Scale Statistics of Current Sheets in Relativistic Collisionless Plasma Turbulence

We analyze distributions of the spatial scales of coherent intermittent structures -- current sheets -- obtained from fully kinetic, two-dimensional simulations of relativistic plasma turbulence using unsupervised machine-learning data dissection. We find that the distribution functions of sheet length $\ell$ (longest scale of the analyzed structure in the direction perpendicular to the dominant guide field) and curvature $r_c$ (radius of a circle fitted to the structures) can be well-approximated by power-law distributions, indicating self-similarity of the structures. The distribution for the sheet width $w$ (shortest scale of the structure) peaks at the kinetic scales and decays exponentially at larger values. The data shows little or no correlation between $w$ and $\ell$, as expected from theoretical considerations. The typical $r_c$ depends linearly on $\ell$, which indicates that the sheets all have a similar curvature relative to their sizes. We find a weak correlation between $r_c$ and $w$. Our results can be used to inform realistic magnetohydrodynamic sub-grid models for plasma turbulence in high-energy astrophysics.