Bayesian method in optical emission spectroscopy: temporal evolution of electron density from time-integrated Hα emission and validation with time-resolved measurements for pulsed nanosecond discharges in water

Abstract The characterization of in-liquid discharges is known to be a challenging feat due to their stochastic nature and nanosecond time scale evolution. In this study, the time-resolved electron density ( n e ) of a spark discharge in water is analyzed by coupling optical emission spectroscopy (OES) measurements with a Bayesian model. It is first highlighted that a single Voigt profile cannot adequately describe the time-averaged H α line profile; this is due to the significant time evolution of the discharge properties. To overcome this limitation, a model describing the temporal evolution of the line emission intensity and shape is developed and used to fit the time-integrated spectrum. The unknown parameters in the model are determined using the Dynesty python package, according to the Bayesian nested sampling method. With such model, the simulated and measured spectrum of the H α transition agree very well. Over the range of experimental conditions investigated, it is found that the electron density rapidly reaches <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mstyle scriptlevel="0"/> <mml:mstyle scriptlevel="0"/> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>25</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mstyle scriptlevel="0"/> <mml:mrow> <mml:msup> <mml:mrow> <mml:mtext>m</mml:mtext> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> </mml:math> and then decreases exponentially with a decay time of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mstyle scriptlevel="0"/> <mml:mstyle scriptlevel="0"/> <mml:mn>238</mml:mn> <mml:mrow> <mml:mtext> ns</mml:mtext> </mml:mrow> </mml:mrow> </mml:math> . These values are consistent with those determined using time-resolved measurements and analysis of the H α and O I line broadenings. Overall, this study shows that time-resolved plasma properties can be obtained from time-integrated OES data by applying a Bayesian-based modeling approach. Further studies are needed to expand the scope of the developed model and determine plasma properties over a broad range of conditions.