Numerical analysis on the contribution of the singular perturbation by the Hall term to the spectrum of MHD turbulence using a shell model

We have developed a new shell model for the Hall magnetohydrodynamic (MHD) system to investigate the spectral properties of the plasma turbulence. Through the numerical simulation of the shell model, in the Hall MHD case, we find that the energy spectral index of the flow field indicates -5/3 in the whole inertial range, while the energy spectral index of the magnetic field indicates -5/3 (-7/3) in the large- (small-)scale region of the inertial range. The simulation of the conventional MHD case was also carried out, and we find that the energy spectral index of both the flow and magnetic fields indicate -5/3.