Improved Line Intensity Analysis of Neutral Helium by Incorporating the Reabsorption Processes in a Helium Collisional-Radiative Model

Abstract

In this study, eight emission lines in the visible wavelength range of neutral helium were used to diagnose the electron density and temperature of the Large Helical Device (LHD) helium plasma instead of the conventional three-line method. The collisional-radiative (CR) model for low-pressure helium plasma was revised to include the optical escape factors for spontaneous transition from the n1P states to the ground state so that the influence of the absorption effect under optically thick conditions could be considered. The developed algorithm was based on fitting the number densities of eight excited states obtained using optical emission spectroscopy (OES). The electron density, electron temperature, ground-state density, and optical escape factors were selected as the fitting parameters. The objective function was set as the summation of the residual errors between the number densities measured in the experiment and those calculated using the revised model. A regularization term was introduced for the optical escape factor and optimized through bias and variance analyses. The results show that the agreement between the number density calculated by the algorithm and its counterpart measured in the experiment was generally improved compared to the method using three lines.

Quantitative analysis of optical emission spectroscopy for plasma process monitoring

“…52) Namely, Λ qp can be approximated as Λ qp ; 1 when p ≠ 1, although this may be reconsidered for metastable states. 42,51,[71][72][73] On the other hand, for the ground state, the optical escape factor must be considered for general argon plasmas, with its discharge pressure P > 10 Pa. Particularly, when the kinetic processes are discussed for the resonant state p = 3 and 5, (4s[3/2] 1 and [ ] ¢ 4s 3 2 1 , respectively), 74) which are connected to the ground state by optically allowed transition and whose population densities are increased due to radiation trapping, the effect of the optical thickness must be included into the model quantitatively.…”

“…To do so, a contour map of the excited-state density ratio should be drawn on a map with the electron temperature and density as the vertical and horizontal axes, and using two different level pairs that tend to have different dependencies on the electron temperature and density. 51,[94][95][96][97][98] As shown in Fig. 9, if two contour lines are calculated with the original CR model, each of which corresponds to the density ratio between two excited states, and if they are not parallel to each other, that is, two intensity ratios calculated from four excited states, T e and N e can in principle be determined as the intersection of the two contour lines.…”

“…9, if two contour lines are calculated with the original CR model, each of which corresponds to the density ratio between two excited states, and if they are not parallel to each other, that is, two intensity ratios calculated from four excited states, T e and N e can in principle be determined as the intersection of the two contour lines. 51,[94][95][96][97][98] However, the drawback is that it is extremely dependent on the reaction rate coefficient of the atoms and molecules used, and the accuracy of the cross-sectional area. Therefore, such efforts are being carried out while revising the cross-section data.…”

“…Therefore, the first part of this paper is devoted to explaining the principles and practical methods of OES measurement of depressurized process plasma, based on line spectrum analysis, and the applicability of the measurement to actual equipment. The most essential discussion is concentrated on the analysis of the excitation kinetics to determine the number densities of excited states based on elementary atomic processes, 41,48,50,51) which will be explained later on.…”

Plasma-Driven Sciences: Exploring Complex Interactions at Plasma Boundaries

“…Electron density and temperature can be predicted using a machinelearning method for helium emission line intensities in Magnum-PSI [26,27] and PISCES-RF [28]. The prediction precision was improved by modifying the CR model to include the optical escape factor [29].…”