Scholar
Rahman, A., Ali, S., Mushtaq, A. and Qamar, A. 2013b Nonlinear ion acoustic excitations in relativistic degenerate, astrophysical e-p-i plasmas. J. Plasma Phys. 79, 817–823.CrossRefGoogle Scholar
Shapiro, S. L. and Teukolsky, S. A. 1983 Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects. New York, NY: Wiley.CrossRefGoogle Scholar
Svensson, R. 1982 Electron positron pair equilibria in relativistic plasmas. Astrophys. J. 258, 335–348.CrossRefGoogle Scholar
Taniuti, T. and Yajima, N. 1969 Perturbation method for a nonlinear wave modulation. J. Math. Phys. 10, 1369–1372.CrossRefGoogle Scholar
Veldes, G., Borhanian, J., McKerr, M., Saxena, V., Frantzeskakis, D. J. and Kourakis, I. 2013 Electromagnetic rogue waves in beam-plasma interactions. J. Opt. 15, 064003.CrossRefGoogle Scholar
Vladimirov, S. V. and Popel, S. I. 1995 Modulational processes and limits of weak turbulence theory. Phys. Rev. E 51, 2390–2400.CrossRefGoogle ScholarPubMed
Vladimirov, S. V. and Popel, S. I. 1996 WKB-ansatz and description of modulational processes. Phys. Scripta 53, 92–96.CrossRefGoogle Scholar
Zeba, I., Moslem, W. M. and Shukla, P. K. 2012 Ion solitary pulses in warm plasmas with ultrarelativistic degenerate electrons and positrons. Astrophys. J. 750, 72–77.CrossRefGoogle Scholar