The von Kármán–Howarth equations are derived for three-dimensional Hall magnetohydrodynamics in the case of a homogeneous and isotropic turbulence. From these equations, we derive exact scaling laws for the third-order correlation tensors. We show how these relations are compatible with previous heuristic and numerical results. These multiscale laws provide a relevant tool to investigate the nonlinear nature of the high-frequency magnetic field fluctuations in the solar wind or, more generally, in any plasma where the Hall effect is important.

• Received 1 October 2007

DOI:https://doi.org/10.1103/PhysRevE.77.015302