[en] Ray effect (RE) is a non-physical flaw of discrete ordinate methods characterized by spurious rays becoming sharper when small bright neutron sources radiate through low scattering media. While this effect has low impact on integral parameters (α and K_eff), it can ruin simulations of diagnostic problem in terms of neutron dose received by a detector. 3 cumulative factors may affect the RE intensity: the source size, the scattering cross-sections, and the mesh size. We introduce an adaptive Ray Effect Mitigation (REM) aimed at locally improving the angular accuracy of the 3 dimension AMR (adaptive mesh refinement) deterministic neutron transport code Styx. Promising preliminary results have been obtained using a recursively refined octahedron based sphere tessellation in place of the standard S_N quadrature. This angular mesh, referred to as T_N, has valuable features for local refinement