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With axions now a primary candidate for dark matter, understanding theirindirect astrophysical signatures is of paramount importance. Key to this isthe production of photons from axions in magnetised astrophysical plasmas.While simple formulae for axion-photon mixing in 1D have been sketched severaldecades ago, there has recently been renewed interest in robust calculationsfor this process in arbitrary 3D plasmas. These calculations are vital forunderstanding, amongst other things, the radio production from axion darkmatter conversion in neutron stars, which may lead to indirect axion darkmatter detection with current telescopes or future searches, e.g., by the SKA.In this paper, we derive the relevant transport equations in magnetisedplasmas. These equations describe both the production and propagation ofphotons in an arbitrary 3D medium due to the resonant conversion of axions intophotons. They also fully incorporate the refraction of photons, and we find noevidence for a conjectured phenomenon of dephasing. Our result is free ofdivergences that plagued previous calculations, and our kinetic theorydescription provides a direct link between ray tracing and the productionmechanism. These results mark an important step toward solving one of the majoropen questions concerning indirect searches of axions in recent years, namelyhow to compute the photon production rate from axions in arbitrary 3D plasmas.

Axion-Photon Conversion in 3D Media and Astrophysical Plasmas