Phase-Space Dynamics of Electron Acoustic Turbulence in 2D-2V Inhomogeneous Plasmas

In weakly collisional plasmas, a complete understanding of the turbulent cascade at kinetic scales remains a fundamental and elusive problem. In this regime, spatial and velocity-space fluctuations are inherently coupled, giving rise to complex patterns in which electrostatic waves continuously interact with a network of nonlinear coherent structures. This complex interplay, potentially ubiquitous across turbulent plasma environments, is thought to play a central role in controlling energy transport and dissipation. In this research, we report the first direct investigation of the nonlinear interaction between electrostatic waves and density holes at Debye and sub-Debye scales, using high-resolution Vlasov–Poisson simulations to model the dynamics of a four-dimensional (2D–2V) plasma distribution. In particular, we construct an inhomogeneous equilibrium embedded in a proton background, consisting of a periodic lattice of electron density gaps, and perturb it with nonlinear plasma oscillations in the form of turbulent electron acoustic waves. The resulting dynamics reveal a distinctive regime in which wave–hole interaction redirects the originally one-directional, wave-driven cascade into the full phase space, uncovering a previously unexplored pathway for the emergence of phase-space structures and the transfer of energy across kinetic scales.