Zwei Verfahren zur Lösung der Abelschen Integralgleichung und zur Berechnung der radialen Volumenstrahldichte

Two methods for the calculation of the emission coefficient distribution from the side‐on radiance distribution in an optically thin plasma were elaborated. Firstly, a method for recursive solution of the Abel integral equation was derived. The formulas given by Frie were simplified. In a second method a polynomial was fitted to the data points and then the integral equation was solved analytically. Fluctuations of the solution increase with rising number of pivot points or with rising degree of polynomial and not only with rising scattering of the data points. The first method provides good results for a relatively small number of pivot points. In many cases the second method provides useful results with an even polynomial of the sixth or eighth degree and the numerical effort is slight.