Trapped electrons, trapped ions and quantum effects contributions in instability analysis of dust acoustic waves in dense quantum plasma

A reductive perturbation approach was used for both linear and nonlinear analysis, and the related Quantum Zakharov–Kuznetsov (QZK) equation is deduced for dense quantum Plasma structure that is magnetized and composed of negatively charged heavy dust, electrons which are in quantum trapping distribution and classical trapped positively charged ions. The small-k perturbative expansion approach is used to investigate the instability requirements of nonlinearity that propagate obliquely into an external magnetic field. The current study's principal finding is that the primary properties involving linear and nonlinear modalities and also the dust acoustic wave energy are altered clearly by changes in concentrations and temperature of degenerate trapped electrons and ions. Furthermore, the wave instability growth-rate is discovered to decrease dust density increase or quantum diffraction parameter decrease. The present results help us understand the properties and instability circumstances associated with electrostatic waves in white dwarfs and pulsar magnetosphere as examples of space phenomena. It also contributes to many densely packed systems generated plasmas found in laboratories, such as those in semiconductor, high-intensity laser interactions with solid matter, and within tokamaks, for the development of fusion energy. Understanding quantum plasma and its behavior in tokamaks is critical for attaining and sustaining the conditions required for sustained fusion reactions.