Coherent axion electrodynamics in OSIRIS: a counter-propagating axion-photon parametric instability
We present a coherent axion-electrodynamics extension of the OSIRIS particle-in-cell code and use it to identify and benchmark a parametric axion-photon instability supported by two equal counter-propagating electromagnetic pumps. The module evolves a cell-centered axion field together with a separately stored first-order electromagnetic response on the native staggered OSIRIS grid. Re-examining the previously proposed strictly co-linear branch shows that it is removed when the axion-Maxwell equations are reduced consistently. A closely related standing-wave geometry, however, supports a distinct Floquet instability. We derive the coupled Floquet problem for an equal-amplitude counter-propagating pump pair and obtain a reduced analytic growth rate and cutoff for the dominant long-wavelength envelope branch. For an axion mass-to-pump-frequency ratio of 0.06 and a per-beam vector-potential amplitude of 0.3, simulations at coupling strengths of 0.60, 0.80, and 1.00 reproduce both the growth-rate spectrum and the coupling-dependent instability boundary. The reduced theory predicts envelope-mode cutoffs of 8.44, 10.80, and 13.23, while OSIRIS finds exponential growth through modes 8, 10, and 13, respectively, with the next resolved modes stable. The electromagnetic diagnostics additionally resolve exponentially growing sidebands at twice the pump wavenumber, while the zero-wavenumber electric component exhibits no sustained growth, as expected for the unstable Floquet eigenvector. The agreement provides an end-to-end benchmark of the coherent axion-electromagnetic coupling and demonstrates that parametric growth of the axion field is present in a two-beam pump geometry.