Abel inversion applied to a transient laser induced plasma: implications from plasma modeling

We test the effects of non-uniformity, non-transparency, and non-stationarity of a laser-induced plasma on the results obtained by the Abel inversion method. The method is commonly used for obtaining spatially resolved emissivity of axially symmetric non-homogeneous radiating objects. Besides the axial symmetry, the plasma is assumed to be optically thin. As the method addresses a certain plasma state, the plasma is required to be stationary during measurements. It is difficult to satisfy the aforementioned conditions for transient laser induced plasmas. As such the plasmas are not stationary; they have steep gradients of thermodynamic parameters that rapidly vary during the plasma evolution. Therefore, any conclusion based on time-integrated measurements and the corresponding data processing should account for these effects. In this work, we use the collision-dominated plasma model to generate time- and spatially resolved synthetic spectra. The spectra are processed by executing the Abel inversion using two numerical algorithms. Thus obtained spatially resolved plasma parameters ( emissivity, temperature, and number density) are compared with the exact parameters used to set up the model. In doing so, the accuracy of the Abel inversion method is assessed. Special attention is paid to the dynamic aspect of the expanding plasma and possible errors which result from time-integrated measurements.