The data from the CLUSTER FGM magnetometer, recorded for 20 years at ESA's Cluster Science Archive, as well as the position of the spacecraft, have been used to form a database aligned in time, the...

Cluster multipoint measurements are used to study two successive magnetosheath flux transfer events (FTEs). Magnetic field lines in the leading region are found to be closed magnetospheric field lines. For event 1 these field lines are wounded up by a large current structure oriented eastward and moving poleward. Conversely, the trailing region corresponds to opened magnetic field lines. For both events the leading edge of the FTEs is a tangential discontinuity separating the magnetosheath from closed field lines. In the case of event 1 magnetosheath ions are accelerated through the FTE trailing edge via a rotational discontinuity and penetrate on closed field lines through a second discontinuity. Thus, the ion jet is accelerated equatorward of the spacecraft but the backtracking of the discontinuities and the lack of dispersion show that ion acceleration occurs at less than 2 RE from Cluster. On the other hand the extrapolation forward indicates that the FTE bulge steepens as in simulations of Dorelli and Bhattacharjee (2009). Evidence is given for the penetration of magnetosheath ions inside the core of the FTE, on closed field lines. Magnetosheath electrons are accelerated in parallel and antiparallel directions on open and on closed field lines, thus breaking the frozen-in condition. Event 2 is also split in two distinct regions but no evidence is found for accelerated bidirectional magnetosheath electrons. For event 2 the two discontinuities at the trailing region are stacked together when they are crossed by the spacecraft, suggesting that the current splitting is a reconnection signature.

Turbulence at MagnetoHydroDynamics (MHD) scales in the solar wind has been studied for more than three decades, using data analysis, theoretical and numerical modeling. However, smaller scales have not been explored until very recently. Here, we review recent results on the first observation of cascade and dissipation of the solar wind turbulence at the electron scales. Thanks to the high resolution magnetic and electric field data of the Cluster spacecraft, we computed the spectra of turbulence up to similar to 100 Hz (in the spacecraft reference frame) and found evidence of energy dissipation around the Doppler-shifted electron gyroscale f(rho e). Before its dissipation, the energy is shown to undergo two cascades: a Kolmogorov-like cascade with a scaling f(-1.6) above the proton gyroscale, and a new f(-2.3) cascade at the sub-proton and electron gyroscales. Above f(rho e) the spectrum has a steeper power law similar to f(-4.1) down to the noise level of the instrument. Solving numerically the linear Maxwell-Vlasov equations combined with recent theoretical predictions of the Gyro-Kinetic theory, we show that the present results are consistent with a scenario of a quasi-two-dimensional cascade into Kinetic Alfven modes (KAW). New analyses of other data sets, where the Cluster separation (of about similar to 200 km) allowed us to explore the sub-proton scales using the k-filtering technique, and to confirm the 2D nature of the turbulence at those scales. (c) 2010 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Investigating space plasma turbulence from single-point measurements is known to be characterized by unavoidable ambiguities in disentangling temporal and spatial variations. Solving this problem has been one of the major goals of the Cluster mission. For that purpose multipoint measurements techniques, such as the k-filtering, have been developed. Such techniques combine several time series recorded simultaneously at different points in space to estimate the corresponding energy density in the wavenumber space. Here we apply the technique to both simulated and Cluster magnetometer data in the solar wind (SW) and investigate the errors and limitations that arise due to the separation of the spacecraft and the quality of the tetrahedral configuration. Specifically, we provide an estimation of the minimum and maximum scales that can be accurately measured given a specific distance between the satellites and show the importance of the geometry of the tetrahedron and the relationship of that geometry to spatial aliasing. We also present recent results on characterizing small scale SW turbulence and provide scientific arguments supporting the need of new magnetometers having better sensitivity than the existing ones. Throughout the paper we emphasize technical challenges and their solutions that can be considered for a better preparation of the Cross-Scale mission.

The four-spacecraft, magnetic field measurements on Cluster can produce an accurate determination of the electric current point by point in time (the Curlometer technique). For example, for planar events, the thickness of the current layer can be accurately estimated from its magnetic profile at each spacecraft and the corresponding boundary crossing times. The latter give a determination of boundary motion relative to the Cluster array. For a range of spacecraft separation distances, the estimate of electric current density can be representative even when the configuration of Cluster spacecraft approaches the thickness of the current layer. The magnitude of the current is often accurately represented and in principle can be tracked through any structure. Minimum variance analysis on the curlometer measurements can be used to estimate the normal to a current layer. Other methods exist which are based on estimation of the magnetic gradients, curvature, or temporal derivative. These methods can be used to calculate a number of other properties, such as the dimensionality of the structure and the corresponding velocity, the field curvature, or boundary normals, but have the commonality of providing a quantity at every moment in time, like the curlometer.

The geometrical shape of the tetrahedron formed by the spacecraft is an essential criterion in the choice of scientific investigation which can be performed with data from a multi-spacecraft mission, such as Cluster. The shape of this polyhedron evolves continuously along the orbital trajectory of the spacecraft, and this shape has a major impact on the accuracy of the determination of scientific parameters related to the spatial gradient, such as the current density, which is discussed in Chapter 16. The scientific importance of the shape, combined with its variability, inevitably led to many proposals for “quality factors” to attempt to describe the geometric shape of the tetrahedron, or for “performance indicators”, to indicate the likely error of a particular scientific parameter. While these early geometric factors were all one-dimensional, 2-D parameters to characterise the geometrical shape of the tetrahedron have also been proposed, i.e., the “elongation” E and “planarity” P defined in terms of the eigenvalues of the volumetric tensor described in Chapter 12. In this chapter, we use the E and P parameters to define five characteristic types of tetrahedra and we check the validity and the meaning of the 1-D geometric factors by a numerical simulation using an “homogeneous reservoir of tetrahedra” in the E-P configuration space. As a practical application, we present an example of the Cluster orbit, and the associated computation of the 1-D and 2-D geometric factors. We represent these quantities in the E-P diagram, which allows a better understanding of their meaning. Finally, we demonstrate the limits of the 1-D geometric factors and point out the advantages of a 2-D geometric factor.