Relationship between polytropic index and temperature anisotropy in space plasmas

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 function, having its shape determined by the temperature anisotropies 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 velocity space, and the polytropic index, with the ratio of temperature anisotropy. Moreover, a data and statistical analysis is performed to test the application of the theoretically 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 indices characterize anisotropic plasmas. Finally, possible extensions of the theory considering (i) non-adiabatic polytropic behavior, and (ii) more general distributions, are further discussed.

arXiv comment23 pages, 8 figures

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• The polytropic behavior of Solar Wind protons as observed by Ulysses spacecraft during Solar minimum
• Deriving the bulk properties of solar wind electrons observed by Solar Orbiter: A preliminary study of electron plasma thermodynamics
• Polytropic representation of the kinetic pressure tensor of non-ideal magnetized fluids in equilibrium toroidal structures
• Polytropic representation of non-isotropic kinetic pressure tensor for non-ideal plasma fluids in relativistic jets