Anisotropy in Hall MHD turbulence due to a mean magnetic field

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Abstract
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 β: high-β Hall MHD simulations (β>1) show strong anisotropies relative to the standard MHD case, intermediate-β Hall MHD simulations (β≈1) show smaller anisotropy differences relative to the standard MHD case, and low-β Hall MHD simulations (β<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 Alfvén waves in the field-aligned direction. This is different from the dynamics in the highly oblique directions, where non-propagating density and magnetic-energy anticorrelations appear.

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