Three-dimensional Hall Magnetohydrodynamics Turbulence

Direct numerical simulations of three-dimensional incompressible Hall magnetohydrodynamics are performed in a triple periodic box at moderate resolution. To investigate the transition from a large scale MHD turbulence regime to a small scale dispersive one we introduce a variable ion inertial length scale d(I)(t) which characterizes the strength of the Hall effect. By slowly increasing d(I) we are able to move our window of resolution from the pure MHD scales to the full Hall MHD one. We estimate the value of d(I) from which the Hall MHD regime appears. The present analysis is relevant in the context of solar wind turbulence where the power law spectrum for the magnetic field fluctuations steepens significantly at frequencies higher than a fraction of Hertz. This change of turbulence regime raises fundamental questions in plasma physics about the transition from a fluid model to a pure kinetic one.