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arXiv 0910.5886astro-ph.SR
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线束冠环的平衡分叉与理想MHD不稳定性的关系

On the Relationship between Equilibrium Bifurcations and Ideal MHD Instabilities for Line-Tied Coronal Loops

Thomas Neukirch, Zaharenia Romeou

摘要:

对于冕环的轴对称模型,通过施加线束缚边界条件,研究了磁流体动力学(MHD)平衡序列的分叉点与线性理想MHD不稳定点之间的关系。使用一个很好的研究的例子的基础上的Gold-Hoyle平衡,它表明,如果平衡序列计算使用的Grad-Shafranov方程,不稳定对应于第二个分歧点,而不是第一个分歧点,因为平衡边界条件允许的模式被排除在线性理想的稳定性分析。这是通过计算分叉平衡分支和比较的空间结构的解接近的分歧点与空间结构的不稳定模式。如果使用欧拉势计算平衡序列,则没有找到Grad-Shafranov情况的第一个分歧点,并且欧拉势描述的第一个分歧点与理想的不稳定阈值重合。用线性分叉理论解释了这一结果,并简要讨论了用MHD平衡分叉解释爆发现象的意义。

英文摘要:

For axisymmetric models for coronal loops the relationship between the bifurcation points of magnetohydrodynamic (MHD) equilibrium sequences and the points of linear ideal MHD instability is investigated imposing line-tied boundary conditions. Using a well-studied example based on the Gold-Hoyle equilibrium, it is demonstrated that if the equilibrium sequence is calculated using the Grad-Shafranov equation, the instability corresponds to the second bifurcation point and not the first bifurcation point because the equilibrium boundary conditions allow for modes which are excluded from the linear ideal stability analysis. This is shown by calculating the bifurcating equilibrium branches and comparing the spatial structure of the solutions close to the bifurcation point with the spatial structure of the unstable mode. If the equilibrium sequence is calculated using Euler potentials the first bifurcation point of the Grad-Shafranov case is not found, and the first bifurcation point of the Euler potential description coincides with the ideal instability threshold. An explanation of this results in terms of linear bifurcation theory is given and the implications for the use of MHD equilibrium bifurcations to explain eruptive phenomena is briefly discussed.

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