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tokens: of the field at the cusp with respect to the current sheet axis is zero. The analysis of such irregular cusp structures in the literature were performed either analytically (e.g., Vekstein Priest 1992 , 1993 ; Uzdensky Kulsrud 1997 ; Wiegelmann et al. 1998 , 2000 ) or based on numerical simulations (e.g., Karlický Bárta 2007 ). In all of these investigations, the inner structure of the current distribution was neglected. Figure 1. Sketch of a helmet streamer with cusp point and singular current sheet and zoom to the inner cusp point region within the current sheet. The tiny red box inside the zoom defines the domain of our analysis. In this work, we investigate the internal structure of the current sheet at magnetic cusps. We concentrate on regular, mathematical cusp structures with a finite scale of the current distribution, in contrast to the singular current sheets mentioned before. This means that we are considering regular magnetic flux functions in the very close vicinity of the singular magnetic point, here the cusp point, to characterize the topological connections of the involved physical fields and to allow for transverse components of the magnetic field inside the current sheet (right part of Figure 1 ). 2. Objectives and Methodology The investigation of topological properties not only of the magnetic field , but also of the plasma flow and the non-idealness , requires the violation of ideal Ohm’s law, . The reason is that in 2D, the electric field is , where E z = const in the case of stationary translational invariant MHD. If the electric field component in z -direction does not vanish, i.e., , no regular solutions exist for the velocity field at a magnetic null point, meaning that the velocity field diverges. Therefore, one typically has to use nonideal Ohm’s law,to describe flows around a magnetic null point. In the case of resistive MHD, the nonideal term (or total electric field) is given by where η is the resistivity and is the electric current in the 2D case. In the following, we restrict the analysis to stationary flows. More specifically, we concentrate on the investigation of nonideal Ohm’s law, as it reflects magnetic topology and magnetic flux conservation and their violation. Furthermore, we focus on cusp configurations that are structurally unstable but topologically classifiable magnetic singularities. For structurally stable magnetic null points, an indispensable criterion for magnetic reconnection is that the plasma flow can cross magnetic separatrices, where the plasma flow is usually connected to an X-type stagnation-point flow. Cusp structures are thought to result from reconnection processes. However, as in the strict mathematical sense, no magnetic separatrices exist at or near cusps, the question arises how the plasma streams in the vicinity of such structures. To describe such flows, it is necessary to find solutions of the nonideal Ohm’s law, meaning that the plasma flow and the non-idealness are