剪切磁场下的瑞利-泰勒不稳定性
Rayleigh-Taylor instabilities with sheared magnetic fields
摘要：
磁瑞利-泰勒（MRT）不稳定性可能在许多天体物理问题中起着相关的作用。在这项工作中，磁剪切的MRT不稳定性的增长率的影响进行了研究。假设平衡态中磁场的方向发生变化，即，存在磁剪切。在不可压缩区域求解线性化的磁流体动力学（MHD）方程，发现在磁剪切存在的情况下，增长率是有界的。我们已经推导出简单的最大增长率的解析表达式，对应于系统的最不稳定的模式。这些表达式提供了生长速率对各种平衡参数的明确依赖性。对于小的角度的增长时间是线性比例的剪切角，在这种制度的单界面问题和平板问题趋于相同的结果。相反，在大角度的限制和界面问题的增长时间基本上是独立的剪切角。在这种情况下，我们也已经能够计算出近似表达式的生长时间的平板配置。磁剪切对不稳定性的增长率有很大的影响。作为本文结果的一个应用，我们利用日珥线的寿命和结构的阿尔文速度的估计，间接确定了日珥线的剪切角。
英文摘要：
Magnetic Rayleigh-Taylor (MRT) instabilities may play a relevant role in many astrophysical problems. In this work the effect of magnetic shear on the growth rate of the MRT instability is investigated. The eigenmodes of an interface and a slab model under the presence of gravity are analytically calculated assuming that the orientation of the magnetic field changes in the equilibrium, i.e., there is magnetic shear. We solve the linearised magnetohydrodynamic (MHD) equations in the incompressible regime.We find that the growth rate is bounded under the presence of magnetic shear. We have derived simple analytical expressions for the maximum growth rate, corresponding to the most unstable mode of the system. These expressions provide the explicit dependence of the growth rate on the various equilibrium parameters. For small angles the growth time is linearly proportional to the shear angle, and in this regime the single interface problem and the slab problem tend to the same result. On the contrary, in the limit of large angles and for the interface problem the growth time is essentially independent of the shear angle. In this regime we have also been able to calculate an approximate expression for the growth time for the slab configuration. Magnetic shear can have a strong effect on the growth rates of the instability. As an application of the results found in this paper we have indirectly determined the shear angle in solar prominence threads using their lifetimes and the estimation of the Alfvén speed of the structure.
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