The paper derives the complete formulations of polytropic behaviour for plasmas described by kappa distributions. This is achieved by employing both positive and negative types of phase‐space kappa distributions of a Hamiltonian for a nonzero potential energy, while the cases of positive and negative potential energies are analysed separately. Then, we develop the general polytropic‐barometric formula that describes the profiles of density, temperature, and thermal pressure. Furthermore, it is shown how the kappa and polytropic indices can be derived from observational measurements of the temperature altitude gradient. As an example, we calculated the kappa κ ≈ 3.35 and polytropic γ ≈ 0.74 indices of the terrestrial atmosphere at ∼100 km, revealing the existence of heating processes that add thermal energy to atmospheric particles.

中文翻译：

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用kappa分布描述的血浆中的多向性–在大气模拟中的应用

本文通过kappa分布推导了血浆多方性行为的完整公式。这可以通过对非零势能采用哈密顿量的正负类型的相空间kappa分布来实现，而正负电势的情况将分别进行分析。然后，我们开发了通用的多气压计公式，该公式描述了密度，温度和热压的曲线。此外，还显示了如何从对温度高度梯度的观测测量中得出卡伯值和多变指数。作为一个例子，我们计算了卡帕κ  ≈3.35和多变γ 约100 km处地球大气的≈0.74指数，表明存在加热过程，这些加热过程将热能添加到大气颗粒中。