Electrostatic solitary pulses in magnetized relativistic spin-polarized quantum plasma

A Magnetized Relativistic Quantum Hydrodynamics model is used to study the behavior of low fRequency electrostatic solitons in relativistic magnetized spin-polarized quantum plasma. The constituents of the plasma are inertia-less relativistic quantum electrons having concentration of both spin-up n(e up arrow) and spin-down n(e down arrow) species, and relativistic classical ions. We have used two-dimensional geometry in which a uniform ambient magnetic field is applied in the z-direction i.e. B = B-0(z) over bar. The linear analysis shows the presence of two types of modes; slow (acoustic) mode and a fast Langmuir-like mode. A nonlinear Zakharov-Kuznetsov (ZK) type equation is derived for the electrostatic potential by using reductive perturbation technique. The dependence of the spin density polarization ratio. on the properties of solitary wave profile is being investigated. It has been demonstrated that amplitude as well as width of the soliton depend significantly on the spin density polarization ratio, obliqueness and relativistic effects. We have also observed that the soliton solution of the ZK equation is unstable to the oblique perturbations. The instability growth rate varies appreciably with the density polarization and relativistic effects.