Distribution of emitters in an elliptical source Page: 4 of 18
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III. ELLIPTICAL CASE
For the elliptical case, we seek a form similar to (2).
Referring to Fig. 2, the elliptical surfaces, u, are also assumed
to possess constant emissivity; these surfaces can be defined by
^2 + ^ = u2, 0 < u2 < 1 . (4)
An observer viewing the plasma along the line of sight, 8,,
determined by the angular position, £, would detect an intensity
£ (u) dJl
/ 2 2\1/2 / 2 \1/2
Since dS, = dxll + dy /dzt J = dxll + tan4 C) = dx/cos E ,
K5) = f Mu) 3^ . (6)
To obtain the desired form of (2), the integral above must
be written entirely in terms of the variable, u. Note that E,
like y in (2), is constant for each measurement. The geometrical
arrangement enables us to write
y = z - (P - x) tan E
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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/m1/4/: accessed March 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.