[Table of Contents]

Plasma and Fusion Research

Volume 4, 018 (2009)

Regular Articles

Nonlinear Dynamics of Rotating Multi-Component Pair Plasmas and e-p-i Plasmas
Ioannis KOURAKIS, Waleed M. MOSLEM1,2), Usama M. ABDELSALAM3,4), Refaat SABRY1,5) and Padma Kant SHUKLA1)
Centre for Plasma Physics, Queen‘s University Belfast, BT7 1 NN Northern Ireland, UK
Institut für Theoretische Physik IV, Fakultät für Physik und Astronomie, D-44780 Bochum, Germany
Department of Physics, Faculty of Education-Port Said, Suez Canal University, Egypt
Fakultät für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany
Department of Mathematics, Faculty of Science, Fayoum University, Egypt
Department of Physics, Faculty of Science, Mansoura University, New Damietta 34517, Egypt
(Received 8 September 2008 / Accepted 15 March 2009 / Published 29 May 2009)


The propagation of small amplitude stationary profile nonlinear electrostatic excitations in a pair plasma is investigated, mainly drawing inspiration from experiments on fullerene pair-ion plasmas. Two distinct pair ion species are considered of opposite polarity and same mass, in addition to a massive charged background species, which is assumed to be stationary, given the frequency scale of interest. In the pair-ion context, the third species is thought of as a background defect (e.g. charged dust) component. On the other hand, the model also applies formally to electron-positron-ion (e-p-i) plasmas, if one neglects electron-positron annihilation. A two-fluid plasma model is employed, incorporating both Lorentz and Coriolis forces, thus taking into account the interplay between the gyroscopic (Larmor) frequency ωc and the (intrinsic) plasma rotation frequency Ω0. By employing a multi-dimensional reductive perturbation technique, a Zakharov-Kuznetsov (ZK) type equation is derived for the evolution of the electric potential perturbation. Assuming an arbitrary direction of propagation, with respect to the magnetic field, we derive the exact form of nonlinear solutions, and study their characteristics. A parametric analysis is carried out, as regards the effect of the dusty plasma composition (background number density), species temperature(s) and the relative strength of rotation to Larmor frequencies. It is shown that the Larmor and mechanical rotation affect the pulse dynamics via a parallel-to-transverse mode coupling diffusion term, which in fact diverges at ωc → ±2Ω0. Pulses collapse at this limit, as nonlinearity fails to balance dispersion. The analysis is complemented by investigating critical plasma compositions, in fact near-symmetric (T- ≈ T+) “pure” (n- ≈ n+) pair plasmas, i.e. when the concentration of the 3rd background species is negligible, case in which the (quadratic) nonlinearity vanishes, so one needs to resort to higher order nonlinear theory. A modified ZK equation is derived and analyzed. Our results are of relevance in pair-ion (fullerene) experiments and also potentially in astrophysical environments, e.g. in pulsars.


pair plasma, electron-positron plasma, soliton, Zakharov-Kuznetsov equation

DOI: 10.1585/pfr.4.018


  • [1] N. Iwamoto, Phys. Rev. E 47, 604 (1993).
  • [2] G.P. Zank and R.G. Greaves, Phys. Rev. E 51, 6079 (1995).
  • [3] F.F. Chen, Introduction to Plasma Physics (Plenum, New York, 1974) p.121.
  • [4] J.O. Hall and P.K. Shukla, Phys. Plasmas 12, 084507 (2005).
  • [5] W. Oohara and R. Hatakeyama, Phys. Rev. Lett. 91, 205005 (2003); W. Oohara, D. Date and R. Hatakeyama, Phys. Rev. Lett. 95, 175003 (2005); R. Hatakeyama and W. Oohara, Phys. Scr. 116, 101 (2005).
  • [6] M.J. Rees, The Very Early Universe (Cambridge Univ. Press, 1983).
  • [7] H.R. Miller and P.J. Witta, Active Galactic Nuclei (Springer-Verlag, Berlin, 1987) p.202.
  • [8] F.C. Michel, Rev. Mod. Phys. 54, 1 (1982).
  • [9] R.G. Greaves and C.M. Surko, Phys. Rev. Lett. 75, 3847 (1995); V.I. Berezhiani, D.D. Tskhakaya and P.K. Shukla, Phys. Rev. A 46, 6608 (1992); C.M. Surko, M. Levelhal, W.S. Crane, A. Passne and F. Wysocki, Rev. Sci. Instrum 57, 1862 (1986); C.M. Surko and T. Murphay, Phys. Fluid B 2, 1372 (1990).
  • [10] I. Kourakis, A. Esfandyari-Kalejahi, M. Mehdipoor and P.K. Shukla, Phys. Plasmas 13, 052117 (2006); A. Esfandyari-Kalejahi, I. Kourakis and P.K. Shukla, Phys. Plasmas, 13, 122310 (2006).
  • [11] A. Esfandyari-Kalejahi et al, J. Phys. A: Math. Gen. 39, 13817 (2006).
  • [12] F. Verheest, Phys. Plasmas 13, 082301 (2006).
  • [13] H. Saleem, J. Vranjes and S. Poedts, Phys. Lett. A 350, 375 (2006).
  • [14] H. Schamel and A. Luque, New J. Phys. 7, 69 (2005); J. Plasma Phys., published online (2008); doi:10.1017/S0022377808007472.
  • [15] I.J. Lazarus, R. Bharuthram and M.A. Hellberg, J. Plasma Phys. 74, 519 (2008).
  • [16] F. Verheest and T. Cattaert, Phys. Plasmas 12, 032304 (2005).
  • [17] M. Salahuddin, H. Saleem and M. Saddiq, Phys. Rev. E 66, 036407 (2002).
  • [18] I. Kourakis, F. Verheest and N. Cramer, Phys. Plasmas 14, 022306 (2007).
  • [19] S.S. Chandrasekhar, Mon. Not. R. Astron. Soc. 113, 667 (1953).
  • [20] B. Lehnert, Astrophys. J. 119, 647 (1954); R. Hide, Philos. Trans. R. Soc. London, A 259, 615 (1954).
  • [21] C. Uberoi and G.C. Das, Plasma Phys. 12, 661 (1970); F. Verheest, Astrophys. Space Sci. 28, 91 (1974); E. Engels and F. Verheest, Astrophys. Space Sci. 37, 427 (1975); H. Alfven, Cosmic Plasmas (Reidel, Dordrecht, 1981), §IV.14.
  • [22] U.A. Mofiz, Phys. Rev. E 55, 5894 (1997); A. Mushtaq and H.A. Shah, Phys. Plasmas 12, 072306 (2005); G.C. Das and A. Nag, Phys. Plasmas 13, 082303 (2007); ibid, 14, 083705 (2007).
  • [23] R. Sabry, W.M. Moslem, P.K. Shukla, Phys. Lett. A 372, 5691 (2008).
  • [24] W.M. Moslem et al, Solitary and blow-up electrostatic excitations in rotating magnetized electron-positron-ion plasmas, submitted to New J. Physics.
  • [25] F. Verheest, Waves in Dusty Space Plasmas (Springer, 2001).
  • [26] M. Wadati, J. Phys. Soc. Jpn. 38, 673 (1975).

This paper may be cited as follows:

Ioannis KOURAKIS, Waleed M. MOSLEM, Usama M. ABDELSALAM, Refaat SABRY and Padma Kant SHUKLA, Plasma Fusion Res. 4, 018 (2009).