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We analyze the stability of a dilute plasma with thermal and compositiongradients in the limit where conduction is slow compared to the dynamicaltimescale. We find necessary and sufficient conditions for stability when thebackground magnetic field is either parallel or perpendicular to the thermaland composition gradients that are parallel to the gravitational field. Weprovide approximate solutions for all the relevant modes involved, which aredriven by gravity, conduction, and diffusion. We discuss the astrophysicalimplications of our findings for a representative galaxy cluster where heliumhas sedimented.

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