Theoretical modeling combined with experimental spectroscopic measurements for the diagnosis of high-Z erosion and transport applications in plasmas

Abstract

Understanding plasma-material interaction (PMI) continues to be a challenge for future fusion reactors. High-Z materials (e.g. tungsten, molybdenum) have emerged as leading solutions for plasma facing materials. Erosion and transport of these high-Z elements remains an open area of research which warrants study. The properties of emission from ions in a plasma provides both potential for plasma diagnostics and key information required for plasma modeling. Generalized collisional ra- diative theory is a powerful tool for modeling of low and moderately dense plasmas. A new Python program (ColRadPy) has been developed that solves the collisional-radiative and ionization balance equations within the Generalized Collisional-Radiative framework. It has applications to fusion, basic laboratory and astrophysical plasmas. It produces generalized coefficients that can be easily imported into existing plasma modeling codes and spectral diagnostics. A spectral survey of tungsten emission in the ultraviolet region has been completed in the DIII-D tokamak and the Compact Toroidal Hybrid (CTH) torsatron to assess the potential benefit of UV emission for the diagnosis of gross W erosion. A total of 53 W I spectral lines are observed from the two experiments using both survey and high-resolution spectrometers between ∼ 200 − 400 nm. The level identifications presented in this work are based upon a previous atomic structure calculation and new high quality atomic data for neutral W. Of the 53 W I observed lines, 32 have not previously been reported at fusion relevant divertor plasmas conditions (T e ∼ 10−20 eV, n e ∼ 1×10 13 cm −3 ), including an intense line at 265.65 nm which could be important for benchmarking the frequently employed line at 400.88 nm. The impact of metastable level populations on the W I emission spectrum and any erosion measurement utilizing a spectroscopic technique is potentially significant and is quantified in this work. Nevertheless, the high density of W I emission in the UV region allows for determination of the relative metastable fractions and plasma parameters local to the erosion region. There are also over 15 singly ionized tungsten emission lines as well as more than 10 doubly ionization emission lines that are also observed in the UV. W IV spectral lines could be observed in the UV, which is consistent with CR modeling. While the W I emission lines can be used to measure the gross tungsten erosion, the simultaneous observation of W I emission combined with W II lines identified in this work could be used to estimate the net erosion of tungsten from plasma facing components. Similarly, the fraction of tungsten that is promptly re-deposited could also be inferred. Identified lines can be used for collisional radiative based diagnostics such as line ratio diagnostics. Key to this study are the new spin-changing collisional rate coefficients between po- tential metastable levels allowing the dynamics of metastable levels to be explored in detail for the first time. Long-lived metastable states in neutral tungsten can potentially impact measurements of tungsten erosion from plasma facing components. Time-dependent col- lisional radiative modeling of neutral tungsten is used to analyze the role of these states in tungsten emission and ionization. The large number of non-quasistatic atomic states in neutral tungsten can take on the order of milliseconds to reach equilibrium, depending on plasma conditions, causing erosion measurements to be affected by the time-dependence of the metastable populations. Previous measurements using the 400.88 nm neutral tungsten emission line could be affected by these non-quasistatic metastable effects. Therefore, a scheme for measuring the relative metastable fractions is proposed through simultaneous observation of multiple ultraviolet spectral lines of neutral tungsten. The accuracy of ero- sion measurements could potentially be increased by including these previously unconsidered metastable effects. The Chodura sheath provides a region of low electron density on the order of centimeters (orders of magnitude larger than the Debye sheath) making time-dependent effects important due to the large number of metastable levels in neutral tungsten. A simple model is developed to account for the effects of the Chodura sheath on the time-dependent neutral tungsten system. Eroded tungsten is assumed to sputter into the plasma as ground state atoms with ballistic velocity through the sheath until ionized. The collisional radiative coefficients used in erosion measurements can be modified by up to a factor of 10 by addition of the sheath model at high electron densities. The ratio of the 254.14 to the 265.65 nm neutral tungsten lines is shown to be a promising temperature diag- nostic from collisional radiative modeling. Comparisons between Langmuir probe measured electron temperatures and temperatures inferred from collisional radiative modeling of the line ratio yields good agreement for CTH plasmas. Thus, the work of this dissertation, and the new atomic data for neutral tungsten that has been generated for this project, provide the basis for accurate tungsten erosion and redeposition measurements on fusion relevant devices and yield a general roadmap for how to model the spectral emission from complex species such as tungsten.