Determination of the tungsten gross erosion rate based on the multiple atomic spectral lines

Measuring the in situ erosion rate of tungsten using an optical emission spectroscopic diagnostic technique, so called the S/XB method, has recently gained attention in current fusion research. This method calculates the erosion rate by multiplying the S/XB value, which represents ionization per photon emission, with the intensity of the specific spectral line. The S/XB value was given by the ionization rates (S) and the excitation rates (X) from the ground and the metastable levels and the branching ratio (B) for the specific radiative transition of neutral tungsten (W I), assuming a corona equilibrium among the ground, metastable, and upper resonance levels. The conventional S/XB method assumes a Boltzmann distribution for metastable level densities and introduces the free parameter of the tungsten atomic characteristic temperature (). Herein, we propose an improved S/XB method to measure the erosion rates of tungsten in a divertor to eliminate the ambiguity caused by . Our approach directly calculates the densities of ground and metastable levels using a set of photon emission equations that relate their densities to multiple spectral line intensities within the framework of coronal equilibrium. Subsequently, the sputtered flux is obtained from the matrix operator form of S/XB and the multiple spectral line intensities given by the measurement. Our proposed method was experimentally tested using the plasma beam irradiation facility by comparing the gross tungsten erosion rates calculated using our method with those obtained from conventional approaches and those determined through the sputtering yield by the Ar+ ion beam flux. From the experiment, we obtained the sputtered tungsten flux of 4.0 × 1020 m−2 s−1 (2.1 × 1020) using our method at a discharge current of 150 A from the plasma source and an ion incident energy of 100 eV, while the previous method yielded a range from 1.4 × 1020 m−2 s−1–1.9 × 1021 m−2 s−1 by varying and spectral lines. Using the sputtering yield method, a sputtered flux of 4.1 × 1020 m−2 s−1 (1.1 × 1019) was measured as a reference value. The results demonstrate that our S/XB method significantly reduces ambiguity in the selection of spectral lines and the parameter, and closely agrees with the reference values, offering a more accurate and consistent approach for measuring tungsten erosion in fusion reactors.