# Partial and Total Dielectronic Recombination Rate Coefficients for W$^{55+}$ to W$^{38+}$

## TL;DR

This paper provides detailed partial and total dielectronic recombination rate coefficients for tungsten ions W$^{55+}$ to W$^{38+}$, crucial for plasma modeling in fusion reactors like ITER, using advanced relativistic calculations.

## Contribution

It extends previous calculations by providing comprehensive DR data for a wider range of tungsten ions using the autostructure code, emphasizing the importance of relativistic effects.

## Key findings

- DR rate coefficients agree within 7-19% with previous data for W$^{46+}$
- Relativistic configuration mixing causes ~2x differences in DR rates between IC and CA
- Ionization fractions differ significantly from previous average-atom method results

## Abstract

Dielectronic recombination (DR) is the dominant mode of recombination in magnetically confined fusion plasmas for intermediate to low-charged ions of W. Complete, final-state resolved partial isonuclear W DR rate coefficient data is required for detailed collisional-radiative modelling for such plasmas in preparation for the upcoming fusion experiment ITER. To realize this requirement, we continue {\it The Tungsten Project} by presenting our calculations for tungsten ions W$^{55+}$ to W$^{38+}$. As per our prior calculations for W$^{73+}$ to W$^{56+}$, we use the collision package {\sc autostructure} to calculate partial and total DR rate coefficients for all relevant core-excitations in intermediate coupling (IC) and configuration average (CA) using $\kappa$-averaged relativistic wavefunctions. Radiative recombination (RR) rate coefficients are also calculated for the purpose of evaluating ionization fractions. Comparison of our DR rate coefficients for W$^{46+}$ with other authors yields agreement to within 7-19\% at peak abundance verifying the reliability of our method. Comparison of partial DR rate coefficients calculated in IC and CA yield differences of a factor $\sim{2}$ at peak abundance temperature, highlighting the importance of relativistic configuration mixing. Large differences are observed between ionization fractions calculated using our recombination rate coefficient data and that of P\"{u}tterich~\etal [Plasma Phys. and Control. Fusion 50 085016, (2008)]. These differences are attributed to deficiencies in the average-atom method used by the former to calculate their data.