  The ring system and small satellites of Neptune were discovered during
Voyager 2 flyby in 1989 (Smith et al.1989). In this work we analyse the
diffusion maps which can give an overview of the system. As a result we found
the width of unstable and stable regions close to each satellite. The innermost
Galle ring, which is further from the satellites, is located in a stable
region, while Lassel ring (W = 4000 km) has its inner border in a stable region
depending on its eccentricity. The same happens to the Le Verrier and Adams
rings , they are stable for small values of the eccentricity. They can survive
to the close satellites perturbation only for values of e < 0.012. When the
solar radiation force is taken into account the rings composed by 1{$\mu$}m
sized particles have a lifetime of about $10^4$ years while larger particles
(10{$\mu$}m in radius) can survive up to 10 5 years. The satellites Naiad,
Thalassa and Despina can help replenish the lost particles of the Le Verrier,
Arago and Lassel rings, while the ejecta produced by Galatea, Larissa and
Proteus do not have enough velocity to escape from the satellite gravity.

Earth and Planetary Astrophysics