Study of the applicability of the curlometer technique with the four Cluster spacecraft in regions close to Earth

Knowledge of the inner magnetospheric current system (intensity, boundaries, evolution) is one of the key elements for the understanding of the whole magnetospheric current system. In particular, the calculation of the current density and the study of the changes in the ring current is an active field of research as it is a good proxy for the magnetic activity. The curlometer technique allows the current density to be calculated from the magnetic field measured at four different positions inside a given current sheet using the Maxwell-Ampere's law. In 2009, the CLUSTER perigee pass was located at about 2 RE allowing a study of the ring current deep inside the inner magnetosphere, where the pressure gradient is expected to invert direction. In this paper, we use the curlometer in such an orbit. As the method has never been used so deep inside the inner magnetosphere, this study is a test of the curlometer in a part of the magnetosphere where the magnetic field is very high (about 4000 nT) and changes over small distances (ΔB = 1nT in 1000 km). To do so, the curlometer has been applied to calculate the current density from measured and modelled magnetic fields and for different sizes of the tetrahedron. The results show that the current density cannot be calculated using the curlometer technique at low altitude perigee passes, but that the method may be accurate in a [3 RE; 5 RE] or a [6 RE; 8.3 RE] L-shell range. It also demonstrates that the parameters used to estimate the accuracy of the method are necessary, but not sufficient conditions.