Bayesian plasma model selection for Thomson scattering.

Laser Thomson scattering (LTS) is a measurement technique that can determine electron velocity distribution functions in plasma systems. However, accurately inferring quantities of interest from an LTS signal requires the selection of a plasma physics submodel, and comprehensive uncertainty quantification (UQ) is needed to interpret the results. Automated model selection, parameter estimation, and UQ are particularly challenging for low-density, low-temperature, potentially non-Maxwellian plasmas like those created in space electric propulsion devices. This paper applies Bayesian inference and model selection to a Raman-calibrated LTS diagnostic in the context of such plasmas. Synthetic data are used to explore the performance of the method across signal-to-noise ratios and model fidelity regimes. Plasmas with Maxwellian and non-Maxwellian velocity distributions are well characterized using priors that span a range of accuracy and specificity. The model selection framework is shown to accurately detect the type of plasmas generating the electron velocity distribution submodel for signal-to-noise ratios greater than around 5. In addition, the Bayesian framework validates the widespread use of 95% confidence intervals from least-squares inversion as a conservative estimate of the uncertainty bounds. However, epistemic posterior correlations between the variables diverge between least-squares and Bayesian estimates as the number of variable parameters increases. This divergence demonstrates the need for Bayesian inference in cases where accurate correlations between electron parameters are necessary. Bayesian model selection is then applied to experimental Thomson scattering data collected in a nanosecond pulsed plasma, generated with a discharge voltage of 5 and 10 kV at a neutral argon background pressure of 7 Torr-Ar. The Bayesian maximum a posteriori estimates of the electron temperature and number density are 1.98 and 2.38 eV and 2.6 × 1018 and 2.72 × 1018 m-3, using the Maxwellian and Druyvesteyn submodels, respectively. Furthermore, for this dataset, the model selection criterion indicates strong support for the Maxwellian distribution at 10 kV discharge voltage and no strong preference between Maxwellian and Druyvesteyn distributions at 5 kV. The logarithmic Bayes' factors for these cases are -35.76 and 1.07, respectively.

An incoherent Thomson scattering system for measurements near plasma boundaries.

Laser Thomson scattering (LTS) is a minimally invasive measurement technique used for determining electron properties in plasma systems. Sheath model closure validation requires minimally invasive measurements of the electron properties that traverse the boundaries between the bulk plasma, the presheath, and the plasma sheath. Several studies have probed the radial properties along the surface of discharge electrodes with laser-based diagnostics and electrostatic probes. These measurements provide valuable insight into the electron properties in this dynamic region. However, sheath model calibration requires plasma property measurements perpendicular to plasma bounding surfaces, in this case, along the electrode normal vector between discharge electrodes. This work presents the development of a discharge plasma cell and laser Thomson scattering system with a measurement volume step of 1 mm normal to plasma bounding surfaces. The laser Thomson scattering measurements are made between a set of discharge electrodes separated by ∼25 mm that are used to generate a pulsed argon plasma. The spatial distribution of electron temperature and density is measured at several discharge voltages between 8 and 20 kV at a pressure of 8 Torr-Ar. It is determined that the system is statistically stationary and resembles a classic DC discharge plasma. The results are some of the first laser diagnostic-based "between electrode" measurements made along the plasma bounding electrode normal vector. A one-dimensional sheath model is applied to determine the near cathode electron properties, and it is determined that the edge of the presheath is probed in the high-voltage cases. As the lengths of the presheath and sheath decrease with decreasing voltage, the region recedes below the closest probed point to the cathode. To improve the performance of the diagnostic, the step size of the interrogation volume should decrease by an order of magnitude from 1 mm to less than 100 µm, and the data acquisition strategy should be revised to increase the signal-to-noise ratio.

Megahertz-rate background-oriented schlieren tomography in post-detonation blasts.

The understanding and predictive modeling of explosive blasts require advanced experimental diagnostics that can provide information on local state variables with high spatiotemporal resolution. Current datasets are predominantly based on idealized spherically symmetric explosive charges and point-probe measurements, although practical charges typically involve multidimensional spatial structures and complex shock-flow interactions. This work introduces megahertz-rate background-oriented schlieren tomography to resolve transient, three-dimensional density fields, as found in an explosive blast, without symmetry assumptions. A numerical evaluation is used to quantify the sources of error and optimize the reconstruction parameters for shock fields. Average errors are ∼3% in the synthetic environment, where the accuracy is limited by the deflection sensing algorithm. The approach was experimentally demonstrated on two different commercial blast charges (Mach ∼1.2 and ∼1.7) with both spherical and multi-shock structures. Overpressure measurements were conducted using shock-front tracking to provide a baseline for assessing the reconstructed densities. The experimental reconstructions of the primary blast fronts were within 9% of the expected peak values. The megahertz time resolution and quantitative reconstruction without symmetry assumptions were accomplished using a single high-speed camera and light source, enabling the visualization of multi-shock structures with a relatively simple arrangement. Future developments in illumination, imaging, and analysis to improve the accuracy in extreme environments are discussed.

Bayesian framework for THz-TDS plasma diagnostics.

Terahertz time-domain spectroscopy (THz-TDS) is an optical diagnostic used to noninvasively measure plasma electron density and collision frequency. Conventional methods for analyzing THz-TDS plasma diagnostic data often do not account for measurement artifacts and do not quantify parameter uncertainties. We introduce a novel Bayesian framework that overcomes these deficiencies. The framework enables computation of both the density and collision frequency, compensates for artifacts produced by refraction and delay line errors, and quantifies parameter uncertainties caused by noise and imprecise knowledge of unmeasured plasma properties. We demonstrate the framework with sample measurements of a radio frequency inductively-coupled plasma discharge.

Linear absorption tomography with velocimetry (LATV) for multiparameter measurements in high-speed flows.

We present a linear model for absorption tomography with velocimetry (LATV) to reconstruct 2D distributions of partial pressure, temperature, and streamwise velocity in a high-speed flow. Synthetic measurements are generated by multi-beam tunable diode laser absorption spectroscopy (TDLAS). The measurement plane is tilted relative to the streamwise direction and absorbance spectra are Doppler-shifted by the gas flow. Reconstruction comprises two stages. First, the thermodynamic state is obtained by reconstructing two or more integrated absorption coefficients and evaluating local Boltzmann plots. Second, the velocity field is directly reconstructed from absorbance-weighted linecenters. Absorbance data are inferred by Voigt fitting and reconstructions are quickly computed by matrix-vector multiplication. Nonlinear parameter combinations, such as the mass flow, are more accurate when computed by LATV than estimates obtained by assuming uniform gas properties along each beam.