by Georgios Nicolaou (MSSL, UCL)
The effective polytropic index of space plasmas γ is crucial for understanding the dynamics of the plasma particles. For instance, numerous theoretical descriptions and simulations of plasmas, demand the knowledge of the effective polytropic index for accurate calculations.
Several studies, determined γ within different plasma regions, using single spacecraft observations of the plasma density n and temperature T. The effective polytropic index γ is typically determined from a linear chi-squared minimization fitting of lnT as a function of lnn.
In this paper, we investigate the accuracy of γ calculations based on the standard fitting analysis, considering plasma n and T measurements with a certain level of uncertainty σn and σT respectively (see Figure 1). We model typical plasmas, and we show that uncertainty in the plasma density measurements introduces a systematic error in the calculation of γ, and potentially leads to artificial isothermal indices (Figure 1, left). On the other hand, uncertainty in the plasma temperature measurements introduces a statistical error in the calculation of γ (Figure 1, right). We analyze Wind spacecraft observations of solar wind protons in order to investigate the propagated uncertainties in real plasma applications, confirming our model predictions (Figure 1).
These results highlight how uncertainties in plasma measurements can lead to erroneous values of the poytropic index. In this study we present a new data-analysis approach for reducing the number of erroneous data-points from future analyses.
Figure 1. Normalized histograms of (left) γ as a function of σn/n, for σT/T < 15% and (right) γ as a function of σT/T, for σn/n < 1%. The white line is the mean value of the histogram in each column. We display only the range of uncertainties for which we have more than 100 data points. On each panel, we show the predictions of our model (red) for plasma parameters corresponding to the mode values of each parameter for the analyzed intervals.
For more information, please see the paper:
Nicolaou, G., G. Livadiotis, R. T. Wicks (2019). On the Calculation of the Effective Polytropic Index in Space Plasmas. Entropy, 21, 997. https://doi.org/10.3390/e21100997.