Self-generated Turbulent Reconnection in Three-dimensional Hall magnetohydrodynamics*

The plasmoid instability is known to mediate fast reconnection in collisional plasmas described by resistive magnetohydrodynamics (MHD). As a result of the plasmoid instability, the reconnection layer transforms into a chain of plasmoids interconnected by secondary current sheets in two dimensions (2D), and in three dimensions (3D) it gives rise to self-generated turbulent reconnection. In systems such as the solar atmosphere, reconnection can start in the collisional regime but transition to the collisionless regime as the current sheet fragmentation progresses. It is crucial to capture this change in reconnection physics. Within the realm of fluid descriptions, Hall MHD model is generally considered a minimal model that captures some key aspects of collisionless reconnection. However, 2D Hall MHD simulations often result in single-X-line reconnection after the onset of the plasmoid instability. This behavior significantly differs from that of fully kinetic particle-in-cell simulations, which often continue to form new plasmoids. In this work, we show that single-X-line reconnection is less likely in 3D Hall MHD simulations compared to that in 2D. In a certain parameter regime, the 3D Hall MHD simulation develops self-generated turbulent reconnection, whereas the 2D counterpart forms a single X-line. We contrast the self-generated turbulent state in Hall MHD with the corresponding resistive MHD result and theoretical predictions on Hall MHD turbulence.