In this work, we relate some recent advances in the simulation of non-linear behavior of TWTs by means of a home made lagrangian large signal code. Instead of using the well known charged particle model based on infinite planes weighted by space charge reduction factor, we compute the interaction among particles using the n-body interaction force calculated via the Green's function method. The e-beam particles are assumed to be rigid and uniformly charged disks with infinitesimal thickness. This beam model can be used for either non-relativistic klystron and TWT simulations. Preliminary results on amplification are shown here.