Axion dissipation in conductive media and neutron star superradiance

In axion electrodynamics, magnetic fields enable axion-photon mixing. Recent proposals suggest that rotating, conductive plasmas in neutron star magnetospheres could trigger axion superradiant instabilities -- an intriguing idea, given that such instabilities are typically associated with rotating black holes. In this work, we extend these investigations by properly incorporating plasma dynamics, particularly the plasma-induced photon effective mass, which suppresses the axion-photon mixing. Using two toy models for the conductive regions in the magnetosphere and accounting for fluid dynamics in both the frequency and time domain, we show that typical astrophysical plasma densities strongly inhibits the axionic instability. While our results assumes flat spacetime, the conclusions also apply to axion bound states in curved spacetimes, making neutron star superradiance less viable than previously thought. As a byproduct of our work, we provide a detailed description of axion electrodynamics in dissipative plasmas and uncover phenomena such as low-frequency axion "tails" and axion-induced electrostatic fields in dense plasmas.