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Thanks to multi-spacecraft mission, it has recently been possible to directlyestimate the current density in space plasmas, by using magnetic field timeseries from four satellites flying in a quasi perfect tetrahedronconfiguration. The technique developed, commonly called 'curlometer' permits agood estimation of the current density when the magnetic field time series varylinearly in space. This approximation is generally valid for small spacecraftseparation. The recent space missions Cluster and Magnetospheric Multiscale(MMS) have provided high resolution measurements with inter-spacecraftseparation up to 100 km and 10 km, respectively. The former scale correspondsto the proton gyroradius/ion skin depth in 'typical' solar wind conditions,while the latter to sub-proton scale. However, some works have highlighted anunderestimation of the current density via the curlometer technique withrespect to the current computed directly from the velocity distributionfunctions, measured at sub-proton scales resolution with MMS. In this paper weexplore the limit of the curlometer technique studying synthetic data setsassociated to a cluster of four artificial satellites allowed to fly in astatic turbulent field, spanning a wide range of relative separation. Thisstudy tries to address the relative importance of measuring plasma moments atvery high resolution from a single spacecraft with respect to themulti-spacecraft missions in the current density evaluation.

On the estimation of the current density in space plasmas: multi versus single-point techniques