圆柱几何中刚性旋转磁层的三维解析磁流体静力平衡
Three-dimensional analytical magnetohydrostatic equilibria of rigidly rotating magnetospheres in cylindrical geometry
摘要：
本文给出了磁化刚性旋转圆柱外磁流体静力学方程在同向旋转坐标系中的三维解。我们没有对磁场作对称性假设，但是为了能够进行分析，我们忽略流出，并指定电流密度的特定形式。磁流体静力学方程可以被简化为一个单一的线性偏微分方程的赝势$U$，从该磁场可以通过微分计算。$U$的方程可以通过标准方法求解。这些解也可用于确定等离子体压力、密度和温度作为所有三个空间坐标的函数。尽管这种方法有明显的局限性，但它可以作为一种简单的工具来创建旋转磁层的闭合场线区域的三维模型，而无需旋转对称。
英文摘要：
We present three-dimensional solutions of the magnetohydrostatic equations in the co-rotating frame of reference outside a magnetized rigidly rotating cylinder. We make no symmetry assumption for the magnetic field, but to be able to make analytical progress we neglect outflows and specify a particular form for the current density. The magnetohydrostatic equations can then be reduced to a single linear partial differential equation for a pseudo-potential $U$, from which the magnetic field can be calculated by differentiation. The equation for $U$ can be solved by standard methods. The solutions can also be used to determine the plasma pressure, density and temperature as functions of all three spatial coordinates. Despite the obvious limitations of this approach, it can for example be used as a simple tool to create three-dimensional models for the closed field line regions of rotating magnetospheres without rotational symmetry.
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