A comparison of methods for finding magnetic nulls in simulations and in situ observations of space plasmas

Context. Magnetic nulls are ubiquitous in space plasmas, and are of interest as sites of localised energy dissipation or magnetic reconnection. As such, a number of methods have been proposed for detecting nulls in both simulation data and in situ spacecraft data from Earth's magnetosphere. The same methods can be applied to detect stagnation points in flow fields.Aims. In this paper we describe a systematic comparison of different methods for finding magnetic nulls. The Poincare index method, the first-order Taylor expansion (FOTE) method, and the trilinear method are considered.Methods. We define a magnetic field containing fourteen magnetic nulls whose positions and types are known to arbitrary precision. Furthermore, we applied the selected techniques in order to find and classify those nulls. Two situations are considered: one in which the magnetic field is discretised on a rectangular grid, and the second in which the magnetic field is discretised along synthetic "spacecraft trajectories" within the domain.Results. At present, FOTE and trilinear are the most reliable methods for finding nulls in the spacecraft data and in numerical simulations on Cartesian grids, respectively. The Poincare index method is suitable for simulations on both tetrahedral and hexahedral meshes.Conclusions. The proposed magnetic field configuration can be used for grading and benchmarking the new and existing tools for finding magnetic nulls and flow stagnation points.