Abstract
Abstract The paper develops a theoretical relationship between the polytropic index and the temperature anisotropy that may characterize space plasmas. The derivation is based on the correlation among the kinetic energies of particles with velocities described by anisotropic kappa distributions. The correlation coefficient depends on the effective dimensionality of the velocity distribution, which is determined by the temperature anisotropy caused by the ambient magnetic field; on the other hand, the effective dimensionality is directly dependent on the polytropic index. This analysis leads to the connection between the correlation coefficient, effective dimensionality of the velocity space, and the polytropic index, with the temperature anisotropy. Moreover, a data and statistical analysis is performed to test the developed model in the solar wind proton plasma near 1 au. The derived theoretical relationship is in good agreement with observations, showing that the lowest and classical value of the adiabatic polytropic index occurs in the isotropic case, while higher values of the adiabatic index characterize more anisotropic plasmas. Finally, possible extensions of the theory considering (i) nonadiabatic polytropic behavior and (ii) more general distributions, are further discussed.
Highlights
The polytropic behavior is a thermodynamic property of the particle system – the plasma
The purpose of this paper is to (i) develop a theoretical model that connects the adiabatic polytropic index and the temperature anisotropy; a similar connection will be developed for the non-adiabatic polytropic indices; and (ii) perform a data and statistical analysis in order to examine the validity of the theoretically developed model in the case of the solar wind proton plasma near 1 AU; this will be performed using datasets taken from Wind S/C
The paper showed a relationship between the polytropic index γ and the temperature anisotropy α that may characterize space plasmas
Summary
The polytropic behavior is a thermodynamic property of the particle system – the plasma. Many space plasmas exhibit positive correlations between density and temperature, with their most frequent polytropic index close to the value of the adiabatic process, that is, γ=5/3. There are rarer cases, where space plasmas have negative correlations between their density and temperature; these were found in the outer heliosphere (Elliott et al 2019), inner heliosheath (e.g., Livadiotis et al 2011; Livadiotis & McComas 2013), and the planetary magnetospheres, namely, terrestrial low latitude boundary layer (e.g., Sckopke et al 1981), central plasma sheet (e.g., Pang et al 2015), and bow shock (e.g., Pang et al 2020); Jovian ionosphere (Allegrini et al 2020), magnetosheath and boundary layer (e.g., Nicolaou et al 2014b; 2015); and Saturnian magnetosphere (e.g., Dialynas et al 2018) Space plasmas have polytropic indices with sub-adiabatic (1
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