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In this study we investigate the two-ion stream instability of plasma with a generalized Fermi-Dirac equation
of state (EoS) for electron fluid. We use a hydrodynamic set
of evolution equations for electron-ion plasma in order to
obtain the linearized set of equations from which the dispersion relation of the plasma is obtained in the presence
of ion acoustic wave instability. It is remarked that changes
in the electron plasma fluid parameters such as the chemical potential and electron fluid temperature have fundamental effects on the growth rate of ion acoustic waves instability. It is however found that the plasma degeneracy has
rather more significant effect on the two stream instability
phenomenon. The generalized equation of state of electrons
used in this research is valid for a wide density-temperature
regimes of plasmas relevant to both laboratory as well as astrophysical environments including high-energy density fusion plasmas and fully degenerate compact stellar plasmas.
We believe that using such a wide scope of plasma EoS provides a broader view of underlying physical mechanisms in
plasma dynamics and instabilities and better understanding
of astrophysical harsh plasma environments.
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