Gravitational instability in partially ionized plasmas: A two-fluid approach

We propose a new two-fluid model for a partially ionized magnetoplasma under gravity, where electrons and neutrals are treated as a single fluid, and singly charged positive ions are a separate fluid. We observe that the classical result of gravitational instability (also known as Rayleigh-Taylor instability) in fully ionized plasmas is significantly modified by the influence of ion-neutral collisions (with frequency $\nu_{\rm{in}}$) and transverse wave numbers ($k_x$ and $k_y$). The instability growth rate can be enhanced or decreased depending on the values of the ratios $\kappa\equiv k_x/k_y$ and $f\equiv\nu_{\rm{in}}/\Omega_{\rm{ci}}$, where $\Omega_{\rm{ci}}$ is the ion-cyclotron frequency. We also estimate the growth rates relevant to the ionospheric E-region and solar atmosphere, noting that such growth rates can be maximized for $\kappa,~f\ll1$, or for $\kappa>1$ and $f\sim0.64$, and minimized for $f\gg1$ irrespective of the value of $\kappa$. Furthermore, the timescale of instability ranges from $1$ minute to $2$ minutes in the solar atmosphere, while in the E region, it ranges from $1$ minute to $80$ minutes. The latter can be a satisfactory result for the reported lifetime of solar prominence threads.