Rotational temperature measurements of the Princeton FRC using non-optical electron-impact excitation selection rules

Spectroscopic rotational temperature measurement techniques are often used in molecular gas dynamics and generally can be related to the gas translational temperature. Many authors assume a low-mass electron cannot significantly disturb the molecular rotational level distribution, enforcing a rotational selection rule $\Delta K =0$. Others believe optical selection rules apply $(\Delta K =0, \pm 1)$. In either case, these selection rules allow for the use of simple Boltzmann plots to estimate the rotational temperature. However, rotational transitions for $\Delta K >1$ are in fact allowed by molecular symmetries and dipole selection rules. It has been found through this study that these larger transitions $(\Delta K = \pm2)$ for the hydrogen Fulcher- $\alpha$ emission $(H_2 \ d ^3 \Pi_u \rightarrow a ^3 \Sigma_g^+)$ can affect the rotational distributions by up to $40\%$ for $K=5$ upper rotational states and also results in inferred rotational temperatures about $30\%$ lower than would be obtained with Boltzmann plots and optical selection rules. This broader use of non-optical selection rules is applied to measuring rotational temperatures radially across the plasma column of the Princeton Field-Reversed Configuration device at a variety of pressures.