Recent observations of the solar wind have pointed out the existence of a cascade of magnetic energy from the scale of the proton Larmor radius ρ(p) down to the electron Larmor radius ρ(e) scale. In this Letter we study the spatial properties of magnetic field fluctuations in the solar wind and find that at small scales the magnetic field does not resemble a sea of homogeneous fluctuations, but rather a two-dimensional plane containing thin current sheets and discontinuities with spatial sizes ranging from l >/~ ρ(p) down to ρ(e) and below. These isolated structures may be manifestations of intermittency that localize sites of turbulent dissipation. Studying the relationship between turbulent dissipation, reconnection, and intermittency is crucial for understanding the dynamics of laboratory and astrophysical plasmas.
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