Numerical Analysis of Resonant Axion-Photon Mixing: Part I

Many present-day axion searches attempt to probe the mixing of axions and photons, which occurs in the presence of an external magnetic field. While this process is well-understood in a number of simple and idealized contexts, a strongly varying or highly inhomogeneous background can impact the efficiency and evolution of the mixing in a non-trivial manner. In an effort to develop a generalized framework for analyzing axion-photon mixing in arbitrary systems, we focus in this work on directly solving the axion-modified form of Maxwell's equations across a simulation domain with a spatially varying background. We concentrate specifically on understanding resonantly enhanced axion-photon mixing in a highly magnetized plasma, which is a key ingredient for developing precision predictions of radio signals emanating from the magnetospheres of neutron stars. After illustrating the success and accuracy of our approach for simplified limiting cases, we compare our results with a number of analytic solutions recently derived to describe mixing in these systems. We find that our numerical method demonstrates a high level of agreement with one, but only one, of the published results. Interestingly, our method also recovers the mixing between the axion and magnetosonic-t and Alfv\'en modes; these modes cannot escape from the regions of dense plasma, but could non-trivially alter the dynamics in certain environments. Future work will focus on extending our calculations to study resonant mixing in strongly variable backgrounds, mixing in generalized media (beyond the strong magnetic field limit), and the mixing of photons with other light bosonic fields, such as dark photons.