Nonlinear electrostatic solitary pulses in magnetized quantum plasma with relative density effects of spin-up and spin-down electrons

Abstract

A separated spin evolution quantum hydrodynamics model is employed to study low frequency electrostatic waves in plasmas having inertia-less degenerate electrons with spin-up ne↑ and spin-down ne↓ states and inertial classical ions. A two-dimensional plasma geometry is assumed having a uniform magnetic field, directed along the z-axis, i.e., B=B0ẑ. A Zakharov-Kuznetsov (ZK) type equation is derived for the electrostatic potential via the Reductive Perturbation Technique. The parametric role of the spin density polarization ratio κ in the characteristics of solitary wave structures is investigated. We have observed that both the amplitude and width of the soliton are significantly affected by the spin polarization but the amplitude remains largely un-affected by variation in the magnetic field strength. We have also carried out pulse stability analysis and have found that the pulse soliton solution of the ZK equation is unstable to oblique perturbations. The dependence of the instability growth rate on the density polarization ratio κ along with other significant plasma parameters is traced analytically. We have shown that the first order growth rate of the instability decreases with an increase in the angle between the transverse component of the perturbation and the direction of the magnetic field, in the range (0≤θ<37.8°). We have also observed that the spin polarization affects the growth and increases as we move from the strongly spin-polarized plasma to a zero polarization case.