Helical Mode Absolute Statistical Equilibrium of Ideal Three-Dimensional Hall Magnetohydrodynamics

Using the Fourier helical decomposition, we obtain the absolute statistical equilibrium spectra of left- and right-handed helical modes in the incompressible ideal Hall magnetohydrodynamics (MHD). It is shown that the left-handed helical modes play a major role on the spectral transfer properties of turbulence when the generalized helicity and magnetic helicity are both positive. In contrast, the right-handed helical modes will play a major role when both are negative. Furthermore, we also find that if the generalized helicity and magnetic helicity have opposite signs, the tendency of equilibrium spectra to condense at the large or small wave numbers will be presented in different helical sectors. This indicates that the generalized helicity dominates the forward cascade and the magnetic helicity dominates the inverse cascade properties of the Hall MHD turbulence.