Polytropic index of central plasma sheet ions based on MHD Bernoulli integral

This paper uses the data of Cluster from 2001 to 2009 to study the polytropic processes of central plasma sheet (CPS) ions. We first adopt the approach of MHD Bernoulli integral (MBI) to identify homogeneous streamflow tubes (quasi-invariant MBI regions) and then calculate the polytropic index of ions for those streamflow tubes whose outward electromagnetic energy ratios δ  < 0.05. The central plasma sheet is actually a complicated system, which comprises many streamflow tubes with different polytropic relations and the transition layers in between. The polytropic indexes of the CPS ions range from 0.1 to 1.8 and have a quasi-Gaussian distribution. The median polytropic index is 0.93 for AE < 200 nT and 0.91 for AE ≥ 200 nT. Thus, there is no obvious difference between the polytropic indexes of the quiet time and the substorm time CPS ions, which suggests that the thinning and thickening processes of plasma sheet during substorm times do not change obviously the polytropic relation of the CPS ions. The statistical analysis using different δ (δ < 0.05, 0.025, and 0.01) shows that the outward emission of electromagnetic energy is an effective cooling mechanism and can make the polytropic index to decrease and shift toward isobaric. It is inferred that the CPS ions as a whole much likely behave in a way between isobaric and isothermal.