Polytropic index of magnetosheath ions based on homogeneous MHD Bernoulli Integral

Abstract

This paper uses Cluster data during the period from 2001 to 2010 to study the polytropic processes of magnetosheath ions. Utilizing the method of homogeneous magnetohydrodynamic (MHD) Bernoulli integral (MBI), we first identify streamflow tubes, then use the constant of polytropic relation to guarantee that the streamflow tube experiences an unchanged polytropic process, and finally determine the polytropic index of ions in these streamflow tubes. The statistical results show that the magnetosheath is a complicated system in which the polytropic index of ions ranges from −2 to 3. The polytropic index distribution of ions is dependent on the electromagnetic energy flux perpendicular to the streamline. The median polytropic index of ions in the magnetosheath is 0.960, 0.965, and 0.974 for perpendicular electromagnetic energy ratio δE × B < 5%, δE × B < 3%, and δE × B < 1%, respectively. There are two basic polytropic processes in the magnetosheath: the dominant isothermal process and the isobaric process. When there is no exchange of electromagnetic energy between neighboring streamflow tubes, the magnetosheath ions are isothermal. However, when the perpendicular electromagnetic energy ratio increases, the isobaric polytropic process starts to emerge. The magnetosheath ion flows are highly localized because most streamflow tubes experiencing same polytropic processes last less than 60 s. Thus, the polytropic index of magnetosheath ion flows is highly variable.

Kinetic Analysis of the Energy Transport of Two‐Flow Components in the Plasma Sheet

“…Zhu (1990) statistically analyzed the data of plasma number density and pressure measured by ISEE satellite from and found that the polytropic index in the CPS is 1.08 for AE < 100 nT and 1.31 for AE > 100 nT, respectively. The approach of MHD Bernoulli Integral is considered to be one of the best methods to calculate polytropic index since it can guarantee that the used data come approximately from the same unit (Kartalev et al, 2006;Nicolaou et al, 2014;Pang et al, 2016). The approach of MHD Bernoulli Integral is considered to be one of the best methods to calculate polytropic index since it can guarantee that the used data come approximately from the same unit (Kartalev et al, 2006;Nicolaou et al, 2014;Pang et al, 2016).…”

“…Pang et al (2015aPang et al ( , 2015b adopted the approach of MHD Bernoulli integral and found that the polytropic index of background plasma sheet ions have a wide distribution around γ~1.0. The approach of MHD Bernoulli Integral is considered to be one of the best methods to calculate polytropic index since it can guarantee that the used data come approximately from the same unit (Kartalev et al, 2006;Nicolaou et al, 2014;Pang et al, 2016). Baumjohann and Paschmann (1989) also show that the polytropic index is 1.39 in the quiet (AE < 100 nT) plasma sheet and 1.64 in the active (AE > 100 nT) plasma sheet, respectively.…”

Dependence of Thermodynamic Processes on Upstream Interplanetary Magnetic Field Conditions for Magnetosheath Ions

“…Therefore, the polytropic index can be estimated from either the number density‐thermal pressure ( n ‐ p ) relation or the number density‐temperature ( n ‐ T ) relation. Using the linear fit between the logarithms of number density and those of thermal pressure (or temperature), previous studies examined thermodynamic conditions for plasmas in the various regions near the terrestrial magnetosphere, such as the interplanetary space (Kartalev et al, ; Newbury et al, ; Nicolaou et al, ), the magnetosheath (Pang et al, ; Song et al, ), and the plasma sheet (Baumjohann & Paschmann, ; Frühauff et al, ; Huang et al, ; Pang et al, ; Zhu, ).…”

“…Pudovkin et al () and Meister et al () examined the thermodynamic properties for magnetized anisotropic plasma using the anisotropic magnetohydrodynamics (MHD) with the double‐adiabatic law and suggested that the effective polytropic index, which is characterized by the relationship between the total thermal energy and the number density of the plasma in their studies, depends both on the characteristics of the plasma flow and on the temperature anisotropy. Using the polytropic relation and Bernoulli's theorem, Pang et al () examined the polytropic indices for magnetosheath ions estimated along the same streamline and found that their probability distribution has a major peak near 1 (that is, quasi‐isothermal process) with a minor peak near 0 (that is, quasi‐isobaric process). Moreover, they suggested that the isobaric process for magnetosheath ions is attributed to the electromagnetic energy, which exchanges across the streamlines.…”

“…In this study, we statistically examine the thermodynamic processes for magnetosheath ions from the polytropic index estimation. The polytropic relation and Bernoulli's theorem are used to clarify whether the polytropic index is estimated in the same specific streamline (Kartalev et al, ; Livadiotis, ; Nicolaou et al, ; Pang et al, , ). The preferred thermodynamic nature for magnetosheath ions is examined by using the probability distribution of the polytropic index.…”