Small-Scale Magnetic Flux Rope Structures Across the Earth's Bow Shock

This work identifies and characterizes magnetic structures, especially in terms of small-scale magnetic flux ropes (SFRs), in the solar wind and magnetosheath across the Earth's bow shock. We investigate the differences between the properties of SFR structures in these regions immediately upstream and downstream of the bow shock by employing two data analysis methods: one based on wavelet transforms and the other based on the Grad-Shafranov (GS) detection and reconstruction techniques. In situ magnetic field and plasma data from the Magnetospheric Multiscale and Time History of Events and Macroscale Interactions during Substorms missions are used to identify these coherent structures through the two approaches. We identify thousands of SFR event intervals with a range of variable duration over a total time period of $\lesssim$1,000 hr in each region. We report parameters associated with the SFRs such as scale size, duration, magnetic flux content, and magnetic helicity density, derived from primarily the GS-based analysis results. These parameters are summarized through statistical analysis, and their changes across the bow shock are shown based on comparisons of their respective distributions. We find that in general, the distributions of various parameters follow power laws. The SFR structures seem to be compressed in the magnetosheath, as compared with their counterparts in the solar wind. A significant rotation in the $z$-axis defining the orientation of the structures is also seen across the bow shock. We also discuss the implications for the elongation of the SFRs in the magnetosheath along one spatial dimension.