Artificial Polytropic Behavior of Plasmas Determined from the Application of Chi-squared Minimization Analysis to Data with Significant Statistical Uncertainty

Abstract

The effective polytropic index of plasmas is typically determined from the analysis of the plasma temperature (or pressure) and density, which are plasma bulk parameters determined from analyses of in situ plasma observations. Here, we show that the use of the typical chi-squared minimization method in plasma observation analyses results in artificial correlations between the plasma density and temperature, which will introduce errors in the determination of the plasma polytropic relationship. We quantify this potential error by analyzing simulated plasma observations. We specifically show that even in cases of nonvarying plasma, a significant statistical uncertainty in the observations leads to the determination of plasma parameters, which seemingly follow a nearly adiabatic model. Moreover, we consider isobaric plasma variations and discuss the error in the determined polytropic relationship as a function of the actual plasma variations and the statistical uncertainties of the determined parameters. We finally show that the use of an alternative analysis method improves the accuracy of the results.