Extragalactic photon-ALP conversion at CTA energies

Magnetic fields in extragalactic space between galaxy clusters may induce conversions between photons and axion-like particles (ALPs), thereby shielding the photons from absorption on the extragalactic background light. For TeV gamma rays, the oscillation length ($l_{\mathrm{o}\mathrm{s}\mathrm{c}}$) of the photon-ALP system becomes inevitably of the same order as the coherence length of the magnetic field ($l$) and the length over which the field changes significantly (transition length $l_{\mathrm{t}}$) due to refraction on background photons. We derive exact statistical evolution equations for the mean and variance of the photon and ALP transfer functions in the non-adiabatic regime ($l_{\rm osc} \sim l \gg l_{\rm t}$). We also make analytical predictions for the transfer functions in the quasi-adiabatic regime ($l_{\mathrm{o}\mathrm{s}\mathrm{c}}\ll l,l_{\mathrm{t}}$). Our results are important in light of the upcoming Cherenkov Telescope Array (CTA), and may also be applied to models with non-zero ALP masses.