  The interconversion of axionlike particles (ALPs) and 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). We present the first systematic study of ALP-photon conversion in more
realistic, turbulent fields from dedicated magnetohydrodynamic (MHD)
simulations, which we compare with GRF models. For GRFs, we analytically derive
the distribution of conversion ratios at fixed energy and find that it follows
an exponential law. We find that the MHD models agree with the exponential law
for typical, small-amplitude mixings but exhibit distinctly heavy tails for
rare and large mixings. We explain how non-Gaussian features, e.g.~coherent
structures and local spikes in the MHD magnetic field, are responsible for the
heavy tail. Our results suggest that limits placed on ALPs using GRFs are
robust.
