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Manuscript Title: Inversion of Abel's integral equation - application to plasma spectroscopy.
Authors: C. Fleurier, J. Chapelle
Program title: ABEL
Catalogue identifier: AAAC_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 7(1974)200
Programming language: Fortran.
Computer: IBM 360/25.
Operating system: DOS/360.
RAM: 7K words
Word size: 32
Keywords: Plasma physics, Spectroscopy, Abel integral equation, Least squares, Approximation, Data interpretation.
Classification: 19.4.

Nature of problem:
The purpose of this program is to determine the radial distribution of the emission coefficient from the measured intensity distribution emitted by an extended source of radiation, particularly a plasma source. The source is assumed to be optically thin and axially symmetrical.

Solution method:
This problem is solved by inverting Abel's integral equation. A smoothing procedure is made on the experimental curve in order to attenuate the random errors before computing the derivative. The integral is calculated analytically in a small interval on the right of the discontinity point, the other part is estimated numerically.

Restrictions:
The computation is nearly entirely numerical and needs equally spaced points for the data.

Running time:
For an experimental curve defined by 21 points the calculation time is less than 30 s on the IBM 360/25 computer.