Distribution of emitters in an elliptical source Page: 2 of 18
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Several plasma diagnostic experiments require Abel inversion
techniques to determine the radial distribution of emitters from
line integrated measurements. The detection of x-ray and micro-
wave emission are two well-known examples which use this technique
to deduce the radial profiles of electron temperature and density,
respectively. Such calculations have been routinely performed for
plasmas with circular cross sections using methods developed by
Bockasten  and Barr , Recently, there has been interest in
inversion schemes that are applicable to non-circular plasma shapes.
In particular, tokamaks possessing divertors, such as PDX and ASDEX
(poloidal divertors), can produce plasmas with approximately ellip-
tical cross sections.
Sauthoff and von Goeler  have discussed methods for recon-
structing non-circular source distributions if the surfaces of
constant emissivity are approximated by a series of poloidal har-
monics. In this report we show that methods, normally applied to
sources with circular symmetry, can be simply modified to yield
the radial distribution for any elliptically shaped source.
II. CIRCULAR CASE REVISITED
We briefly review the Abel inversion procedure for surfaces
with circular symmetry. Assuming surfaces of constant emissivity,
e(r), with typical units of ergs/(cm3 - sec), the total integrated
intensity detected by an observer at vertical position y = yQ
(refer to Fig. 1) is
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Silver, E. & Roney, W. Distribution of emitters in an elliptical source, report, January 1, 1980; New Jersey. (https://digital.library.unt.edu/ark:/67531/metadc1092908/m1/2/: accessed March 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.