Dissipative cylindrical fast magnetoacoustic waves in planetary magnetospheres

Abstract

Nonlinear cylindrical fast magnetoacoustic waves are investigated in a dissipative magnetoplasma comprising of electrons, positrons, and ions. In this regard, cylindrical Kadomtsev-Petviashvili-Burgers (CKPB) equation is derived using the small amplitude perturbation expansion method. Furthermore, cylindrical Burgers-Kadomtsev-Petviashvili (Cyl Burgers-KP) for a fast magnetoacoustic wave is derived, for the first time, for spatial scales larger than the electron/positron skin depths, c/ω p(e,p). Using the tangent hyperbolic method, the solutions of both planar KPB and Burgers-KP equations are obtained and then subsequently used as an initial profile to solve their respective counterparts in the cylindrical geometry. The effect of positron concentration, kinematic viscosity, and plasma β are explored both for the KPB and the Burgers-KP shock waves and the differences between the two are highlighted. The temporal evolution of the cylindrical fast magnetoacoustic wave is also numerically investigated. The present study may be beneficial to study the propagation characteristics of nonlinear electromagnetic shock waves in planetary magnetospheres.