Spatiotemporal evolution of excitation temperature of vacuum arcs by tomography

The excitation temperature is crucial for understanding the dynamic processes of a vacuum arc. The traditional methods based on optical emission spectroscopy can only provide 1D or 2D temperature distribution. Due to the absorption effect, it is difficult to obtain accurate information about the radiation emitted by the arc. This can result in measurement errors or even lead to incorrect conclusions. To address these issues, we developed a 3D tomography reconstruction algorithm that takes the absorption effect into account. The method reconstructed the emission coefficients of the vacuum arc and calculated the excitation temperature from spectral line ratios. Absorption coefficients are then calculated using Kirchhoff's law and integrated along optical paths to determine optical depths. Finally, the tomography algorithm was corrected for optical depth using the Beer-Lambert law. The results indicate that, under the axial magnetic field, the excitation temperature is radially nonuniform and deviates from the axisymmetric distribution. After considering the absorption effect, the calculated values of excitation temperature would increase and the measurement deviations are related to the axial position. Additionally, the increments across the arc slice are comparable to each other.