AI 中文总结
本研究推导了偶极坐标系下低β等离子体的RMHD方程，结合计算机代数系统开展分析，可用于磁层-电离层耦合问题，为复杂几何下的多尺度摄动分析提供模板。
AI 中文摘要
约化磁流体动力学（RMHD）方程以计算易处理的方式从磁流体动力学（MHD）中分离出阿尔文能量传输和湍流动力学。本研究中，我们使用多尺度分析，在与背景磁场对齐的偶极坐标系下推导了低β等离子体的RMHD方程。利用Kreiss定理推导了背景条件在MHD湍流时间尺度上必须满足的平衡条件，由此我们发现了沿通量管的等离子体流动与阿尔文速度变化之间的联系，这种联系可能驱动非线性波效应。最终的方程表明，场向电流与等离子体涡旋之间存在紧密耦合，其中包含了非均匀通量管面积和真实等离子体密度分布的影响。本研究可直接应用于地球磁层中的磁层-电离层耦合问题，因为它提供了一种以自洽方式将磁层中动态演化的场向电流（在地磁暴和亚暴期间尤为重要）与低高度处磁流体动力学湍流的发展联系起来的方法。这也阐明了在这些非均匀情况下，阿尔文波作为能量传输机制的作用，同时保持足够简单以进行预测。此外，本研究利用了一种新颖的方法——计算机代数系统，来完成复杂坐标系下的大部分代数运算。我们希望这种方法能成为在任意复杂几何结构下进行可复现、可验证的多尺度摄动分析的模板。
英文摘要
The equations of reduced magnetohydrodynamics (RMHD) isolate the Alfvénic energy transfer and turbulence dynamics from MHD in a computationally tractable way. In this study, we derive the equations of RMHD for a low $β$ plasma in a dipole coordinate system aligned with the background magnetic field using a multiscale analysis. The Kreiss theorem is used to derive the equilibrium conditions that the background conditions must satisfy on the time scale of MHD turbulence. From these, we find a connection between plasma flow along flux tubes and changes in the Alfvén speed that may drive nonlinear wave effects. The final equations demonstrate an intimate coupling between field aligned currents and plasma vorticity including the effects of nonuniform flux tube area and realistic plasma density profiles. This work has immediate application to the magnetosphere-ionosphere coupling problem in the Earth's magnetosphere as it provides a way to link dynamically evolving field aligned currents from the magnetosphere, especially important during geomagnetic storms and substorms, with the development of magnetohydrodynamic turbulence at low altitudes in a self-consistent manner. This also clarifies the role of Alfvén waves as a transfer mechanism of energy under these inhomogeneous circumstances while remaining simple enough to make predictions. Furthermore, this study makes use of a novel methodology, a computer algebra system, in performing the brunt of algebraic work under complicated coordinate systems. We hope this approach serves as a template for performing reproducible and verifiable multiscale perturbation analysis under arbitrarily complex geometries.
Comments23 pages, 3 figures, 1 supplementary material (pdf), and 4 Python scripts
