We describe URCHIN, a reverse ray tracing radiative transfer scheme optimised to model self-shielding from the post-reionisation ultraviolet (UV) background in cosmological simulations. The reverse ray tracing strategy provides several benefits over forward ray tracing codes including: (1) the preservation of adaptive density field resolution (2) completely uniform sampling of gas elements by rays; (3) the preservation of galilean invariance; (4) the ability to sample the UV background spectrum with hundreds of frequency bins; and (5) exact preservation of the input UV background spectrum and amplitude in optically thin gas. The implementation described here focuses on Smoothed Particle Hydrodynamics (SPH). However, the method can be applied to any density field representation in which resolution elements admit ray intersection tests and can be associated with optical depths. We characterise the errors in our implementation in stages beginning with comparison to known analytic solutions and ending with a realistic model of the z = 3 cosmological UV background incident onto a suite of spherically symmetric models of gaseous galactic halos.
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