Low-frequency mirror waves are frequently observed in the planetary magnetosheaths for the plasma conditions of and . This study first shows that the thermodynamic conditions of the observed mirror events may well be described by a set of double-polytropic (DP) laws first proposed by Hau and Sonnerup (1993, https://doi.org/10.1029/93gl01706), and , with the polytropic values being in the ranges of and . The physical basis of the empirical thermodynamic relations is then examined based on the mixed Vlasov-MHD formulation for low-frequency linear mirror instability (Ferrière & Andre, 2002, https://doi.org/10.1029/2002JA009273) which shows that the theoretical energy equations possess the DP forms with and being functions of ; in particular, for mirror unstable cases and . The theoretical predictions are found to be in high agreements with the empirical polytropic values with the average errors of ∼6.5%.

中文翻译：

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观察到的镜波是否存在能量闭包？

低频镜波在的等离子体条件行星magnetosheaths经常观察和。这项研究首先表明，观察到的镜像事件的热力学条件可以很好地由 Hau 和 Sonnerup (1993, https://doi.org/10.1029/93gl01706) 首次提出的一组双多变 (DP) 定律描述，并且，与多变值的范围是和。然后基于低频线性镜不稳定性的混合 Vlasov-MHD 公式（Ferrière & Andre，2002，https://doi.org/10.1029/2002JA009273）检查经验热力学关系的物理基础，这表明理论能量方程具有与DP形式和的是功能; 特别是对于镜像不稳定的情况和. 发现理论预测与经验多方值高度一致，平均误差约为 6.5%。