Calibration of a Hall Thruster numerical model using a Bayesian approach

One-dimensional fluid Hall thruster models are useful tools for the analysis of the properties evolution within the plasma discharge, and the surge and onset of instabilities. In particular, the use of such models permits to gain some insight into the behaviour and the growth of the so-called breathing mode. However, this type of model contains a series of simplifications and assumptions that result in a lack of self-consistency, in particular regarding the issue of cross-field electron transport, as well as other uncertanties regrading wall interaction and injection plane conditions. All this leads to the use of additional free parameters, which make it necessary to calibrate the model results against experimental data. However, proper calibration requires a systematic exploration of the multidimensional parameter space, requiring a large amount of model runs and prohibitively time-consuming operations. Moreover, a means for quantifying the goodness of a certain combination of parameter values is necessary. The present research introduces a novel strategy for the automated calibration of fluid 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. The methodology is put to test using a Lorenz attractor model, and a benchmark model of a Hall thruster discharge. Solutions in which the parameters of noisy synthetic data are inferred demonstrate the capability (and limitations) of the methodology to calibrate such models, as well as the possibility of using it to reconstruct anomalous transport profiles along the channel, and their related uncertainties. The developed Bayesian methodology sets the ground for the future development of an Integrated Data Analysis suite for Hall thrusters, which will permit to realize a consistent reconstruction of the thruster operation and the plasma properties, and to gain further insight on the different processes which take place within the plasma.