Observations from the EISCAT Svalbard Radar, for instance, demonstrate that the symmetry of the naturally occurring ion line can be broken by an enhanced, non-thermal, level of fluctuations, i.e., Naturally Enhanced Ion-Acoustic Lines (NEIALs). In a significant number of cases, the entire ion spectrum can be distorted, with the appearance of a third line, corresponding to a propagation velocity significantly below the ion acoustic sound speed. By numerical simulations, we consider one possible model accounting for the observations, suggesting that a primary process can be electron acoustic waves excited by a cold electron beam. Subsequently, an oscillating two-stream instability excites electron plasma waves which in turn decay to asymmetric ion lines. Our code solves the full Vlasov equation for electrons and ions, with the dynamics coupled through the electrostatic field derived from Poisson's equation.