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The purpose of this paper is to develop a mathematical tool and an experimental platform to be able to reconstruct thermal plasmas in three dimensions (3D) in order to characterize 3D plasma and to validate models in 3D. Indeed, a lack of experimental data allowing validating 3D models exists.

The paper is realized with a transferred argon arc configuration. The 3D character is due to the form of the cathode electrode. The reactor design is defined by a previous theoretical study. This previous paper has shown that tomographic method through four views allows reconstructing 3D object. The light emitted by the plasma along four directions (four windows) is so spectrally resolved and treated by a multiplicative algebraic reconstruction technique algorithm. Following the emissivity profiles, two methods are used, the absolute line intensity method, and for an out off‐axis maximum of the emissivity the Folwer Milne method.

After a validating approach of the optical measurements in symmetrical configuration using Abel inversion, the reconstructed method is used. The results show the possibility of the tomographic method spectrally and spatially resolved to be applied to thermal plasma in order to characterise the medium and to validate the 3D models. The plasma medium is well described with a spatial resolution equal to 0.2 mm.

The method is applicable to thermal plasma presenting high emissivity. Even if the theoretical reconstruction method is applied to low temperatures or to theoretical plasma presenting out off‐axis of emissivity, future researches need to be performed to analyse the ability of the method to spatially resolve the areas presenting low emissivity.

The paper's originality can be demonstrated by the poor number of studies in thermal plasma reconstruction in 3D. Studies on plasma imaging can be found but not spectrally resolved. The special care on the spectral acquisition along the plasma radius combined with the tomographic reconstruction method lead to the originality of this paper.