A two-dimensional numerical study of ion-acoustic turbulence*

We conduct a set of comprehensive simulations to investigate the linear and nonlinear evolution of ion-acoustic instability (IAI) in a collisionless plasma. The simulations are performed using a two-dimensional (2D2V) Vlasov-Poisson numerical method for the first time. To ensure the physical realizability of the system, we initialize a stable configuration and gradually drive it towards instability by applying a weak external electric field, thereby avoiding super-critical initial conditions. The nonlinear evolution of ion-acoustic turbulence (IAT) is carefully examined, including the analysis of particle distribution functions, particle heating, two-dimensional wave spectrum, and the resulting anomalous resistivity.  Our simulations reveal a significant finding: a steady saturated nonlinear state is not achieved during the simulation time. Instead, we observe that the strong heating of ions gradually suppresses the instability, leading to its eventual shutdown, which implies that the anomalous resistivity associated with IAT is transient and short-lived. During the late nonlinear evolution of the system, we observe the triggering of electron acoustic waves (EAWs). These waves emerge as a result of the strong modifications to the particle distribution caused by the presence of IAT. This observation aligns with recent numerical and experimental studies that have investigated ion-acoustic waves.