Kinetic-scale current sheets in the solar wind at 1 AU: Scale-dependent properties and critical current density

We present analysis of 17,043 proton kinetic-scale current sheets collected over 124 days of Wind spacecraft measurements in the solar wind at 11 Samples/s magnetic field resolution. The current sheets have thickness $\lambda$ from a few tens to one thousand kilometers with typical value around 100 km or from about 0.1 to 10$\lambda_{p}$ in terms of local proton inertial length $\lambda_{p}$. We found that the current density is larger for smaller scale current sheets, $J_0\approx 6\; {\rm nA/m^2} \cdot (\lambda/100\;{\rm km})^{-0.56}$ , but does not statistically exceed critical value $J_A$ corresponding to the drift between ions and electrons of local Alv\'{e}n speed. The observed trend holds in normalized units, $J_0/J_{A}\approx 0.17\cdot (\lambda/\lambda_{p})^{-0.51}$. The current sheets are statistically force-free with magnetic shear angle correlated with current sheet spatial scale, $\Delta \theta\approx 19^{\circ}\cdot (\lambda/\lambda_{p})^{0.5}$. The observed correlations are consistent with local turbulence being the source of proton kinetic-scale current sheets in the solar wind, while mechanisms limiting the current density remain to be understood.