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

Abstract

We propose a new two-fluid model for a partially ionized magnetoplasma under gravity, in which electrons and neutrals are treated as a single fluid, while 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 becomes significantly modified by the influence of ion-neutral collisions (with frequency $\hat{I}{½}_{\mathrm{in}}$) 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 $\hat{I}º\equiv k_x/k_y$ and $f\equiv \hat{I}{½}_{\mathrm{in}}/\hat{I}{\text{c◯}}_{\mathrm{ci}}$, where $\hat{I}{\text{c◯}}_{\mathrm{ci}}$ 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 have a maximum for $\hat{I}º,f\ll 1$, or for $\hat{I}º>1$ and $f\sim 0.64$, and minimized for $f\gg 1$ irrespective of the value of $\hat{I}º$. 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.

8 pages, 2 figures; Revised throughout the text, Figure 1 added, and typos rectified