Modulational instability and ion-acoustic envelopes in dense plasmas with trapped/untrapped electrons

The linear and nonlinear properties of ion-acoustic rogons and associated modulational instability (MI) are studied in an unmagnetized dense electron-ion plasma, containing degenerate trapped/untrapped electrons and classical adiabatic ions. Solving the quantum hydrodynamic equations by using the standard multiscale reductive perturbation technique, a nonlinear Schrödinger equation is derived, which admits potential envelopes to be stable (unstable) against the perturbations for PQ < 0 (PQ>0). Here, P and Q are the dispersion and nonlinearity coefficients, respectively. It is numerically shown that for the vanishing ionic temperature ratio (σ=0), the parametric regime at perturbation wavelengths λ≥2.5λeff (λ≤2.5λeff) is always modulationally stable (unstable); here, λeff is the effective screening length. Moreover, the finite ionic temperature (Ti≤10 eV) restores the modulational stability at relatively short wavelengths by confining MI within the perturbation range 4.5λeff≤λ≤1.3λeff. The parameter Θ(=Te/22μ) shows the impact of the untrapped electrons which not only enhances (reduces) the angular frequency (group speed) of the envelope but also piles up the wave crests (energy) to produce the MI. Furthermore, due to degenerate trapped electrons, the instability domain gets widened in the limit PQ > 0 and leads to the onset of MI and unstable excitations. The study has important results for understanding the mechanism of MI and unstable modes in the context of astrophysical environments (white dwarfs, neutron stars, etc.,) and high density experiments.