Maximum Aligned Directional Derivative (MADD) Technique for Planar Structure Analysis in Space

Abstract

Interplanetary discontinuities are the most common intermittent structures in the solar winds, whose jump conditions conform to the Rankine–Hugoniot relations. The identification and analysis of such planar structures rely on an accurate determination of the normal vectors. In this study, we perform a benchmark test of a technique designed to estimate the dimensionality and orientation of the magnetic fields based on four spacecraft measurements. Such a technique operates on the fact that in a strictly planar magnetic field, three columns of ∇ B are all aligned and the characteristic direction corresponding to the maximum aligned directional derivative (MADD; i.e., the maximum of $| {\boldsymbol{\nabla }}{\boldsymbol{B}}\cdot \widehat{{\boldsymbol{r}}}| $ ) can be considered the normal vector of the structure. A benchmark test of this technique, using both the simulation data and numerical models of planar structures, shows that the MADD technique can identify planar magnetic field structures efficiently. For a discontinuity with translational and rotational motion, MADD is able to estimate its normal vector with second-order precision and the speed of motion with first-order precision. Two demonstrations of the MADD application to the tangential discontinuity and shock structures are presented to show its efficiency and superiority. In principle, MADD is suitable for all types of planar structures in space. Compared with the minimum variance analysis and timing techniques, MADD is superior in the study of intermediate shocks that exhibit magnetic coplanarity and rapid spatial evolution.

Keywords

• Interplanetary discontinuities
• Astronomy data analysis
• Interplanetary magnetic fields
• Solar wind