Detailed Study of the Stark Broadening of Balmer Lines in a High-Density Plasma

Abstract

The Stark-broadened profiles of the Balmer lines ${\mathrm{H}}_{\alpha }$, ${\mathrm{H}}_{\beta }$, ${\mathrm{H}}_{\gamma }$, and ${\mathrm{H}}_{\delta }$, have been measured in a high-current, wall-stabilized arc operated in hydrogen. Temperatures and electron densities have been determined with a plasma model assuming partial local thermodynamic equilibrium (LTE), after a detailed plasma analysis revealed small deviations from complete LTE. The temperatures have been determined from line-to-continuum intensity ratios using ${\mathrm{H}}_{\beta }$ and continuum points in the near uv, and the electron densities were derived from absolute intensity measurements. The investigations cover the range of electron densities between 1.5 × ${10}^{16}$ and ${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and temperatures between 0.9 × ${10}^4$ and 1.4 × ${10}^4$ K. Extensive comparisons with recent Stark-broadening theories and other experiments have been undertaken with the following principal results: The most pronounced differences between this experiment and theory occur in and near the line centers, where the measured profiles show systematically less structure than the calculations predict. Comparisons of the calculated and precisely measured ratios between the ½, ¼, and $\frac{1}{8}$ widths within each line show that the recent theories are internally consistent within 6% for ${\mathrm{H}}_{\beta }$ and ${\mathrm{H}}_{\gamma }$, whereas for ${\mathrm{H}}_{\alpha }$ inconsistencies of order 25% occur. Similar inconsistencies, somewhat larger respectively, are found for the theoretical values of the half-width ratios between different Balmer lines. For the most important line ${\mathrm{H}}_{\beta }$, the measured half-widths agree within 7% with the calculated values. The total experimental error in this comparison, which originates predominantly in the electron-density measurement, is estimated not to exceed 6%. Very reproducible asymmetries and red shifts are observed for ${\mathrm{H}}_{\beta }$ and ${\mathrm{H}}_{\gamma }$. Somewhat smaller red shifts are also obtained for ${\mathrm{H}}_{\alpha }$. The shifts are approximately linear functions of the electron density. Comparisons with other experimental data show appreciable scatter between the various results. We estimate that for the most-often-studied line ${\mathrm{H}}_{\beta }$ the uncertainties in the theoretical Stark widths are of the order of (5-7)% for the range of our experiment.