Ion-acoustic double layers in magnetized plasma consisting of warm adiabatic ions and non-thermal electrons having vortex-like velocity distribution: existence and stability

A combined Schamel's modified Korteweg-de Vries-Zakharov- Kuznetsov (S-KdV-ZK) equation efficiently describes the nonlinear behaviour of ion-acoustic waves in a plasma consisting of warm adiabatic ions and non-thermal electrons (due to the presence of fast energetic electrons) having vortex-like velocity distribution function (due to the presence of trapped electrons), immersed in a uniform (space-independent) and static (time-independent) magnetic field, when the vortex-like velocity distribution function of electrons approaches the non-thermal velocity distribution function of electrons as prescribed by Cairns et al. (1995 Electrostatic solitary structures in non-thermal plasmas. Geophys. Res. Lett. 22, 2709-2712), i.e. when the contribution of trapped electrons tends to zero. This combined S-KdV-ZK equation admits a double-layer solution propagating obliquely to the external uniform and static magnetic field. The condition for the existence of this double-layer solution has been derived. The three-dimensional stabilities of the double-layer solutions propagating obliquely to the external uniform and static magnetic field have been investigated by the multiple-scale perturbation expansion method of Allen and Rowlands (1993 Determination of growth rate for linearized Zakharov-Kuznetsov equation. J. Plasma Phys. 50, 413-424 1995 Stability obliquely propagating plane solitons of the Zakharov-Kuznetsov equation. J. Plasma Phys. 53, 63-73). It is found that the double-layer solutions of the combined S-KdV-ZK equation are stable at the lowest order, i.e. up to the order k, where k is the wave number of perturbation.