We investigate how initially high‐m, poloidal Alfvén waves evolve using a numerical model solving the ideal, cold, linear magnetohydrodynamic (MHD) equations in a 2‐D dipole coordinate system. The curved magnetic geometry provides a key difference between the poloidal and toroidal Alfvén frequencies of any one field line. A polarization rotation from poloidal toward toroidal predicted from the Cartesian box model theory still occurs but now with the waves following contours of Alfvén frequency, which moves the Alfvén wave across field lines. The structure of these contours depends on the harmonic mode along the field line and the equilibrium. We find that the amplitude peak of the poloidal mode moves significantly radially outward in time. When the typically observed azimuthal phase motion of such waves is included, hodograms show a polarization rotation from purely poloidal to a mixed poloidal/toroidal polarization at all locations. Such features could be used to help interpret satellite observations of Pc4‐5 poloidal ultralow frequency (ULF) waves in Earth's magnetosphere.

中文翻译：

---

偶极子磁场中高m倍性Alfvén波的演化

我们探讨如何最初高米，极向阿尔芬波演变使用数值模型求解在2 d偶极理想，冷，线性磁流体（MHD）方程坐标系。弯曲的磁几何形状提供了任意一条磁力线的极坐标和环形Alfvén频率之间的关键区别。笛卡尔盒模型理论所预测的从极点向环形的极化旋转仍然发生，但是现在波跟随Alfvén频率的轮廓，从而使Alfvén波跨场线。这些轮廓的结构取决于沿磁力线的谐波模式和平衡。我们发现，极谱模式的振幅峰值在时间上显着径向向外移动。当包括通常观察到的此类波的方位角相位运动时，全息图在所有位置均显示从纯极极化到混合极/环极化的极化旋转。这些功能可以用来帮助解释卫星对地球磁层中Pc4-5极谱超低频（ULF）波的观测。