This paper, using the data of Cluster during 2001–2010, studies the polytropic processes of solar wind ions near the Earth. We calculate the polytropic index of ions for different outward electromagnetic energy ratios δ E × B and entropy parameter changes δ entropy based on the approach of the homogeneous magnetohydrodynamic Bernoulli integral (MBI). Solar wind ions have a broad distribution of polytropic indices with multiple peaks in the range of [−7.0, 6.0]. The median polytropic indices are 1.264, 1.321, and 1.418 at δ entropy = 5% for δ E × B  ≤ 5%, 3%, and 1% and 1.241 and 1.097 at δ E × B  ≤ 5% for δ entropy ≤ 3% and 1%. In most of the dayside, the median polytropic index of the solar wind basically increases with increasing geocentric distance and has an obvious dawn–dusk asymmetry because of the solar wind–magnetosphere interaction. The polytropic indices near the bow shock are basically within the range from ∼−1.0 to ∼3.0, and their median values are between 0.5 and 1.3. Those polytropic indices of solar wind ions far away from the bow shock are basically in the range from ∼−2.0 to ∼6.0 and have median values between 1.6 and 2.2. Near the terminator, the median polytropic index has no obvious radial distribution, but it has an obvious dawn–dusk asymmetry. The above results suggest that polytropic indices in the solar wind become smaller after being scattered or rebounded by a fast shock wave. It is also found that the polytropic processes in the solar wind near the Earth are closely related to those in the magnetosheath.

We, using the Cluster data from 2001 to 2010, studied spatial distribution of the ion polytropic index in the magnetosheath, and the modulation of polytropic process by the low-frequency disturbances (4–18 mHz). The total of 30,3283 samples is divided into two sorts: quasi-perpendicular and quasi-parallel propagating ones. The median polytropic index increases with spreads narrowing from the bow shock to the magnetopause. The median polytropic indices are basically between isothermal and adiabatic in the inner magnetosheath, and between isothermal and isobaric in the outer magnetosheath. The spatial distributions of the correlation coefficient (CC) between the perturbed ion number density and the parallel magnetic field CC (δn, δB ∥) have a good correlation with those of polytropic index. The quasi-perpendicular disturbances are mostly mirror-like modes (D r ≪ 1) except for some slow-mode disturbances (D r ≥ 1) in the regions near the Sun–Earth line and the inner magnetosheath. The polytropic indices in the inner and middle magnetosheath modulated by mirror-like-mode disturbances are between 0.9 and 1.3. The quasi-parallel propagating low-frequency disturbances are predominantly slow modes in the inner and middle magnetosheath, and Alfvén modes in the outer magnetosheath. For the samples with quasi-parallel propagating disturbances, the polytropic processes are basically between isothermal and isobaric except near the magnetopause. The good correlation between the spatial distributions of polytropic index and low-frequency disturbances indicates that the distribution of the polytropic index in the magnetosheath is modulated by low-frequency disturbances.