Measurement of Hydrogen Molecular Rotational Temperatures in LTX-$\beta$ for the Thermometry of Plasma-Facing Lithium Surfaces*

LTX-$\beta$ is a spherical tokamak device operated with plasma-facing surfaces coated with solid and liquid lithium. We measured the variation of the H$_{2}$ $d$-state rotational temperature ($T_{\rm rot}$) in LTX-$\beta$ to deduce the surface temperature because phase change or passivation of lithium may reduce the accuracy of conventional surface thermometry using an infrared camera. H$_{2}$ emission line spectra (Q1-Q5(0-0) of Fulcher-$\alpha$ band) were observed under three surface conditions: fresh solid lithium, passivated solid lithium, and liquid lithium. We used two radial viewing chords directed to the inboard limiter and a spectrometer (F/1.8, and 70 pm wavelength resolution) for the measurement. $T_{\rm rot}$ was estimated from the relative intensities of the emission lines assuming a Boltzmann distribution. The estimated $T_{\rm rot}$ was higher for the liquid surface than for the fresh solid surface. No obvious dependence of $T_{\rm rot}$ on the electron density near the limiter was observed for densities in the range of 0.2--1.2$\times 10^{18}$ ${\rm m}^{-3}$.