The Growth Rate of Langmuir Waves and Beam-Driven Mode, While Behavior of Relativistic Quantum Plasmas Under Ion Beam Influence: Dispersion and Instability Analysis

The dispersion characteristic of Langmuir, ion-acoustic, and beam-driven modes exciting in three species relativistic plasmas consisting of degenerate electrons with exchange potential effects, classical ions, and beam ions is investigated. The insertion of an ion beam enables the excitation of waves and instability in the plasma system. A quantum hydrodynamic (QHD) fluid model is applied to derive the dispersion relation of the aforementioned modes. It is found that the dispersion characteristics of Langmuir and ion-acoustic waves are significantly affected by the ion beam velocity and its number density. Numerical analysis of the dispersion relation indicates the presence of stable and unstable modes, and the exchange correlation has a significant effect on them. These findings are devoted to explaining the behavior of the modified electron plasma mode: similar to Langmuir waves, low-frequency ion-acoustic waves, and ion beam-driven modes. It is observed that beam modes dominate at small values of wavenumber. It is found that as the exchange potential decreases, the growth rate of Langmuir waves and beam-driven mode increases, while ion-acoustic waves have a very low frequency in the presence of exchange potential and high density. This work would help us understand complex astrophysical phenomena, semiconductor plasmas, etc.