Abstract
Three-dimensional (3D) modulational instability (MI) and ion-acoustic (IA) envelopes are studied in a quantized degenerate magnetoplasma, whose constituents are the trapped/untrapped electrons and anisotropic positive ions. By using quantum hydrodynamic equations and the multiscale reductive perturbation technique, a 3D nonlinear Schrödinger equation is derived to account for electron quantization and ion pressure anisotrophy effects. The potential excitations are shown stable (unstable) against the perturbations for
K
c
<
0
(
K
c
>
0
)
, where
K
c is a critical parameter that accounts for the longitudinal (transverse) dispersion(s) and nonlinearity effects. Numerically, the nonlinear evolution of IA wavepackets into a 3D MI may be revealed in the ranges of low and high frequencies
0
<
ω
≤
0.05 and
0.75
≤
ω
≤
1.1. The quantizing magnetic field reduces (enhances) the group speed (wave frequency) of IA excitations, concentrating the wave energy to favor the modulational instability. Finite electronic temperature
(
viz
.
,
T
e
≤
10
keV
) enhances the untrapped electrons and significantly widens the instability domain
K
c
>
0. The ionic pressure anisotropy increases the wave frequency
(
ω
), piles up the harmonics under
K
c
>
0, and give rise to modulational instability. The quantized magnetic field and anisotropic pressure reduce the amplitude and spatial extension of the IA rogons. This study is important for understanding the 3D MI and unstable excitations in degenerate plasmas, relevant to white dwarfs, neutron stars, and high-energy density experiments, where strong magnetic field quantizes the dynamics of trapped/untrapped electrons.