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arXiv 2212.04735astro-ph.SR
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三维太阳活动区磁流体静力学模型及其稳定性

Three-dimensional solar active region magnetohydrostatic models and their stability using Euler potentials

Jaume Terradas, Thomas Neukirch

备注：
Accepted for publication in A&A
发表信息：
A&A 671, A31 (2023)
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摘要：

活动区是太阳大气中的典型磁结构。我们计算了几种磁流体静力学（MHS）平衡模型，其中包括有限等离子体- $β$和重力的影响，并且代表了这些三维结构。该模型的构建是基于使用两个欧拉势，$α$和$β$，表示磁场为${\bf B}=\nabla α\times \nabla β$。在固定的三维矩形区域内，用有限元数值求解理想MHS非线性偏微分方程。边界条件最初选择对应于一个潜在的磁场（无电流）与已知的相应的欧拉电位的解析表达式。其显著特点是，我们纳入了剪切的影响，逐步变形的初始位磁场。这个过程是相当通用的，并允许我们生成各种各样的MHS模型。通过气体压力和温度对欧拉势的依赖关系，将AR的热结构纳入其中。使用这种方法，我们实现了在AR中发现的特征热和过密等离子体，但我们表明，该方法也可以应用于研究开放的磁场线的配置。此外，我们调查的基本拓扑结构，包括中性线。我们的重点是结构的力平衡，我们不考虑在构建的模型中的能量平衡。此外，我们解决了计算的3D模型的稳定性的困难问题。我们发现，如果等离子体是对流稳定的，那么系统是不容易在一般发展磁瑞利-泰勒不稳定性。

英文摘要：

Active regions (ARs) are typical magnetic structures found in the solar atmosphere. We calculate several magnetohydrostatic (MHS) equilibrium models that include the effect of a finite plasma-$β$ and gravity and that are representative of these structures in three dimensions. The construction of the models is based on the use of two Euler potentials, $α$ and $β$, that represent the magnetic field as ${\bf B}=\nabla α\times \nabla β$. The ideal MHS nonlinear partial differential equations are solved numerically using finite elements in a fixed 3D rectangular domain. The boundary conditions are initially chosen to correspond to a potential magnetic field (current-free) with known analytical expressions for the corresponding Euler potentials. The distinctive feature is that we incorporate the effect of shear by progressively deforming the initial potential magnetic field. This procedure is quite generic and allows us to generate a vast variety of MHS models. The thermal structure of the ARs is incorporated through the dependence of gas pressure and temperature on the Euler potentials. Using this method we achieve the characteristic hot and over-dense plasma found in ARs, but we demonstrate that the method can also be applied to study configurations with open magnetic field lines. Furthermore, we investigate basic topologies that include neutral lines. Our focus is on the force balance of the structures and we do not consider the energy balance in the constructed models. In addition, we address the difficult question of the stability of the calculated 3D models. We find that if the plasma is convectively stable, then the system is not prone in general to develop magnetic Rayleigh-Taylor instabilities.

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