"Longitudinal space charge (LSC) effects are generally considered as detrimental in free-electron lasers as they can seed unwanted energy modulations and emittance growth. There has however been an increasing interest in devising accelerator beam lines capable of sustaining this LSC instability as a mechanism to operate as a coherent light source. In such a cascaded longitudinal space charge amplifier (LSCA), initial noise present in the beam density is amplified via the interplay of longitudinal space charge forces and properly located dispersive sections. To date most of these studies have been carried out with a one-dimensional impedance model for the LSC. We use an available grid-less three-dimensional N-body ``Barnes-Hut'' algorithm to simulate the 3D space charge force in the beam combined with ELEGANT and explore the limitations of the 1D model often used. We investigate, via numerical simulations, the performances of a cascaded LSCA beam line at the Fermilab's Advanced Superconducting Test Accelerator (ASTA)."