Four‐point discontinuity observations using Cluster magnetic field data: A statistical survey

Abstract

[1] Using magnetic field data from the four Cluster spacecraft between February and May 2001, a detailed statistical analysis of interplanetary discontinuities is accomplished. In order to find the surface normals, we apply three different methods:(1) minimum variance analysis (MVA), (2) cross-product method, and (3) triangulation, the latter being the only one that needs information from all four spacecraft. Whereas the cross-product normals are always almost the same at the position of the four spacecraft, strong deviations between the MVA normals are observed. The crossproduct normals also agree fairly well with the triangulation normals, which mostly point in a direction approximately perpendicular to the magnetic field. The scatter of the MVA normals around the triangulation normal can be reduced by triggering the parameters controlling the MVA accuracy, i.e., l 2 /l 3 L , the lower limit of the MVA eigenvalue ratio, and w L , the lower limit of the spreading angle. Our analysis allows to compare the impact of these two parameters on the MVA normals. The error analysis shows that both parameters have strong impact on the MVA accuracy; however, l 2 /l 3 L is more important. In order to ensure reliable normal estimates, MVA should only be applied if w L > 60°. The MVA error analysis also enables us to provide a new criterion to distinguish rotational discontinuities (RDs) from tangential discontinuities. However, the triangulation results show that there are no clearly identified RDs in our data set. We will discuss implications for the theory of solar wind discontinuity generation processes. A practical consequence is that the cross-product method presumably yields better normal estimates than MVA when B n is small. The colinerarity of the cross-product normals at the positions of the four spacecraft demonstrate that the discontinuities are one-dimensional structures on the Cluster separation scale.

Survey of large-amplitude flapping motions in the midtail current sheet

“…Using the TIM normals as our guess of the true normal in these cases, we used MVA determinations from each of the 4 spacecraft to compare their angular deviations from true normal as a function of r 23 (in total having 428 intervals). Figure 2 indicates that indeed the angular deviation is small for large r 23 values, and grows with a decrease of this ratio; similar to the results by Knetter et al (2004) the error curve shows a considerable change around the r 23 =8 threshold. However, the amount of events strongly decreases when the r 23 decreases from 20 until 3, so for practical purposes one should compromise between the requirements, to obtain a good accuracy and to keep a large enough and representative data set for doing statistics.…”

“…Previous Cluster-based studies of solar wind discontinuities (based on a comparison between timing and MVA methods) indicated that it is possible to obtain the success criteria for the MVA to work. Particularly, for solar wind discontinuities Knetter et al (2004) found the good accuracy of MVA (with sufficient amount of measurement points in the discontinuity) when the magnetic shear was large and the medium-to-minimal eigenvalues ratio r 23 =λ 2 /λ 3 was large (>8 in their case). Unfortunately, these practical criteria cannot be easily transferred to another object (to the tail current sheet, in our case), where the underlying physics can be different.…”

What is the best method to calculate the solar wind propagation delay?

“…We have therefore not utilized Clusters four-spacecraft capability in this study, and most of the Cluster measurements are taken from the C3 spacecraft. However, some of the events included in this work has also been studied by Knetter et al (2004) and Knetter (2004), where the nature of the discontinuity as well as a comparison of single-and multi spacecraft methods are discussed in detail. In particular, these authors concluded that results based on four-spacecraft triangulation agreed fairly well with the cross product method, which we have also used.…”

“…In a survey, Knetter et al (2003Knetter et al ( , 2004) applied multispacecraft timing methods to a number of discontinuities observed by Cluster in the solar wind, and concluded that most of the observed discontinuities could be classified as TDs. Also, in a recent publication, Weimer and King (2008), adapted the MVAB-0 method, and performed a thorough check of the method, and basically confirmed its usefulness for propagation delay calculations.…”

“…More sophisticated methods require in-situ measurements and then trying to estimate the normal from multi spacecraft timing or gradient methods (e.g. Horbury et al, 2001b;Knetter et al, 2004), or use the local field or plasma measurements from a single spacecraft (see e.g. overviews in Sonnerup et al, 2006;Volwerk, 2006).…”