Spontaneous Chiral Symmetry Breaking of Hall Magnetohydrodynamic Turbulence

Hall magnetohydrodynamics (MHD) is investigated through three-dimensional direct numerical simulations. We show that the Hall effect induces a spontaneous chiral symmetry breaking of the turbulent dynamics. The normalized magnetic polarization is introduced to separate the right-(R) and lefthanded (L) fluctuations. A classical k(-7/3) spectrum is found at small scales for R magnetic fluctuations which corresponds to the electron MHD prediction. A spectrum compatible with k(-11/3) is obtained at large-scales for the L magnetic fluctuations; we call this regime the ion MHD. These results are explained heuristically by rewriting the Hall MHD equations in a succinct vortex dynamical form. Applications to solar wind turbulence are discussed.