Compressive and rarefactive ion-acoustic solitons in bi-ion plasmas

Abstract

Nonlinear propagation of ion-acoustic solitary structures in plasmas with an admixture of heavy ions is studied in the wave frame, where they are stationary, using a recently developed gas-dynamic approach, as an alternative to the conventional Sagdeev pseudopotential method. This viewpoint brings out the gas-dynamic aspects, which then allow a characterization of the solitary wave structures in terms of the species’ sonic points, the global charge neutral points, and critical collective Mach numbers. It is shown that the concepts of a critical density in the Korteweg–de Vries (KdV) treatment, and of a changeover from compressive to rarefactive soliton character, correspond to the formation of a second charge neutral point (outside equilibrium) in the rarefactive regime, at which the electric stresses maximize. It is possible therefore that in certain regions of parameter space compressive and rarefactive solitons can co-exist. The compressive solitons are not predicted by a weakly nonlinear KdV treatment, except very close to the changeover region at sufficiently small enough amplitudes, as typified by the “modified” KdV (mKdV) equation. Their prediction requires a fully nonlinear treatment. Existence criteria are deduced and evaluated numerically in the parameter space of soliton Mach number and normalized density of the heavy species for compressive and rarefactive ion-acoustic solitons in a plasma with negative ion admixture.