. The simple model of reconnected field line motion developed by Cooling et al. (2001) has been used in several recent case studies to explain the motion of flux transfer events across the magnetopause. We examine 213 FTEs observed by all four Cluster spacecraft under a variety of IMF conditions between November 2002 and June 2003, when the spacecraft tetrahedron separation was ~5000 km. Observed velocities were calculated from multi-spacecraft timing analysis, and compared with the velocities predicted by the Cooling model in order to check the validity of the model. After excluding three categories of FTEs (events with poorly defined velocities, a significant velocity component out of the magnetopause surface, or a scale size of less than 5000 km), we were left with a sample of 118 events. 78% of these events were consistent in both direction of motion and speed with one of the two model de Hoffmann-Teller (dHT) velocities calculated from the Cooling model (to within 30° and a factor of two in the speed). We also examined the plasma signatures of several magnetosheath FTEs; the electron signatures confirm the hemisphere of connection indicated by the model in most cases. This indicates that although the model is a simple one, it is a useful tool for identifying the source regions of FTEs.

/pdf/motion-of-flux-transfer-events-a-test-of-the-cooling-model-1k5ii19kpb.pdf

Motion of flux transfer events: a test of the Cooling model

This paper describes a general-purpose algorithm for computing the gradients in space and time of a scalar field, a vector field, or a divergence-free vector field, from in situ measurements by one or more spacecraft. The algorithm provides total error estimates on the computed gradient, including the effects of measurement errors, the errors due to a lack of spatio-temporal homogeneity, and errors due to small-scale fluctuations. It also has the ability to diagnose the conditioning of the problem. Optimal use is made of the data, in terms of exploiting the maximum amount of information relative to the uncertainty on the data, by solving the problem in a weighted least-squares sense. The method is illustrated using Cluster magnetic field and electron density data to compute various gradients during a traversal of the inner magnetosphere. In particular, Cluster is shown to cross azimuthal density structure, and the existence of field-aligned currents in the plasmasphere is demonstrated.

/pdf/least-squares-gradient-calculation-from-multi-point-3r9xeqmyah.pdf

Least-squares gradient calculation from multi-point observations of scalar and vector fields: methodology and applications with Cluster in the plasmasphere

[1] Flux transfer events are bursts of dayside reconnection, which give rise to local perturbations of the magnetic field that can be observed by spacecraft near the magnetopause. Although it is commonly accepted that flux transfer events are caused by reconnection, various models exist to explain their structure. A key difference between mechanisms is that when the magnetic shear across the magnetopause is close to 180°, some models will give rise to a structure whose axis is oriented north-south, whereas others will result in a dawn-dusk-oriented structure. Several techniques for determining the axial direction of such structures have been suggested: minimum variance analysis on the magnetic field, minimization of the axial electric field, and Grad-Shafranov reconstruction. We apply these techniques to a series of flux transfer events observed by Cluster at a high-shear magnetopause crossing on 27 March 2007. Minimum variance analysis on the signatures caused by the draping of unreconnected magnetic flux around the flux transfer events consistently results in an axial direction that is dawn-dusk oriented. However, the electric field technique, applied to flux transfer events that are penetrated by the spacecraft, results in a mixture of north-south and dawn-dusk axes. Testing these axial directions with Grad-Shafranov reconstruction suggests that the axes of events which appear to be oriented dawn-dusk might be more reliably determined than the axes of events which appear to be north-south. Using the Grad-Shafranov method alone to determine the axial direction of the penetrated events gives dawn-dusk axial directions, consistent with the results of minimum variance analysis on the draping events. Overall, these observations are consistent with the formation of flux transfer events by processes involving relatively long reconnection lines (e.g., single or multiple X-line reconnection) rather than elbow-shaped flux tubes, as originally envisaged. Furthermore, examination of one particular flux transfer event that was observed by Cluster 1 but not by Cluster 2 (which was closer to the magnetopause) allows us to preclude the elbow-shaped model for this event.

