We have implemented non-ideal Magneto-Hydrodynamics (MHD) effects in the
Adaptive Mesh Refinement (AMR) code RAMSES, namely ambipolar diffusion and
Ohmic dissipation, as additional source terms in the ideal MHD equations. We
describe in details how we have discretized these terms using the adaptive
Cartesian mesh, and how the time step is diminished with respect to the ideal
case, in order to perform a stable time integration. We have performed a large
suite of test runs, featuring the Barenblatt diffusion test, the Ohmic
diffusion test, the C-shock test and the Alfven wave test. For the latter, we
have performed a careful truncation error analysis to estimate the magnitude of
the numerical diffusion induced by our Godunov scheme, allowing us to estimate
the spatial resolution that is required to address non-ideal MHD effects
reliably. We show that our scheme is second-order accurate, and is therefore
ideally suited to study non-ideal MHD effects in the context of star formation
and molecular cloud dynamics