Multi-Spacecraft Magnetic Field Reconstructions: A Cross-Scale Comparison of Methods

Space plasma studies frequently use in situ magnetic field measurements taken from many spacecraft simultaneously. A useful data product of these measurements is the reconstructed magnetic field in a volume near the spacecraft observatory. We compare a standard Linear method of computing the magnetic field at arbitrary spatial points to two novel approaches: a Radial Basis Function interpolation and a time-dependent 2D inverse distance weighted interpolation scheme called Timesync. These three methods, which only require in situ measurements of the magnetic fields and bulk plasma velocities at a sparse set of spatial points, are implemented on synthetic data drawn from a time-evolving numerical simulation of plasma turbulence. We compare both the topology of the reconstructed field to the ground truth of the simulation and the statistics of the fluctuations found in the reconstructed field to those from the simulated turbulence. We conclude that the Radial Basis Function and Timesync methods outperform the Linear method in both topological and statistical comparisons. Spacecraft are often used to measure things, such as magnetic fields, which can only be measured at a single point, the point where a spacecraft is located. When multiple spacecraft are deployed to measure the magnetic field, we get an understanding of how the magnetic field changes by comparing the measurements made by each of the spacecrafts against one another. When multiple spacecraft are taking measurements, scientists also use mathematical techniques to estimate the magnetic field at points in space where a spacecraft is not located. The process of using a small number of magnetic field measurements, taken from spacecraft, to estimate the value of the magnetic field everywhere is called magnetic field reconstruction. This work has compared the effectiveness of three of these magnetic field reconstruction techniques: one established and two novel. We conclude that the two novel methods are more accurate than the established mathematical tool commonly used to reconstruct magnetic fields. We propose two new reconstruction methods that only require measurements of the magnetic field and bulk plasma velocity The two new methods result in reconstructions with less error than previously employed Linear methods The new methods preserve the statistical distribution of scale-dependent fluctuations from the ground-truth turbulence simulation