Extraction of Ion Distributions from Magnetospheric ENA and EUV Images

Edmond C. Roelof (1) and Andrew J. Skinner (2)

1 Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, U.S.A.  
  (E-mail: roelof@jhuapl.edu)
2 Welkin Research, College Park, MD 20740, U.S.A. 
  (E-mail: skinner@welkinresearch.com)
  
           Energetic neutral atom (ENA) and extreme ultra-violet photon (EUV) 
images will soon be probing magnetospheric ion distributions from the NASA 
space missions IMAGE and TWINS. AlthoughENA 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.  

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Space Science Reviews, IMAGE Special Issue, Vol. 91, pp. 437-459, February, 2000