DETERMINING THE EMISSION COEFFICIENT RADIAL DISTRIBUTION FROM A PLASMA SOURCE USING MATHCAD PROGRAM

摘要

The purpose of this paper is to determine the emission coefficient radial distribution from the measured intensity distribution emitted by an extended source of radiation, particularly an application to plasma spectroscopy (He-Ne plasma). The plasma was produced inside a gas tube by a DC electrical discharge. The source was assumed to be optically thin and axially symmetrical. 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. Abel's integral equation is frequently applied in the study of extended radiation sources with cylindrical symmetry. A measurement of the transverse distribution I(y) of the intensity emitted perpendicularly to the source axis allows the calculation of the emission coefficient radial distribution, F(r). F(r) can be deduced from I(y) by the inverse formula known as Abel's integral equation. I(r) and F(r) need not necessarily be the transverse intensity and the local emission coefficient respectively; they can also represent other physical quantities such as the optical thickness and the absorption coefficient of cylindrical absorbing plasma, and the optical path and the refractive index of cylindrical plasmas. The integral is calculated using a polynomial of second degree for the approximation of dI(y)/dy in a small interval on the right of the discontinuity point; the other part is calculated using an approximate numerical method made with a Mathcad program.