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

## TL;DR

This paper evaluates the accuracy of the curlometer technique for estimating current density in space plasmas using synthetic data, comparing multi-spacecraft measurements at various scales with single-spacecraft high-resolution data.

## Contribution

It investigates the limitations of the curlometer method across different spacecraft separations and assesses the importance of high-resolution single-spacecraft measurements.

## Key findings

- Curlometer underestimates current density at sub-proton scales.
- High-resolution single-spacecraft data can complement multi-spacecraft techniques.
- Synthetic data analysis reveals scale-dependent accuracy of the curlometer.

## Abstract

Thanks to multi-spacecraft mission, it has recently been possible to directly estimate the current density in space plasmas, by using magnetic field time series from four satellites flying in a quasi perfect tetrahedron configuration. The technique developed, commonly called 'curlometer' permits a good estimation of the current density when the magnetic field time series vary linearly in space. This approximation is generally valid for small spacecraft separation. The recent space missions Cluster and Magnetospheric Multiscale (MMS) have provided high resolution measurements with inter-spacecraft separation up to 100 km and 10 km, respectively. The former scale corresponds to the proton gyroradius/ion skin depth in 'typical' solar wind conditions, while the latter to sub-proton scale. However, some works have highlighted an underestimation of the current density via the curlometer technique with respect to the current computed directly from the velocity distribution functions, measured at sub-proton scales resolution with MMS. In this paper we explore the limit of the curlometer technique studying synthetic data sets associated to a cluster of four artificial satellites allowed to fly in a static turbulent field, spanning a wide range of relative separation. This study tries to address the relative importance of measuring plasma moments at very high resolution from a single spacecraft with respect to the multi-spacecraft missions in the current density evaluation.