Impact of pressure anisotropy on the cascade rate of Hall-MHD turbulence with biadiabatic ions

The impact of ion pressure anisotropy on the energy cascade rate of Hall-MHD turbulence with biadiabatic ions and isothermal electrons is evaluated in three-dimensional direct numerical simulations, using the exact (or third-order) law derived in \citet{simon_exact_2022}. It is shown that pressure anisotropy can enhance or reduce the cascade rate, depending on the scales, in comparison with the prediction of the exact law with isotropic pressure, by an amount that correlates well with pressure anisotropy $a_p=\frac{p_\perp}{p_\parallel}\neq1$ that develops in simulations initialized with an isotropic pressure (${a_p}_0=1$). A simulation with initial pressure anisotropy, ${a_p}_0=4$, confirms this trend, exhibiting a stronger impact on the cascade rate, both in the inertial range and at larger scales, close to the forcing scales. Furthermore, a Fourier-based numerical method, to compute exact laws in numerical simulations in the full $(\ell_\perp,\ell_\parallel)$ increment plane, is presented.