Hall-MHD in driven turbulence FLASH simulations

Magnetic fields are present in various astrophysical environments, and they play a dynamic role in shaping cosmic phenomena. Traditional mechanisms that generate seed magnetic fields in initially unmagnetized plasma fall short in explaining the observed magnitudes of astrophysical magnetic fields. Mechanisms that amplify and maintain magnetic fields at observed levels address this disparity. The fluctuation dynamo is one such mechanism where stochastic motions of plasma lead to the stretching, twisting, and folding of magnetic field lines. In this process, magnetic fields undergo exponential amplification, leading to saturation and approximate equipartition with fluid kinetic energy. While the fluctuation dynamo is well understood within the framework of resistive magnetohydrodynamics (MHD), our work aims to explore beyond ideal/resistive MHD. The transport of magnetic flux and energy in high energy density plasma experiments are governed by an extended magnetohydrodynamics (xMHD) ansatz, which includes the Hall term in the generalized Ohm's law. Here, we discuss the details of the Hall-MHD implementation in the FLASH code, a publicly available, high-performance computing, multiphysics simulation code, developed by the Flash Center for Computational Science. We investigate the role of the Hall effect in magnetic field generation and evolution by studying 3D simulations of the Hall-MHD equations subjected to stochastic drive. Our results reveal variations in the efficiency of the dynamo process under a range of conditions. Specifically, we observe that as the Hall parameter tends towards conditions resembling resistive MHD, the small-scale dynamo exhibits faster growth and saturates at larger amplitudes of the magnetic field. Conversely, larger Hall parameter values, indicating a dominant Hall effect, cause saturation of the magnetic field at smaller amplitudes.