Abstract On March 30, 2002 within 17 min the four CLUSTER spacecraft crossed the Earth’s high-latitude magnetopause three times. We found that all three magnetopause current sheets are nearly co-planar on the scales of the CLUSTER spacecraft separation. The thickness of the current sheets changes from 1 to 40 magnetosheath-proton thermal gyro-radii. The thinnest (first crossed) magnetopause current sheet is locally open and might be electron driven. The frozen-in condition of the thermal ions is violated, the Hall term (Lorentz force term) is comparable to the electric field. Substantial electrostatic wave intensities are observed at lower-hybrid frequencies on the magnetospheric side of the thinnest magnetopause current sheet. We obtained that the quasi-linear diffusion rate due to lower-hybrid drift waves would not explain the formation of the adjacent boundary layer and a fast magnetopause thickening. Instead, the diffusion is enhanced due to strong, non-linear wave-particle interactions. We estimate the anomalous collision- and diffusion rates by calculating the correlation between the fluctuations of current density and magnetic field. The resulting strong anomalous diffusion can account for the formation of the adjacent magnetopause boundary layers and eventually the fast magnetopause thickening.