Errors and uncertainty in complex plasma chemistry models

Abstract

Many, perhaps even most, applications of low-temperature plasmas involve mixtures of molecular gases that give rise to complex chemistry. Often, an important task in developing, optimizing and perhaps controlling such applications is understanding which chemical species are important, and by what mechanisms these important species are created and destroyed. Developing a model can be an important step in articulating an understanding of the application. However, such chemistry models can frequently become complex, with tens of species and hundreds or even thousands of reactions. Each of the reactions in a chemistry model is characterized by a rate constant (or equivalently a cross section), and of course the predictions of the model are a function of the values assigned to these rate constants. The set of rate constants is in principle obtained from antecedent work, incorporating a wide variety of experimental and theoretical approaches. These however have a common characteristic, which is that none of them is exact. As a consequence, the predictions of the chemistry model cannot be exact either. The main aim of the present work is to investigate the relationship between the uncertainty in these rate constants and the uncertainty in the model predictions of, for instance, species densities. This is done by assigning a probability distribution to each rate constant, and then using a Monte Carlo procedure to propagate the uncertainty into model predictions. We find that the uncertainty in the model predictions is unequally distributed over the product species densities, and varies appreciably in time. In extreme cases, the range of uncertainty is as much as a factor of ten in species that are thought important in applications. This is likely at least comparable with the uncertainty in measured species densities, so that comparisons between models and experiments may be significant only if the uncertainty in both is considered. A further conclusion of the present work is that the quality of transmission of data from primary sources to modern plasma chemistry models is often poor, so that in addition to irreducible uncertainty, most models contain avoidable errors that also affect the resulting predictions.