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The conversion of axionlike particles (ALPs) into photons in magnetised astrophysical environments provides a promising route to search for ALPs. The strongest limits to date on light ALPs use galaxy clusters as ALP-photon converters. However, such studies traditionally rely on simple models of the cluster magnetic fields, with the state-of-the-art being Gaussian random fields (GRFs). In this talk I discuss the first systematic study of ALP-photon conversion in more realistic, turbulent fields from dedicated magnetohydrodynamic (MHD) simulations, which are compared to GRF models. An important result is that MHD models agree with the exponential law for typical, small-amplitude mixings but exhibit distinctly heavy tails for rare and large mixings. This behavior is associated to non-Gaussian, local spikes in the MHD magnetic field. Limits placed on ALPs using GRFs are conservative but MHD models are necessary to reach the full potential of astrophysical searches.