Traceable Bayesian Uncertainty Quantification in Single-Shot Terahertz Spectroscopy of Plasmas

Single-shot terahertz (THz) time-domain spectroscopy is an ultrafast diagnostic that is necessary to probe transient processes in reacting plasmas, but single-shot implementations based on spectral encoding face significant challenges from chirp-induced spectral distortions in conventional configurations. The inference of plasma parameters, such as path-integrated electron density $\boldsymbol{\left(\tilde n_e\right)}$ and collision frequency $\boldsymbol{\left(\nu\right)}$, typically relies on least-squares (LS) fitting of the Drude model to measured waveforms. However, LS methods produce biased estimates of $\boldsymbol{\tilde n_e}$ and $\boldsymbol{\nu}$ with curvature-based uncertainties, failing to account for unmodeled detection physics, measurement noise, and parameter degeneracies. To overcome these challenges, we introduce Supercontinuum-Enhanced THz Spectroscopy (SETS), leveraging broadband supercontinuum probes to double the usable spectral bandwidth, minimize chirp penalties, and mitigate null frequencies that give rise to phase nonlinearities in the retrieved THz response. We combine SETS measurements with Bayesian Markov Chain Monte Carlo (MCMC) inference by developing a unified forward model that explicitly integrates the plasma response and the spectral-encoding detection physics into a single computational framework. This approach allows for the joint estimation of the distorted THz signal and physical parameters, while incorporating traceable prior uncertainties on nuisance parameters derived from independent optical diagnostics and plasma geometry constraints. Applied to radio-frequency inductively coupled plasma measurements (150 – 500 W), SETS captures systematic waveform evolution from increasing ionization, while Bayesian analysis recovers the associated $\boldsymbol{\tilde n_e}$ and $\boldsymbol{\tilde\nu}$ with well-constrained credible intervals (+10/-4\% to +18/-5\% for $\boldsymbol{\tilde n_e}$ and $\pm$2–4\% for $\boldsymbol{\tilde\nu}$). Autocorrelation functions decay to zero within 100 lags with an effective sample size exceeding $\boldsymbol{>10^3}$, demonstrating robust MCMC convergence, while pairwise cross-correlations reveal strong physical degeneracies, quantitative insights that are inaccessible in the LS fitting method.