Uncertainty and error in complex plasma chemistry models

Abstract

Chemistry models that include dozens of species and hundreds to thousands of reactions are common in low-temperature plasma physics. The rate constants used in such models are uncertain, because they are obtained from some combination of experiments and approximate theories. Since the predictions of these models are a function of the rate constants, these predictions must also be uncertain. However, systematic investigations of the influence of uncertain rate constants on model predictions are rare to non-existent. In this work we examine a particular chemistry model, for helium–oxygen plasmas. This chemistry is of topical interest because of its relevance to biomedical applications of atmospheric pressure plasmas. We trace the primary sources for every rate constant in the model, and hence associate an error bar (or equivalently, an uncertainty) with each. We then use a Monte Carlo procedure to quantify the uncertainty in predicted plasma species densities caused by the uncertainty in the rate constants. Under the conditions investigated, the range of uncertainty in most species densities is a factor of two to five. However, the uncertainty can vary strongly for different species, over time, and with other plasma conditions. There are extreme (pathological) cases where the uncertainty is more than a factor of ten. One should therefore be cautious in drawing any conclusion from plasma chemistry modelling, without first ensuring that the conclusion in question survives an examination of the related uncertainty.