https://doi.org/10.1140/epjp/s13360-024-04866-0
Regular Article
A laser-induced plasma analysis based on the inversion of Abel transformation
1
School of Science, Jiangsu University of Science and Technology, 212003, Zhenjiang, Jiangsu, China
2
School of Physics, Central South University, 410083, Changsha, Hunan, China
3
Division of Basic Researches, National University of Defense Technology, 210039, Nanjing, Jiangsu, China
4
School of Mathematical Sciences, Queen Mary University of London, E1 4NS, London, UK
Received:
23
September
2023
Accepted:
4
January
2024
Published online:
25
January
2024
A numerical method for the inverse Abel transformation that can reconstruct plasma emissivity from a projected intensity profile is proposed. After calculating the derivatives of the projected intensity profile using a Volterra integral equation of the first kind, we approximate the derivative function in the Abel inversion transform using discrete least-squares approximation, and then, we obtain the emissivity profile using a numerical integral formula. It is shown that this process is numerically stable and efficient, and it is also resistant to noise when applied to experimental data, as demonstrated by our numerical results.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
