Polytropic Index of the Solar Wind Ions near the Earth Calculated Using a Homogeneous Magnetohydrodynamic Bernoulli Integral

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 x 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 x B ≤ 5%, 3%, and 1% and 1.241 and 1.097 at δ E x 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.