Inference of Electron Density in the Hot Spot of NIF Compressed Capsules from Krypton Helium-$\beta $ Stark Line Shapes*

The dHIRES x-ray spectrometer measures Kr He$\alpha $ and He$\beta $ spectra from NIF compressed capsules with 10-eV spectral and 30-ps temporal resolution. Theoretical calculations of the Stark-broadened line shape of the He$\beta $ complex (3 $^{\mathrm{3}}$P$_{\mathrm{1}}$, $^{\mathrm{1}}$P$_{\mathrm{1}}$, $^{\mathrm{1}}$D$_{\mathrm{2}})$ show monotonic variations with density of the line widths, line energies, and intensity of the 3 $^{\mathrm{3}}$P$_{\mathrm{1}}$ and 3 $^{\mathrm{1}}$D$_{\mathrm{2}}$ lines relative to the main, 3 $^{\mathrm{1}}$P$_{\mathrm{1}}$ peak. Comparison of the measured Kr He$\beta $ complex line profiles with the theoretical line shapes provides a measure of the time history of the electron density. These comparisons will be shown for four NIF shots with Kr-doped capsules.