Coulomb bubbles: Overstable driving of magnetoacoustic waves due to the rapid and anisotropic diffusion of energy

We perform a linear magnetohydrodynamic perturbation analysis for a stratified magnetized envelope where the diffusion of heat is mediated by charged particles that are confined to flow along magnetic field lines. We identify an instability, the "Coulomb bubble instability," which may be thought of as standard magnetosonic fast and slow waves, driven by the rapid diffusion of heat along the direction of the magnetic field. We calculate the growth rate and stability criteria for the Coulomb bubble instability for various choices of equilibrium conditions. The Coulomb bubble instability is intimately related to the photon bubble instability. The bulk thermodynamic properties of both instability mechanisms are quite similar in that they require the timescale for heat to diffuse across a wavelength to be shorter than the corresponding wave crossing time. Furthermore, overstability occurs only as long as the driving resulting from the presence of the background heat flux can overcome diffusive Silk damping. However, the geometric and therefore mechanical properties of the Coulomb bubble instability are the complete mirror opposite of the photon bubble instability. The Coulomb bubble instability is most strongly driven for weakly magnetized atmospheres that are strongly convectively stable. We briefly discuss a possible application of astrophysical interest: diffusion of interstellar cosmic rays in the hot T ≲ 10⁶K Galactic corona. We show that for commonly accepted values of the cosmic-ray and gas pressure as well as its overall characteristic dimensions, the Galactic corona is in a marginal state of stability with respect to a cosmic-ray Coulomb bubble instability. The implication being that a cosmic-ray Coulomb bubble instability plays a role in regulating both the pressure and transport properties of interstellar cosmic rays, while serving as a source of acoustic power above the Galactic disk.