  In this work, we investigate the local effects of a single short-range
impurity on the electron system of a short ballistic graphene Josephson
Junction. Within the Dirac-Bogoliubov-De Gennes approach, we systematically
analyze the local density states, whose subgap energy dependence enables us to
distinguish between elastic and inelastic scattering processes and identify the
magnetic nature of the impurity. Furthermore, we observe that the spatial
dependence of the local density of states is a sensitive probe of the
microscopic processes resulting in subgap impurity-induced bound states. The
Fourier analysis evidences the wavevectors related to the momenta of the high
transmissive channels in ballistic graphene.
