Study of parametric regime for the formation of nonlinear structures in pair-ion-electron plasmas beyond the KdV limit

Abstract

The propagation of one dimensional nonlinear electrostatic waves in unmagnetized pair-ion-electron (PIE) plasmas comprising of oppositely charged inertial ions of equal mass but different temperatures and Boltzmann electrons is investigated. In the linear analysis, the acquired biquadratic dispersion relation yields fast and slow modes for PIE plasmas. In the nonlinear regime, the Gardner equation in PIE plasmas is derived in the weak nonlinearity limit. The plasma parameter regime is explicitly shown where the Korteweg de Vries equation used in the earlier studies is no longer valid and the Gardner equation becomes relevant. Solitary and kink solutions of Gardner equation are also presented. Interestingly, it has been observed that these solutions exist for the fast mode; however, no such structure is found to exist for the slow mode. It is hoped that the present study would be beneficial to understand the solitary and kink solutions in laboratory produced PIE plasmas and parametric regimes in which this study is applicable.