Authors: Rebecca Harvey (Department of Space Science, The University of Alabama in Huntsville), Qiang Hu (Department of Space Science, The University of Alabama in Huntsville; Center for Space Plasma and Aeronomic Research (CSPAR), The University of Alabama in Huntsville)

Magnetic flux ropes with a wide range of scale sizes generally have high magnetic helicity, a magnetohydrodynamic (MHD) quantity that characterizes the knottedness of the field lines and can be used to identify flux rope structures. The identification and analysis of structures moving across boundaries such as the Earth’s bow shock will give insight into how their properties change across this boundary as well as further our understanding of the interrelation between these structures. Using high time-resolution data from the MMS and THEMIS missions, we identify small-scale flux ropes using wavelet analysis and determine how they change across boundaries. Wavelet analysis of single-spacecraft data can produce better resolved time and spatial information that will complement other methods of flux rope identification. Wavelet transforms are performed across hours-long intervals, organized by the orbit configuration of the spacecraft, and are used to calculate the reduced, normalized forms of the MHD quantities using wavelet power spectral density. The resulting spectrograms are then searched to identify small-scale structures. In addition, by employing the Grad-Shafranov (GS) equation, which describes the force balance between the Lorentz force and the gradient of the thermal pressure, we use the automated GS flux rope detection algorithm to identify similar structures. A number of parameters, including duration, scale size, maximum magnetic field, and average plasma temperature of the flux rope intervals identified are also recorded and summarized. Comparing the values of magnetic field, plasma beta, and other parameters at the corresponding times and locations leads to interpretations for the flux rope events such as whether they are compressed, decelerated, or undergo any other changes as they evolve.