/pdf/determining-the-axial-direction-of-high-shear-flux-transfer-v1imefc6ay.pdf

Determining the axial direction of high-shear flux transfer events: Implications for models of FTE structure

Ground-based instruments and a number of space missions have contributed to our knowledge of the plasmasphere since its discovery half a century ago, but it is fair to say that many questions have remained unanswered. Recently, NASA’s Image and ESA’s Cluster probes have introduced new observational concepts, thereby providing a non-local view of the plasmasphere. Image carried an extreme ultraviolet imager producing global pictures of the plasmasphere. Its instrumentation also included a radio sounder for remotely sensing the spacecraft environment. The Cluster mission provides observations at four nearby points as the four-spacecraft configuration crosses the outer plasmasphere on every perigee pass, thereby giving an idea of field and plasma gradients and of electric current density. This paper starts with a historical overview of classical single-spacecraft data interpretation, discusses the non-local nature of the Image and Cluster measurements, and emphasizes the importance of the new data interpretation tools that have been developed to extract non-local information from these observations. The paper reviews these innovative techniques and highlights some of them to give an idea of the flavor of these methods. In doing so, it is shown how the non-local perspective opens new avenues for plasmaspheric research.

CLUSTER and IMAGE: New Ways to Study the Earth’s Plasmasphere

Multi-spacecraft missions allow the gradient of important physical quantities in the terrestrial environment to be determined. The gradient can be computed from four simultaneous measurements in a straightforward way, but this computation does not produce proper error estimates, making it hard to assess the meaningfulness of the result. Recently developed least-squares gradient computation techniques offer the possibility to obtain more precise results with all-inclusive error estimates, provided that information about the non-linearity of the space and time variations of the observed quantity is given. The present paper describes several heuristics for estimating these variations, thereby enabling a fully automatic computation of the gradient and the associated error estimates. The performance of these heuristics is illustrated with synthetic data corresponding to 4- and 10-spacecraft configurations.

/pdf/least-squares-multi-spacecraft-gradient-calculation-with-26empprpk9.pdf

Least-squares multi-spacecraft gradient calculation with automatic error estimation

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 Curlometer and other gradient measurements with Cluster

Cluster multipoint measurements are used to study a magnetosheath Flux Transfer Event (FTE), with a typical magnetic signature. A large negative B y (GSE) component is observed before, during and after the event. Cluster data demonstrate that the FTE is a force free configuration, with a current flowing essentially in the Y (GSE) direction. The current density is filamented, and it shows reversals from parallel to antiparallel to B →. Energetic electron and ions, escaping from the magnetosphere (antiparallel to B→), are observed during the magnetic signature of the FTE, as expected. These escaping energetic electrons and ions continue to be observed until 11:33:40; about 2 minutes after the passage of the magnetic structure of the FTE. Surprisingly, during the magnetic signature of the FTE, energetic electrons are also observed in the parallel (to B→) direction, with fluxes comparable to the antiparallel direction, and larger than in perpendicular direction. These enhanced energetic electron fluxes in parallel and anti-parallel directions indicate that field lines are closed inside the FTE, at least during its early phase (11:30:50-11:31:25 for SC1). During the same time interval the density is about 4 times less than in the adjacent magnetosheath, which is also consistent with being on closed field lines (magnetospheric). At ∼11:30:50 the 4 S/C cross the magnetopause, a tangential discontinuity (TD), and remain in the closed magnetosphere for about 30 sec. No compelling evidence for a boundary layer (BL) is found during this first crossing. At ∼11:31:25 the 4 S/C cross a second TD: the boundary between the magnetosphere and a turbulent magnetopause boundary layer (MPBL). From 11:31:25-11:31:50 field lines are alternatively open/closed, as inferred from signatures on energetic electrons. The ion flow velocity is accelerated, at ∼11:31:50, during the crossing of a third discontinuity; a rotational discontinuity (RD), corresponding to an open magnetopause. While crossing this RD the modulus of the ion flow velocity is multiplied by 2. Thus the acceleration of the ion flow is observed on open field lines, as expected from the standard FTE model (see for instance Paschmann et al., 1982 [20]). Yet the ion flow velocity is continuous across the second TD, met at 11:31:25, thus the accelerated ion flow is found to penetrate on closed field lines, through a TD, which is unexpected. Our observations demonstrate that the accelerated flow of ions is not limited to open field lines, which indicates that an efficient anomalous transport of the plasma occurs. It is suggested that the anomalous transport, through the inner edge of the MPBL, is due to a fast spatial diffusion associated with large amplitude electromagnetic ULF fluctuations observed simultaneously.

Study of a flux transfer event with cluster spacecraft.

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The Curlometer and other gradient measurements with Cluster

Study of a flux transfer event with cluster spacecraft.