# Plasma and Fusion Research

## Volume 4, 018 (2009)

# Regular Articles

- Centre for Plasma Physics, Queen‘s University Belfast, BT7 1 NN Northern Ireland, UK
- 1)
- Institut für Theoretische Physik IV, Fakultät für Physik und Astronomie, D-44780 Bochum, Germany
- 2)
- Department of Physics, Faculty of Education-Port Said, Suez Canal University, Egypt
- 3)
- Fakultät für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany
- 4)
- Department of Mathematics, Faculty of Science, Fayoum University, Egypt
- 5)
- Department of Physics, Faculty of Science, Mansoura University, New Damietta 34517, Egypt

### Abstract

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 ω_{c} and the (intrinsic) plasma rotation frequency Ω_{0}.
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 ω_{c} → ±2Ω_{0}.
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.

### Keywords

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

### Full Text

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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).