Extraction of ion distributions from magnetospheric ENA and EUV images

Abstract

Energetic neutral atom (ENA) and extreme ultra-violet photon (EUV) imagers will soon be probing magnetospheric ion distributions from the NASA space missions IMAGE and TWINS. Although ENA and EUV images will differ greatly, the same basic mathematical approach can be applied to deducing the ion distributions: extracting the parameters of a model ion distribution in a model magnetic field (and, in the case of ENA, interacting with a model cold neutral population). The model ion distribution is highly non-linear in its many parameters (as many as 38 have been used) in order to describe the strong spatial gradients of ion intensities in the magnetosphere. We have developed several new computer algorithms to accomplish the extraction by minimizing the differences between a simulated (instrument-specific) image and an observed image (or set of images). Towards the goal of a truly automated `hands-off’ extraction algorithm, we have combined three algorithms into a Hierarchical Simplex Algorithm. At each step of the minimization, it first tries a sophisticated and efficient Adaptive Conjugate Gradient algorithm. Then, if the error function is not reduced, it defers to an intermediate Analytic Simplex algorithm, and (if this step also fails) it finally defaults to the robust but inefficient Downhill Simplex algorithm. Whenever a step is successful, the algorithm begins the next step at the top of the hierarchy. We also offer a completely different approach (without minimization) for the interpretation of sharp `edges’ in the images (e.g., the plasmapause in He + 30.4 nm EUV images of the plasmasphere). We demonstrate mathematically that the equatorial shape of the plasmapause can be constructed directly from the image using a simple graphical algorithm.