球域霍尔磁旋转不稳定性的线性稳定性分析
Linear stability analysis of the Hall magnetorotational instability in a spherical domain
摘要：
我们调查的霍尔-磁流体动力学系统的稳定性，并确定其重要性的中子星在他们的诞生，当他们仍然包括差分旋转等离子体渗透极强的磁场。我们求解了均匀磁场作用下球壳中的线性化Hall-MHD方程。在考虑流场耦合和霍尔效应的情况下，磁旋转不稳定性和霍尔效应共同作用。与旋转轴对齐的磁场和反平行磁场的结果不同。对于磁场的正向排列，对于任何足够大的磁雷诺数，不稳定性在旋转时间尺度上增长。甚至由于磁扩散而相对于MRI稳定的磁场现在也易受剪切霍尔不稳定性的影响。相反，负对齐对场的增长和幅度施加了强烈的限制，阻碍了霍尔-MRI的有效性。虽然MRI的非轴对称模式可以通过足够强的旋转来抑制，但是当存在霍尔效应时，不存在这样的限制。年轻的中子星的磁场的大小和拓扑结构的影响可能是重要的。
英文摘要：
We investigate the stability of the Hall-MHD system and determine its importance for neutron stars at their birth, when they still consist of differentially rotating plasma permeated by extremely strong magnetic fields. We solve the linearised Hall-MHD equations in a spherical shell threaded by a homogeneous magnetic field. With the fluid/flow coupling and the Hall effect included, the magnetorotational instability and the Hall effect are both acting together. Results differ for magnetic fields aligned with the rotation axis and anti-parallel magnetic fields. For a positive alignment of the magnetic field the instability grows on a rotational time-scale for any sufficiently large magnetic Reynolds number. Even the magnetic fields which are stable against the MRI due to the magnetic diffusion are now susceptible to the shear-Hall instability. In contrast, the negative alignment places strong restrictions on the growth and the magnitude of the fields, hindering the effectiveness of the Hall-MRI. While non-axisymmetric modes of the MRI can be suppressed by strong enough rotation, there is no such restriction when the Hall effect is present. The implications for the magnitude and the topology of the magnetic field of a young neutron star may be significant.
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