Modulation instability of ion-acoustic waves and exchange interaction in magnetized quantum plasma with relative density effects of spin-up and spin-down electrons

Abstract

Abstract The separate-spin evolution quantum hydrodynamic (SSE-QHD) model is used to study Ion-Acoustic Waves (IAWs) in a magnetized quantum plasma having electrons with different spin populations in the presence of the spin particle exchange interactions (Coulomb type) in spin-down electrons only. The plasma consists of inertia-less separated spin-up and spin-down electrons states, while ions are inertial and classical. Besides, a uniform magnetic field is assumed to be directed in the Z-direction i.e. B ⃗ = B 0 z ˆ . An interesting interplay between exchange interaction and density polarization ratio κ has been observed on dispersive properties, effective Debye screening length and effective ion-acoustic speed. The non-linear Schrödinger equation is derived through a reductive perturbation approach. Moreover, the modulation instability condition and resulting envelope waves are analyzed. The parametric effects of density polarization ratio κ and Coulomb exchange interaction on dispersion, effective screening length, effective ion-acoustic speed, instability growth rate, and on the solitons profile have been discussed in detail. This model can be helpful to study properties of the dilute magnetic semiconductors and degenerate 2D & 3D Fermi electron gas, where exchange interactions are significant.