Nonlinear evolution of dust-acoustic envelope solitons in electron-depleted dusty plasmas with non-thermal ions

A theoretical investigation has been conducted on the modulation dynamics of dust-acoustic envelope solitons (DAES) and also on their modulational instability criteria in an unmagnetized, electron-depleted dusty plasma system containing inertial positively charged as well as negatively charged dust species and non-inertial positive ions following a non-thermal Cairns distribution function. The nonlinear Schrödinger equation, which describes the formation and stability/instability of envelope modes, is derived via the reductive perturbation approach. The formation of DAES and the occurrence of instability conditions of DAES in the proposed plasma system are analyzed numerically. It is found that the stability and the instability regimes for the propagation of DAES are dependent on the sign of the nonlinear coefficient. It is examined that the fundamental characteristics of DAES, including the modulation instability conditions of the wave profile and the formation of DAES, are significantly influenced by various plasma parameters. These parameters encompass factors such as the mass and charge state of the dust, as well as the number density and temperature of the ions. The results of our present study are expected to contribute significantly to the comprehension of localized envelope modes in various astrophysical contexts [e.g., the Van Allen radiation belt, the solar atmosphere, the D-region (H+,O2−) and F-region (H+, H−) of Earth’s ionosphere, the upper atmosphere of Titan, etc.] and laboratory settings (e.g., plasma processing reactors, the semiconductor industry, intense laser fields, tokamaks, etc.) where the plasma systems comprise both negatively and positively charged massive dust grains alongside non-thermally distributed positive ions.