Dielectronic recombination of the open $4d$-shell of Tungsten: W$^{37+}$ -- W$^{28+}$

Tungsten is an important element for magnetically confined fusion plasmas but has the potential to cool, or even quench the plasma due to it being an efficient radiator. Total and level-resolved dielectronic recombination (DR) rate coefficients, for all ionization stages, are essential to model tungsten. We describe a set calculations performed using the distorted wave code {\sc autostructure} for the tungsten ions W$^{37+}$ to W$^{28+}$. We demonstrate the importance of relativistic configuration mixing in such calculations. In particular, we show that the partial DR rate coefficients calculated in level and configuration resolution can differ by as little as 5\%, and up to as much as 75\%. Using the new data, we calculate a revised steady-state ionization fraction for tungsten. We find that, relative to the ionization fraction calculated using the recombination rate coefficients of Putterich~\etal (Plasma Phys. Control. Fusion, 50, 085016), the peak temperatures of W$^{37+}$ to W$^{28+}$ ionization states are shifted to lower temperatures spanning 0.9-1.6keV. This temperature range is important for understanding the performance of large tokamaks, such as ITER, because the temperatures in the pedestal, edge, scrape-off-layer and divertor region fall in this range.