The Stability of Dilute Plasmas with Thermal and Composition Gradients. I. The Slow Conduction Limit: Overstable Gravity Modes

We analyze the stability of a dilute plasma with thermal and composition gradients in the limit where conduction is slow compared to the dynamical timescale. We find necessary and sufficient conditions for stability when the background magnetic field is either parallel or perpendicular to the thermal and composition gradients that are parallel to the gravitational field. We provide approximate solutions for all the relevant modes involved, which are driven by gravity, conduction, and diffusion. We discuss the astrophysical implications of our findings for a representative galaxy cluster where helium has sedimented.