Ion-acoustic solitons in pair-ion plasma with non-thermal electrons

Abstract

Properties of fully nonlinear ion-acoustic solitary waves in an unmagnetized and collisionless pair-ion (PI) plasma containing superthermal electrons obeying Cairns distribution have been analyzed. A linear biquadratic dispersion relation has been derived, which yields the fast (supersonic) and slow (subsonic) modes in a pair-ion-electron plasma with nonthermal electrons. For nonlinear analysis, Korteweg-de Vries equation is obtained using the reductive perturbation technique. It is found that in case of slow mode, both electrostatic hump and dip type structures are formed depending on the temperature difference between positively and negatively charged ions, whereas, only dip type solitary structures have been observed for fast mode. The present work may be employed to explore and to understand the formation of solitary structures in the space (especially, the Earth’s ionosphere where two distinct pair ion species (H ^±) are present) and laboratory produced pair-ion plasmas with nonthermal electrons.

Appendix

The linear dispersion relation (Eq. (11)) can also be derived by Fourier analysis by using the normalized perturbed quantities up to first order ($n_{s}=1+n_{s}^{(1)}$, $v_{s}=v_{s}^{(1)}$, φ=φ ⁽¹⁾) in Eq. (7). After substitution, the linearized system of equations is

$$ \partial_{x}^{2}\varphi^{(1)}=p\varGamma\varphi ^{(1)}+(1-p)n_{-}^{(1)}-n_{+}^{(1)}, $$

where $n_{s}^{(1)},v_{s}^{(1)}$, φ ⁽¹⁾ are the first order perturbations. Assuming $n_{s}^{(1)},\varphi^{(1)}\sim e^{i(kx-\omega t)}$ where k (wave number) and ω (wave frequency) are normalized by $\lambda_{D+}^{-1}$ and ω _p+ and x, t by λ _D+, $\omega_{p+}^{-1}$, respectively, after eliminating $v_{s}^{(1)}$ and solving the above system of equations gives the following dispersion relation

$$ \bigl( p\varGamma+k^{2} \bigr) -\frac{1-p}{\lambda^{2}-\sigma\delta }-\frac{1}{\lambda^{2}-\sigma}=0 $$

with λ ²=ω ²/k ². In the long wavelength limit, the dispersion relation reduces to

$$ p\varGamma-\frac{1-p}{\lambda^{2}-\sigma\delta}-\frac{1}{\lambda ^{2}-\sigma}=0 $$

or it can be rearranged to Eq. (11),