Pulsar scintillation arcs formed from branched flow

Radio waves propagating through the interstellar medium are influenced by variations in plasma density. For spatially localised plasma structures along the line of sight, time-delay Doppler analyses of pulsars often reveal scintillation arcs in the secondary spectrum, frequently exhibiting a parabolic morphology. In the thin-screen approximation, the arc curvature is commonly used to infer the distance to the plasma concentration, which is modelled - via Kirchhoff-Fresnel diffraction theory - as an effective phase screen imposed by the column density of a localised disturbance. Here, we identify several limitations of the thin-screen model that necessitate a fully three-dimensional treatment, without reducing the problem to a projected screen density. We show that the arc curvature can vary depending on the three-dimensional structure of the plasma, rendering it a less reliable indicator of distance. Moreover, when volume propagation is considered, asymmetries and a richer variety of features emerge in the secondary spectrum compared to those predicted by the thin-screen approximation. We conjecture that these phenomena are linked to the onset of branched flow produced by a sequence of weak but correlated scattering events.