Simulation of Relativistic Force-free Magnetohydrodynamic Turbulence

We present numerical studies of 3-dimensional magnetohydrodynamic (MHD) turbulence in a strongly magnetized medium in the extremely relativistic limit, in which the inertia of the charge carriers can be neglected. We have focused on strong Alfvenic turbulence in the limit. We have found the following results. First, the energy spectrum is consistent with a Kolmogorov spectrum: $E(k)\sim k^{-5\mathrm{/}3}$. Second, turbulence shows a Goldreich-Sridhar type anisotropy: $k_{\mathrm{\parallel }}\propto k_{\perp }^{2\mathrm{/}3}$, where $k_{\mathrm{\parallel }}$ and $k_{\perp }$ are wavenumbers along and perpendicular to the local mean magnetic field directions, respectively. These scalings are in agreement with earlier theoretical predictions by Thompson & Blaes.