Nonlinear streaming instability in viscoelastic quantum dusty plasmas

Abstract

A theoretic model formalism is developed to investigate the nonlinear gravito-electrostatically coupled streaming instability modes excitable in viscoelastic quantum dusty plasmas. It consists of weakly correlated light electrons, ions; and strongly correlated heavy dust grains. We treat the inertialess electrons as a degenerate quantum fluid, inertial ions as a classical inviscid fluid, and massive dust particles as a classical viscoelastic fluid. It considers a dimensionality-dependent parameter, γ = [(D − 2)/3D], termed as the Bohmian quantum correction prefactor (D: System dimensionality). A weakly nonlinear perturbative analysis against the defined hydrodynamic homogeneous equilibrium procedurally results in a unique conjugational construct of gravito-electrostatically coupled extended pair Korteweg-de Vries (ep-KdV) equations with atypical multiparametric coefficients. A numerical analysis upshots in two distinct classes of nonlinear wave structures: (a) Electrostatic regular periodic pulse-like patterns, and (b) Self-gravitational extended bell-shaped solitons. The amplitude variations of the streaming-induced fluctuations are analyzed especially with the constitutive electron-ion equilibrium streams and with the Galilean reference frame velocity in an elaborate comparative platform alongside geometric trajectory analysis illustratively. The main implications and applications of this semi-analytic study are finally outlined from an extensive perspective.