Calibration of a Hall Thruster numerical model using a Bayesian approach

Abstract One-dimensional fluid Hall thruster models are useful tools for the analysis of the plasma evolution within the discharge, and the surge and onset of instabilities. However, this type of model contains a series of simplifications and assumptions that result in a lack of self-consistency, in particular regarding the cross-field electron transport, as well as other uncertainties regarding wall interaction and injection conditions. All this leads to the addition of free parameters, which require calibrating the model against experimental data. Proper calibration requires a systematic exploration of the multidimensional parameter space, involving numerous model runs and time-consuming operations. Moreover, a means for quantifying the goodness of a particular combination of parameter values is necessary. The present research introduces a novel strategy for the automated calibration of fluid plasma models which permits to combine data from different sources, such as discharge current signals, thrust and local plasma measurements, and to better explore the parameter space while greatly reducing the required time and effort with respect to manual calibration. The strategy is developed using a Bayesian approach, which permits to combine physical modelling with multiple types of data, while robustly keeping trace of uncertainties. Likelihood of current signals is evaluated using a Wasserstein distance, while Gaussian likelihoods are used to evaluate thrust and local plasma properties measurements. The present study uses a benchmark model to generate a set of synthetic data to assess the advantages and limitations of the approach, as well as the difficulties arising from the evaluation the uncertainty related to the current signal and to the interaction between the different calibrated parameters. Additionaly, the article shows the limitations of calibrating several parameters relying only on discharge current signals, a clear indication of limited identifiability in the inference process, eventually requiring the use of additional data to obtain reliable calibrations.