Impact of higher-order corrections on the stability analysis of shock structures in magnetized multi-ion plasma

Abstract

This work investigates the nonlinear propagation of ion-acoustic shock waves (IASWs) in a three-component collisionless magnetized plasma comprising trapped electrons, positive ions, and negative ions under an oblique external static magnetic field. Employing the reductive perturbation technique, a standard Burgers equation governing first-order shock dynamics and a higher-order linear inhomogeneous Burgers-type equation for the second-order perturbed potential are systematically derived. The integrability of the Burgers equation is established through a Lax pair construction within the Ablowitz–Kaup–Newell–Segur framework, from which exact one- and two-soliton solutions are obtained via the Darboux transformation. Stationary shock solutions are derived analytically, with higher-order corrections computed through the method of variation of parameters. The higher-order contributions are found to be consistently rarefactive, reducing the overall shock amplitude below first-order predictions. The influence of the trapping parameter, electron temperature, viscosity, obliquity angle, and ion density ratio on shock amplitude, width, and electric field profiles is examined in detail. The results demonstrate that incorporating higher-order effects provides a more complete and physically refined description of shock structures, with significant implications for understanding nonlinear coherent waves in planetary magnetospheres, auroral zones, and laboratory electronegative plasmas relevant to semiconductor fabrication and plasma etching.