Abel inversion applied to a small set of emission data from a microwave plasma.

Area of Science:

• Plasma Physics
• Spectroscopy
• Data Analysis

Background:

• Abel inversion is crucial for determining radial plasma properties from line-integrated emission data.
• Limited experimental data and statistical noise pose challenges for accurate Abel inversion in laboratory plasmas.
• Existing methods like Nestor-Olsen, spline interpolation, and Fourier transforms have varying sensitivities to data quality and quantity.

Purpose of the Study:

• To propose and validate a criterion for applying Abel inversion to small experimental datasets in laboratory plasmas.
• To compare the performance of different Abel inversion techniques (Nestor-Olsen, spline interpolation, Fourier transform) under noisy and limited data conditions.
• To enable the determination of radial distributions of plasma parameters (densities, temperatures) from spectral line profiles.

Main Methods:

• Comparison of Nestor-Olsen, spline interpolation, and Fourier transform Abel inversion methods.
• Analysis of the influence of statistical noise and the number of sampled data points on inversion accuracy.
• Development and application of a novel criterion for selecting appropriate Abel inversion techniques for limited data.
• Testing the criterion using spectral line profiles from a microwave helium plasma column at atmospheric pressure.

Main Results:

• The proposed criterion effectively guides the selection of Abel inversion methods for small, noisy datasets.
• Demonstrated the impact of data limitations and noise on the accuracy of different inversion techniques.
• Successfully obtained radial distributions of plasma parameters (densities, temperatures) using the validated criterion.
• The method was successfully applied to spectral line data from a microwave helium plasma.

Conclusions:

• A practical criterion for applying Abel inversion to limited experimental data in laboratory plasmas has been established.
• The criterion enhances the reliability of determining radial plasma parameter distributions from spectral emission.
• This work provides a valuable tool for plasma diagnostics, particularly in resource-constrained experimental settings.