Three-dimensional solutions of the magnetohydrostatic equations: rigidly rotating magnetized coronae in cylindrical geometry
Three-dimensional solutions of the magnetohydrostatic equations: rigidly rotating magnetized coronae in cylindrical geometry
复制标题
磁流体静力学方程的三维解：圆柱形几何中刚性旋转的磁化日冕
DOI：
10.1051/0004-6361/200913723
复制
发表时间：
2010
影响因子：
6.5
通讯作者：
Al-Salti N
中科院分区：
文献类型：
--
作者：
Al-Salti N
磁流体静力学（MHS）方程的解对于模拟天体物理等离子体（如磁化恒星的日冕）非常重要。真实的模型应该是三维的，即， 不应该有任何空间对称性，但寻找MHS方程的三维解是一项艰巨的任务，目的我们提出了一个一般的理论框架，计算三维MHS解决方案以外的大质量刚性旋转中心体，连同示例的解决方案。一个可能的未来的应用是模拟的快速旋转的stars.MethodsAs第一步，我们在本文中提出的理论和解决方案的情况下，一个大规模的刚性旋转磁化圆柱体，但该理论可以很容易地扩展到其他几何形状，我们假设的解决方案是固定的共同旋转的参考系。为了简化MHS方程，我们使用了一种特殊形式的电流密度，这导致了一个单一的线性偏微分方程的赝potentialU。磁场可由U微分导出。等离子体的密度，压力和温度也是solution.ResultsWe的一部分导出的赝势的基本方程都在坐标独立的形式和圆柱坐标。我们提出了圆柱坐标的情况下的数值例子的解决方案。
ContextSolutions of the magnetohydrostatic (MHS) equations are very important for modelling astrophysical plasmas, such as the coronae of magnetized stars. Realistic models should be three-dimensional, i.e., should not have any spatial symmetries, but finding three-dimensional solutions of the MHS equations is a formidable task.AimsWe present a general theoretical framework for calculating three-dimensional MHS solutions outside massive rigidly rotating central bodies, together with example solutions. A possible future application is to model the closed field region of the coronae of fast-rotating stars.MethodsAs a first step, we present in this paper the theory and solutions for the case of a massive rigidly rotating magnetized cylinder, but the theory can easily be extended to other geometries, We assume that the solutions are stationary in the co-rotating frame of reference. To simplify the MHS equations, we use a special form for the current density, which leads to a single linear partial differential equation for a pseudo-potentialU. The magnetic field can be derived fromUby differentiation. The plasma density, pressure, and temperature are also part of the solution.ResultsWe derive the fundamental equation for the pseudo-potential both in coordinate independent form and in cylindrical coordinates. We present numerical example solutions for the case of cylindrical coordinates.