Evolution of Alfvénic wave envelopes in spin-1/2 quantum Hall-magnetohydrodynamic plasmas

Abstract

The one-dimensional oblique propagation of large amplitude magnetohydrodynamic (MHD) waves in a high-β quantum Hall-MHD plasma is studied with electron spin-1/2 effects. The plasma β becomes high by the condition for the nonrelativistic fluid model to be valid and the condition for the collective effects to be important in quantum plasmas. Such a high-β value is a prerequisite for large perturbations of the perpendicular magnetic field comparable with the longitudinal magnetic field. It is shown that the nonlinear evolution of such waves is described by a derivative nonlinear Schrödinger (DNLS) equation. It is found that the DNLS equation does not depend on the higher order quantum coupling associated with the Bohm potential, rather the pressure such as spin force plays the crucial role. Such an evolution equation is shown to admit spin-modified localized envelope solitons whose width L is reduced by ε2/vB2 and the amplitude increases with increasing ε2/vB2 values, where ε is the temperature normalized Zeeman energy and vB2 is the electron thermal energy normalized by the Alfvén wave energy. Moreover, the MHD waves are found to be modulationally unstable for a wave number exceeding its critical value, which typically depends on ε2/vB2. The growth rate of the modulational instability is also investigated. Furthermore, the effect of dissipation due to plasma resistivity is shown to exhibit envelope shocklike structures instead of envelope solitons. The present nonlinear excitations can account for large scale structures in dense astrophysical plasma environments.