Polytropic index of ions in the Earth magnetosheath

Useing the data of Cluster from 2001 to 2009, the polytropic index of the magnetosheath ions are calculated by the method of homogeneous MHD Bernoulli integral (MBI). The spatial distribution of ion polytropic index and modulation by low frequency MHD disturbances (4-18 mHz) are studied. The main results are as follows: The magnetosheath is a turbulent system in which the polytropic index of ions ranges from -2 to 3. The distribution of ion polytropic index 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%, <3%, and <1%, respectively. There are two basic polytropic processes in the magnetosheath: the dominant isothermal process and the local isobaric process. When there is no exchange of electromagnetic energy between neighboring streamflow tubes, the magnetosheath ions are isothermal. However, when δE×B increases, the isobaric polytropic process starts to emerge. The median polytropic indexes of ions in the GSE X-Y plane of the equatorial magnetosheath decreases from the magnetopause to the bow shock. The magnetosheath ions are basically between isothermal and adiabatic in the inner magnetosheath (near the magnetopause), around isothermal in the middle magnetosheath, and between isothermal and isobaric in the outer magnetosheath. The spatial distributions of the correlation coefficient between the perturbed ion number density and parallel magnetic field CC_δnδB|| have a good correlation with the distribution of polytropic index. The quasi-perpendicular disturbances are basically mirror-like modes (Dr<<1) except some slow mode disturbances (Dr≥1) in the regions near the Sun-Earth line. The polytropic indexes in the inner and middle magnetosheath modulated by mirror-like mode disturbances (CC_δnδB||<0) are between 0.9 and 1.2. The quasi-parallel propagating low frequency disturbances are predominantly slow modes in the inner magnetosheath and Alfvén modes in the middle and outer magnetosheath. For the samples with quasi-perpendicular propagating disturbances, the polytropic process is basically between isothermal and isobaric except near the magnetopause.