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Open AccessArticle

On the Calculation of the Effective Polytropic Index in Space Plasmas

1
Department of Space and Climate Physics, Mullard Space Science Laboratory, University College London, Dorking, Surrey RH5 6NT, UK
2
Southwest Research Institute, San Antonio, TX 78238, USA
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(10), 997; https://doi.org/10.3390/e21100997
Received: 25 September 2019 / Revised: 9 October 2019 / Accepted: 10 October 2019 / Published: 12 October 2019
(This article belongs to the Special Issue Theoretical Aspects of Kappa Distributions)
The polytropic index of space plasmas is typically determined from the relationship between the measured plasma density and temperature. In this study, we quantify the errors in the determination of the polytropic index, due to uncertainty in the analyzed measurements. We model the plasma density and temperature measurements for a certain polytropic index, and then, we apply the standard analysis to derive the polytropic index. We explore the accuracy of the derived polytropic index for a range of uncertainties in the modeled density and temperature and repeat for various polytropic indices. Our analysis shows that the uncertainties in the plasma density introduce a systematic error in the determination of the polytropic index which can lead to artificial isothermal relations, while the uncertainties in the plasma temperature increase the statistical error of the calculated polytropic index value. We analyze Wind spacecraft observations of the solar wind protons and we derive the polytropic index in selected intervals over 2002. The derived polytropic index is affected by the plasma measurement uncertainties, in a similar way as predicted by our model. Finally, we suggest a new data-analysis approach, based on a physical constraint, that reduces the amount of erroneous derivations. View Full-Text
Keywords: polytropic index; space plasmas; solar wind polytropic index; space plasmas; solar wind
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Nicolaou, G.; Livadiotis, G.; Wicks, R.T. On the Calculation of the Effective Polytropic Index in Space Plasmas. Entropy 2019, 21, 997.

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