Tungsten is important for the controlled fusion research as a perspective construction material for tokamaks. Diagnosing its ions in the tokamak plasma requires detailed knowledge of their spectra. The spectra W I through W VII were studied the most thoroughly. The recently completed compilation of energy levels, wavelengths, and transition probabilities of W I and W II [1] contains 771 energy levels and 9887 lines. Critical compilation of spectral data for higher ionization stages of tungsten is currently under way at NIST. For the spectra W III through W VII, that were studied using a sliding-spark light source, now there are several hundreds of known spectral lines. Other light sources like laser-produced plasmas, exploding wires, tokamaks, and electron-beam ion traps produce substantially higher ionization stages. Some experimental data exist now for the following tungsten ions: 13+, 27+ through 48+, and 52+. We select the most accurately measured wavelengths and derive the energy levels that are consistent with them. To resolve line-assignment ambiguities and find the missing ionization potentials, we make ab initio and semi-empirical calculations. For the Na-, Na-, He-, and H-like ions, where there are no measurements, we include the results of accurate calculations, as these spectra are important for plasma diagnostics and for benchmark theory-testing experiments. This work is supported by NASA and Office of Fusion Energy Sciences of the U.S. Department of Energy.

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