Anisotropy in hall MHD turbulence due to a mean magnetic field

The development of anisotropies in an initially isotropic spectrum is studied numerically for compressible magnetohydrodynamic (MHD) turbulence in the presence of the Hall term. Building on a previous study where it was shown that. spectral cascades in the Hall MHD system differ from the standard MHD case, particularly at high cross-helicities, we use an isotropic high cross-helicity initial state to study anisotropies of the Hall MHD system for a variety of mean magnetic field strengths and sonic Mach numbers. Strong anisotropies, which maximize at the ion-inertial length scale, appear for several plasma states and are categorized according to their plasma beta beta: high-beta Hall MHD simulations (beta > 1) show strong anisotropies relative to the standard MHD case, intermediate-beta Hall MHD simulations (beta approximate to 1) show smaller anisotropy differences relative to the standard MHD case, and low-beta Hall MHD simulations (beta < 1) again show strong anisotropies relative to the standard model. It is suggested that these anisotropy enhancements are due to nonlinear cascade suppression of propagating Alfven waves in the field-aligned direction. This is different from the dynamics in the highly oblique directions, where nonpropagating density and magnetic-energy anticorrelations appear.