Large-amplitude current-driven plasma instabilities, which can transition to the Buneman instability, were observed in one-dimensional (1D) simulations to generate high-energy backstreaming ions. We investigate the saturation of multi-dimensional plasma instabilities and its effects on energetic ion formation. Such ions directly impact spacecraft thruster lifetimes and are associated with magnetic reconnection and cosmic ray inception. An Eulerian Vlasov--Poisson solver employing the grid-based direct kinetic method is used to study the growth and saturation of 2D2V collisionless, electrostatic current-driven instabilities spanning two dimensions each in the configuration (D) and velocity (V) spaces supporting ion and electron phase-space transport. Four stages characterise the electric potential evolution in such instabilities: linear modal growth, harmonic growth, accelerated growth via quasi-linear mechanisms alongside non-linear fill-in, and saturated turbulence. Its transition and isotropisation process bears considerable similarities to the development of hydrodynamic turbulence. While a tendency to isotropy is observed in the plasma waves, followed by electron and then ion phase space after several ion-acoustic periods, the formation of energetic backstreaming ions is more limited in the 2D2V than in the 1D1V simulations. Plasma waves formed by two-dimensional electrostatic kinetic instabilities can propagate in the direction perpendicular to the net electron drift. Thus, large-amplitude multi-dimensional waves generate high-energy transverse-streaming ions and eventually limit energetic backward-streaming ions along the longitudinal direction. The multi-dimensional study sheds light on interactions between longitudinal and transverse electrostatic plasma instabilities, as well as fundamental characteristics of the inception and sustenance of unmagnetised plasma turbulence.

翻译：一维（1D）模拟中发现，大振幅电流驱动等离子体不稳定性可演变为Buneman不稳定性，并产生高能反向流离子。我们研究多维等离子体不稳定性的饱和机制及其对高能离子形成的影响。这类离子直接影响航天器推进器寿命，并与磁重联及宇宙射线起源相关。采用基于网格直接动力学方法的欧拉Vlasov-Poisson求解器，研究二维（2D）位形空间和二维（2D）速度空间中无碰撞静电电流驱动不稳定性的增长与饱和过程，该不稳定性支持离子和电子相空间输运。此类不稳定性中的电势演化呈现四个阶段：线性模态增长、谐波增长、通过准线性机制与非线性填充共同驱动的加速增长，以及饱和湍流。其转变和各向同性化过程与流体动力学湍流发展具有显著相似性。尽管等离子体波在数个离子声波周期后呈现各向同性趋势（随后依次为电子和离子相空间），但在2D2V模拟中高能反向流离子的形成比1D1V模拟更受限。二维静电动力学不稳定性形成的等离子体波可向净电子漂移垂直方向传播。因此，大幅值多维波产生高能横向流离子，并最终限制纵向方向的高能反向流离子。该多维研究揭示了纵向与横向静电等离子体不稳定性之间的相互作用，以及无磁场等离子体湍流产生与维持的基本特征。