## Convergence of abundance with respect to the difference in the abundance for every five additional groups of excited states are included, in the cases of (a) W^{23 +} to W^{28 +}, (b) W^{29 +} to W^{34 +}, (c) W^{35 +} to W^{40 +} and (d) W^{41 +} to W^{46 +}

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**Figure 7.** Convergence of abundance with respect to the difference in the abundance for every five additional groups of excited states are included, in the cases of (a) W^{23 +} to W^{28 +}, (b) W^{29 +} to W^{34 +}, (c) W^{35 +} to W^{40 +} and (d) W^{41 +} to W^{46 +}.

**Abstract**

The fractional ion abundance and rates of ionization and recombination of multiple charged tungsten ions in magnetic fusion plasmas are investigated using a collisional radiative model. Using a computer algorithm to generate a set of atomic states to be included in the collisional radiative model, the dominant dielectronic recombination and excitation autoionization channels are determined by a systematic convergence analysis of the level population and ion abundance with respect to the size of the model. The atomic data, such as energy levels and rates of the radiative decay as well as autoionization, are obtained by the *ab initio* calculation using the Hebrew University Lawrence Livermore Atomic Code. The calculations are carried out in the temperature range of 100 eV–5 keV, and the ratio between the abundances of W^{44 +} and W^{45 +} ions agrees well with an experimental result obtained without any artificial adjustment of the atomic rates.