The lithiumbeam diagnostic provides a powerful edge plasma diagnostic. It enables the determination of electron density profiles in the scrape-of-layer and pedestal region with high spatial and temporal resolution (Dt 50ms, Dx 1cm). A fast neutral lithium beam (beam energy at JET: 55keV) is injected into the plasma and the line radiation emitted by the collisionally excited lithium is observed at different spatial positions using a periscope optic. The deconvolution of the emission profiles is based on a collisional-radiative model. The interaction of the Li atoms with the plasma is described by a system of coupled linear differential equations for the population densities Ni of the excited states i as functions of the beam coordinate x.