Abstract
In the analysis of in-situ space plasma and field data, an establishment of the coordinate system and the frame of reference, helps us greatly simplify a given problem and provides the framework that enables a clear understanding of physical processes by ordering the experimental data. For example, one of the most important tasks of space data analysis is to compare the data with simulations and theory, which is facilitated by an appropriate choice of coordinate system and reference frame. While in simulations and theoretical work the establishment of the coordinate system (generally based on the dimensionality or dimension number of the field quantities being studied) and the reference frame (normally moving with the structure of interest) is often straightforward, in space data analysis these are not defined a priori, and need to be deduced from an analysis of the data itself. Although various ways of building a dimensionality-based (D-based) coordinate system (i.e., one that takes account of the dimensionality, e.g., 1-D, 2-D, or 3-D, of the observed system/field), and a reference frame moving along with the structure have been used in space plasma data analysis for several decades, in recent years some noteworthy approaches have been proposed. In this paper, we will review the past and recent approaches in space data analysis for the determination of a structure’s dimensionality and the building of D-based coordinate system and a proper moving frame, from which one can directly compare with simulations and theory. Along with the determination of such coordinate systems and proper frame, the variant axis/normal of 1-D (or planar) structures, and the invariant axis of 2-D structures are determined and the proper frame velocity for moving structures is found. These are found either directly or indirectly through the definition of dimensionality. We therefore emphasize that the determination of dimensionality of a structure is crucial for choosing the most appropriate analysis approach, and failure to do so might lead to misinterpretation of the data. Ways of building various kinds of coordinate systems and reference frames are summarized and compared here, to provide a comprehensive understanding of these analysis tools. In addition, the method of building these systems and frames is shown not only to be useful in space data analysis, but also may have the potential ability for simulation/laboratory data analysis and some practical applications.
Highlights
In physics studies, the establishment of two systems is fundamental: one is the reference frame of a system relative to the observer and another is the coordinate system
We find that the M and L vectors are close to the invariant axis for MVAB and MVAJ, respectively, only when the impact parameter (IP) is close to zero for flux ropes with non-zero axial fields
Zhao et al (2018, private communication) proposed a PQR system, where R is the rope axial direction determined by the minimum variance of the magnetic pressure gradient, Q is along the average direction of the flux rope motion in the spacecraft frame, and P completes the right-hand coordinate system
Summary
The establishment of two systems is fundamental: one is the reference frame of a system relative to the observer and another is the coordinate system. Examples in simulation work include 2-D simulations of magnetic reconnection (e.g., Lin and Swift 1996; Birn and Hesse 2001; Daughton et al 2009) or 1-D simulations of plasma processes (e.g., Dawson 1983), which have all used a D-based coordinate system In these studies, the reference frame is just the frame moving along with the structure, e.g., the current sheet or a flux rope. If we can determine its dimension number, the invariant axis, which corresponds to the axis of the flux rope, can be found Another example is a 1-D current sheet (often seen at the magnetopause and the magnetotail or in a shock front) in which all field quantities vary only along its normal direction. In theory/simulation work, for example, to study a flux tube, reconnection point, or current sheet characteristics, we often need to study the electromagnetic fields and plasma/particle dynamics in the reference frame moving along with the structure.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have