We spectroscopically measure multiple hydrogen Balmer line profiles from laboratory plasmas to investigate the theoretical line profiles used in white dwarf atmosphere models. X-ray radiation produced at the Z Pulsed Power Facility at Sandia National Laboratories initiates plasma formation in a hydrogen-filled gas cell, replicating white dwarf photospheric conditions. Here we present time-resolved measurements of H$beta$ and fit this line using different theoretical line profiles to diagnose electron density, $n_{rm e}$, and $n=2$ level population, $n_2$. Aided by synthetic tests, we characterize the validity of our diagnostic method for this experimental platform. During a single experiment, we infer a continuous range of electron densities increasing from $n_{rm e}sim4$ to $sim30times10^{16},$cm$^{-3}$ throughout a 120-ns evolution of our plasma. Also, we observe $n_2$ to be initially elevated with respect to local thermodynamic equilibrium (LTE); it then equilibrates within $sim55,$ns to become consistent with LTE. This supports our electron-temperature determination of $T_{rm e}sim1.3,$eV ($sim15,000,$K) after this time. At $n_{rm e}gtrsim10^{17},$cm$^{-3}$, we find that computer-simulation-based line-profile calculations provide better fits (lower reduced $chi^2$) than the line profiles currently used in the white dwarf astronomy community. The inferred conditions, however, are in good quantitative agreement. This work establishes an experimental foundation for the future investigation of relative shapes and strengths between different hydrogen Balmer lines.
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