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tokens: that the angle between and x is . Second, we restrict to layers with the minimum variance component . This configuration restricts the analysis of the current to the cases reported in the cartoon of Figure 2 (b). These constraints ensure that the above surrogate computed from the Cluster 4 data is very close to the actual current density. The current layers detected by the PVI method under the above constraints seem to have a self-consistent shape at time lags that range from inertial to sub-proton scales, resembling equilibrium solutions of both fluid-like and kinetic plasmas. The simplest analytical model that could represent thin current layers on kinetic scales is the well-known Harris sheet (Harris 1961 ), which is widely used to describe a plasma sheath confined between two regions of oppositely directed magnetic field. It is a kinetic equilibrium and the earliest exact analytical solution of the Vlasov equation. Under some assumptions, the magnetic field follows a 1D hyperbolic-tangent profile. The number of structures selected by PVI ranges from thousands () to hundreds . Applying the geometrical restrictions of the minimum variance analysis described above, we found that the Harris profiles well describe 5% and 10% of the discontinuities. Figure 3 shows two examples of such as 1D current sheets in their local minimum variance reference frame. The time duration is (a) and (b), which correspond to 60 km and 420 km along x , respectively, assuming the validity of the Taylor frozen-in hypothesis. The maximum variance component B l performs a smooth, large-amplitude rotation, while . Note that B m , albeit very small, displays a multi-polar signature, typical of solar wind reconnection exhausts (Eriksson et al. 2015 ). B l , B m , and B n refer to the fluctuating part of the magnetic field after that the mean value, computed on the time duration of the discontinuity, is subtracted. For the above structures, the direction of the removed average field is almost aligned to and perpendicular to . Moreover, the full magnetic field component along is constant and equal to the removed average field over the interval so that the geometry corresponds to that of a common Harris sheet + guide field, as reported pictorially in Figure 2 (b). Figure 3. Fluctuations of the magnetic field (after subtracting the mean value) in the local minimum variance frame, in a discontinuity at electron (a) and sub-proton (b) scales. B l is reported with a solid (blue), B n with a dotted–dashed (green), and B m with a dashed (red) line. The thick (black) line represents the Harris profile. Panels (c) and (d) report the surrogate current density (red dashed) for the discontinuities in panels (a) and (b), respectively, together with the Harris current (black solid). The best fits from the Harris model , where and λ is the half-thickness of the layer, are also compared in the same figures (thick lines), indicating very good agreement with the plasma equilibrium theory.