In-flight calibration of the Hot Ion Analyser on board Cluster

The Hot Ion Analyser (HIA), part of the Cluster Ion Spectrometry experiment, has the objective to measure the three-dimensional velocity distributions of ions. Due to a variety of factors (exposure to radiation, detector fatigue and aging, changes in the operating parameters, etc.), the particles' detection efficiency changes over time, prompting for continuous in-flight calibration. This is achieved by comparing the HIA data with the data provided by the WHISPER (Waves of HIgh frequency and Sounder for Probing of Electron density by Relaxation) experiment on magnetosheath intervals, for the high-sensitivity section of the instrument, or solar wind intervals, for the low-sensitivity section. The paper presents in detail the in-flight calibration methodology, reports on the work carried out for calibrating HIA and discusses plans to extend this activity in order to ensure the instrument's highest data accuracy

Multiscale estimation of the field-aligned current density

Field-aligned currents (FACs) in the magnetosphere–ionosphere (M–I) system exhibit a range of spatial and temporal scales that are linked to key dynamic coupling processes. To disentangle the scale dependence in magnetic field signatures of auroral FACs and to characterize their geometry and orientation, Bunescu et al. (2015) introduced the multiscale FAC analyzer framework based on minimum variance analysis (MVA) of magnetic time series segments. In the present report this approach is carried further to include in the analysis framework a FAC density scalogram, i.e., a multiscale representation of the FAC density time series. The new technique is validated and illustrated using synthetic data consisting of overlapping sheets of FACs at different scales. The method is applied to Swarm data showing both large-scale and quiet aurora as well as mesoscale FAC structures observed during more disturbed conditions. We show both planar and non-planar FAC structures as well as uniform and non-uniform FAC density structures. For both synthetic and Swarm data, the multiscale analysis is applied by two scale sampling schemes, namely the linear and logarithmic scanning of the FAC scale domain. The local FAC density is compared with the input FAC density for the synthetic data, whereas for the Swarm data we cross-check the results with well-established single- and dual-spacecraft techniques. All the multiscale information provides a new visualization tool for the complex FAC signatures that complements other FAC analysis tools.</p

Gradient estimation using configurations of two or three spacecraft

The forthcoming three-satellite mission Swarm will allow us to investigate plasma processes and phenomena in the upper ionosphere from an in-situ multi-spacecraft perspective. Since with less than four points in space the spatiotemporal ambiguity cannot be resolved fully, analysis tools for estimating spatial gradients, wave vectors, or boundary parameters need to utilise additional information such as geometrical or dynamical constraints. This report deals with gradient estimation where the planar component is constructed using instantaneous three-point observations or, for quasi-static structures, by means of measurements along the orbits of two close spacecraft. A new least squares (LS) gradient estimator for the latter case is compared with existing finite difference (FD) schemes and also with a three-point LS technique. All available techniques are presented in a common framework to facilitate error analyses and consistency checks, and to show how arbitrary combinations of planar gradient estimators and constraints can be formed. The accuracy of LS and FD planar gradient estimators is assessed in terms of prescribed and adjustable discretization parameters to optimise their performance along the satellite orbits. Furthermore, we discuss the implications of imperfect constraint equations for error propagation, and address the effects of sub-scale structures. The two-spacecraft LS scheme is demonstrated using Cluster FGM measurements at a planar and essentially force-free plasma boundary in the solar wind where all three different types of constraints to construct out-of-plane derivatives can be applied

Multipoint Field-Aligned Current Estimates With Swarm

Field-aligned currents (FACs) are a key component of the magnetosphere-ionosphere system, providing the transfer of energy and momentum between the distant collision-free magnetospheric plasma and the collisional ionosphere. The European Space Agency's Swarm mission offers a unique opportunity to explore the FACs low-altitude end by a broad range of single-spacecraft and multispacecraft techniques. The present technical report demonstrates the application of dual- and three-satellite FAC estimation methods based on the least squares approach, with the goal to enhance the use of Swarm data in exploring the high-latitude current structures, beyond the official FAC product presently available to the end user. The dual-satellite method presents some clear advantages since it provides stabler solutions, can be applied on a more general spacecraft configuration, and offers a robust error estimation scheme. Consequently, the method provides significantly more data near the singularity where the satellites' orbits intersect, allows FAC estimation with configurations that involves the upper Swarm satellite, or to fine tune the constellation geometry to the problem at hand. Similarly, the three-satellite method, meant to be applied when Swarm forms a close configuration, brings additional valuable information, associated to a different (larger) scale. Moreover, it can estimate the FAC density with high time resolution when instantaneous measurements are used. The performance of the methods are thoroughly analyzed both on Swarm events and on simulated data, and the results are compared with other available methods. Particular emphasis is put on how different FAC estimation methods complement each other and provide consistent results

