Behavior of axion-like particles in smoothed out domain-like magnetic fields

Understand

Basically, in certain circumstances axion-like particles (ALPs) substantially enhance the photon survival probability $P_{\gamma \to \gamma} ({\cal E})$ of a beam emitted by a far-away source through the mechanism of photon-ALP oscillation (${\cal E}$ denotes the energy).

• But in order for this to work, an external magnetic field ${\bf B}$ must be present.
• In several cases ${\bf B}$ is modeled as a domain-like network with `sharp edges': all domains have the same size $L_{\rm dom}$ (set by the ${\bf B}$ coherence length) and the same strength B, but the direction of ${\bf B}$ changes randomly and abruptly from one domain to the next.
• It is obviously a highly mathematical idealization wherein the components of ${\bf B}$ are discontinuous across the edges (whence the name sharp edges).