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arXiv 1407.0240astro-ph.GAphysics.flu-dyn
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扩散MHD不稳定性：超越Escherasekhar定理

Diffusive MHD Instabilities: Beyond the Chandrasekhar Theorem

Guenther Ruediger, Manfred Schultz, Frank Stefani, Michael Mond

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9 pages, 7 figures
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摘要：

本文研究了轴向无限圆柱流的磁流体动力学稳定性，其中包含一个与线性方位速度具有相同径向轮廓的环形磁场背景场。对于理想流体，如果阿尔芬速度等于背景流的速度，那么Kazrasekhar（1956）已经证明了这种构形的稳定性。然而，对于瑞利线上的磁化泰勒-库埃特流，对于有限扩散率，这种流对非轴对称扰动变得不稳定，其中旋转速率的临界磁雷诺数不依赖于磁普朗特数Pm，如果Pm << 1。为了研究这种新的扩散方位角磁旋转不稳定性，考虑了具有相同径向轮廓但具有不同振幅的流和场。当Pm << 1时，具有最弱磁场和最慢自转速率的不稳定区域位于阿尔芬速度和自转速度等幅的Erasekhar线以下。我们发现，然后与雷诺数和哈特曼数标度的边缘不稳定线。不稳定性所需的场强和旋转速率的最小值（略微）随着越来越平坦的旋转而增长。最后，背景场的相应电流变得如此之强，以至于泰勒不稳定性（即使没有旋转也存在）也出现在小哈特曼数的分叉映射中，取代了所有的方位角磁旋转不稳定性。

英文摘要：

The magnetohydrodynamic stability of axially unbounded cylindrical flows is considered which contain a toroidal magnetic background field with the same radial profile as the linear azimuthal velocity. Chandrasekhar (1956) has shown for ideal fluids the stability of this configuration if the Alfven velocity of the field equals the velocity of the background flow. It is demonstrated for magnetized Taylor-Couette flows at the Rayleigh line, however, that for finite diffusivity such flows become unstable against nonaxisymmetric perturbations where the critical magnetic Reynolds number of the rotation rate does not depend on the magnetic Prandtl number Pm if Pm much << 1. In order to study this new diffusive azimuthal magnetorotational instability, flows and fields with the same radial profile but with different amplitudes are considered. For Pm << 1 the instability domain with the weakest fields and the slowest rotation rates lies below the Chandrasekhar line of equal amplitudes for Alfven velocity and rotation velocity. We find that then the lines of marginal instability scale with the Reynolds number and the Hartmann number. The minimum values of the field strength and the rotation rate which are needed for the instability (slightly) grow for more and more flat rotation. Finally, the corresponding electric current of the background field becomes so strong that the Tayler instability (which even exists without rotation) also appears in the bifurcation map at small Hartmann numbers displacing after all the azimuthal magnetorotational instability.

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