Robust Adaptive Spacecraft Array Derivative Analysis

Multispacecraft missions such as Cluster, Themis, Swarm, and MMS contribute to the exploration of geospace with their capability to produce gradient and curl estimates from sets of spatially distributed in situ measurements. This paper combines all existing estimators of the reciprocal vector family for spatial derivatives and their errors. The resulting framework proves to be robust and adaptive in the sense that it works reliably for arrays with arbitrary numbers of spacecraft and possibly degenerate geometries. The analysis procedure is illustrated using synthetic data as well as magnetic measurements from the Cluster and Swarm missions. An implementation of the core algorithm in Python is shown to be compact and computationally efficient so that it can be easily integrated in the various free and open source packages for the Space Physics and Heliophysics community

A new technique for determining orientation and motion of a 2-D, non-planar magnetopause

For a four-point mission like Cluster, the differences in position and time when the satellites detect the magnetopause or any other discontinuity, can be used to infer the discontinuity local orientation, thickness and motion. This timing technique, commonly assuming a planar geometry, offers an independent check for various single-spacecraft techniques. In the present paper we propose an extension of the timing method, capable of determining in a self-consistent way the macroscopic parameters of a two-dimensional, non-planar discontinuity. Such a configuration can be produced by a local bulge or indentation in the magnetopause, or by a large amplitude wave traveling on this surface, and is recognized in Cluster data when the single spacecraft techniques provide different individual normals contained roughly in the same plane. The model we adopted for the magnetopause assumes a layer of constant thickness of either cylindrical or parabolic shape, which has one or two degrees of freedom for the motion in the plane of the individual normals. The method was further improved by incorporating in a self-consistent way the requirement of minimum magnetic field variance along the magnetopause normal. An additional assumption, required in a previously proposed non-planar technique, i.e. that the non-planarity has negligible effects on the minimum variance analysis, is thus avoided. We applied the method to a magnetopause transition for which the various planar techniques provided inconsistent results. By contrast, the solutions obtained from the different implementations of the new 2-D method were consistent and stable, indicating a convex shape for the magnetopause. These solutions perform better than the planar solutions from the normal magnetic field variance perspective. The magnetopause dynamics and the presence of a non-zero normal magnetic field component in the analyzed event are discussed

Experimental test of the ρ(1-α) evolution for rotational discontinuities: cluster magnetopause observations

Rotational discontinuities (RDs) are governed by two relations: the Walén relation predicting that the plasma velocity observed in the deHoffmann–Teller frame equals the local Alfvén velocity and another relation that connects the variation in plasma mass density, &rho;, to variations in the pressure anisotropy factor, α, defined as &alpha;: &equiv;(p&parallel; &minus; p&perp;) &mu;0/B2, so that &rho;(1 &minus; &alpha;) is constant. While the Walén relation has become a standard tool for classifying magnetopause crossings as RDs , the &rho;(1 &minus; &alpha;)= const. condition has never been directly verified at the same time, largely due to problems with determining &rho; when no ion composition measurements were available. In fact, to overcome the lack of composition information, the validity of the relation has often been assumed and the Walén relation reformulated so that variations in &rho; are replaced by variations in α. In this paper we exploit the availability of high-time-resolution composition measurements on the Cluster spacecraft to directly test the &rho; (1&minus; &alpha;)= const. condition for three magnetopause crossings, identified as RDs from the application of the Walén relation to measurements of plasma ions and magnetic field by the CIS (Cluster Ion Spectrometry) and FGM (flux-gate magnetometer) instruments, respectively. We find that the relation is not fulfilled in either case. In one event, with a fairly large content of oxygen ions, the Walén test improved when the contribution from these ions was taken into account. Through comparisons of the measured ion densities with simultaneously measured total electron densities by the Waves of HIgh frequency and Sounder for Probing of Electron density by Relaxation (WHISPER) instrument, we were able to exclude the possibility that ion populations hidden to the CIS instrument because of their very low energies could have changed &rho; to match the &rho;(1 &minus; &alpha;)= const. condition. We also excluded the possibility that energetic ions above the CIS energy range could have sufficiently changed the true α. It thus appears that the &rho;(1 &minus; &alpha;)= const. condition, for reasons not presently understood, is not valid for the kind of RD-like structures we observe