The role of excited state electron-impact ionization and configuration mixing in the population modeling of neutral Ne and W in fusion-capable plasmas using large-scale R-matrix collisional data

Abstract

This work reports on large-scale non-perturbative \textit{R}-matrix quantum mechanical calculations for neutral neon and tungsten. In addition, generalized collisional-radiative modeling of neutral neon and tungsten is conducted for fusion relevant plasma temperatures and densities. The generalized collisional-radiative coefficients produced are important for impurity transport modeling and in the case of tungsten for measuring erosion rates of tungsten plasma facing components.

Neon is being used in the W7-X stellarator for divertor cooling and spectral diagnostics. The electron-impact \textit{R}-matrix calculations of the present work include cross sections for the excited states of neutral neon ($2p^{5}nl$ through $nl$ = $6p$) and the $5d^{4}6s^{2}$ ($^{5}D$) ground, $5d^{5}6s$ ($^{7}S$) metastable, and a number of excited states arising from the $5d^{6}$, $5d^{5}6s$, $5d^{5}6d$, $5d^{4}6s6p$, $5d^{5}6s6d$, and $5d^{3}6s^{2}6p$ configurations of neutral tungsten. Ionization from the excited states of neutral neon was found to obey an $n$-scaling law allowing the data to be extrapolated to higher excited states. In addition, the generalized collisional-radiative modeling showed that ionization from the excited states is an important contribution to the effective ionization of neutral neon for fusion plasma divertor and edge densities, contributing up to a factor of 3 more than the direct ground state ionization. The atomic data for neutral neon has been archived and made available to the fusion and astrophysical communities.

Tungsten is important because it has been selected as a plasma-facing component (PFC) for the divertor region of ITER and is being used in a number of current tokamaks. Therefore, an accurate real-time diagnostic is needed of tungsten's erosion rate. The S/XB coefficient specifies the ``ionizations per photon" of the atomic species and depends upon an effective ionization rate coefficient, related to the electron-impact ionization out of both the ground and excited states. The work on tungsten reported here is focused on improving the electron-impact ionization data for the ground, metastable, and excited states of neutral tungsten.

The electron-impact ionization calculations for neutral tungsten found a number of important effects. Configuration-mixing present in the target tungsten atom's levels leads to contributions from configurations of lesser mixing percentages, such as from the $5d^{5}nl$ series for the ground state ionization cross section. These contributions can arise from configuration-mixing in either the initial or final target states or both. Additionally, relative differences in the ground and metastable $5d$ and $6s$ ionization cross sections exist when compared to perturbative and semi-classical calculations. These differences can be attributed to channel coupling of the incident electron-atom system due to a shared W$^{+}$ $5d^{4}6s$ core between the $5d^{4}6snl$ and $5d^{5}nl$ series, which was not reflected in previous calculations. The mixing did not allow the \textit{R}-matrix calculation to be split up into smaller calculations for each set of direct ionizations, but instead had to be evaluated as one large calculation. One of the findings for neutral tungsten that should also help guide future high-$Z$ ionization calculations was that the $N+1$ partial waves for a given total spin value produced similar sized cross sections when summed over all of the $L$-values of the partial waves. This allowed the states on the target with the highest spin values to be evaluated relatively quickly and for the case of neutral tungsten, it allowed the ground $^5D$ term to be evaluated.

Tungsten ground and excited state ionization cross sections were fitted with a scaled form of the semi-classical Exchange Classical Impact Parameter (ECIP) method. The scale factors from the ECIP fits demonstrate a scaling with ionization potential that allowed ionization rate coefficients to be generated for two strong separate linear correlations with respect to the term-specific ionization potentials. These linear correlations are distinguished by the parity of the initial target state.

Excited-state ionization for neutral tungsten contributes more than a factor of 12 than the ground state to the effective ionization for low electron temperatures (0 - 30 eV) and $10^{14}$ cm$^{-3}$ electron density. Subsequent tests on the effect of the $6p$ orbital scaling parameter of the tungsten structure on the ECIP scale factors, as well as a ground-resolved S/XB coefficient that is several orders of magnitude higher than previous measurements, suggests ionization cross sections from odd-parity configurations are particularly sensitive to the $6p$ orbital scaling parameter. A continued exploration of the sensitivity of the excited state cross sections to the underlying atomic structure is part of the future work of this project. In addition, other processes may affect the S/XB value in tokamak plasmas, including non-steady state metastable values (particularly if the sputtered tungsten atoms come off the wall with populations greater than the steady state value), sheath effects, and non-Maxwellian electron distributions.