中子星磁场中的霍尔级联与不稳定性
Hall cascades versus instabilities in neutron star magnetic fields
摘要：
霍尔效应是影响中子星内磁场演化的重要非线性机制。对控制方程的理论和数值研究表明，霍尔效应是以能量从大尺度到小尺度的湍流级联方式进行的。我们研究了Rheinhardt和Geppert的线性稳定性分析中证实存在的小尺度Hall不稳定性。相同的线性稳定性分析，找到一个合适的背景场模型Rheinhardt和Geppert的想法。这个领域的非线性演化，然后使用三维伪谱数值MHD代码建模。结合背景场，在线性稳定性分析推断的具有最大正本征值的十个特定本征模处注入能量。能量被转移到系统中的不同尺度，但不会转移到任何可以被解释为霍尔不稳定性的小尺度。任何不稳定性都被迟发的湍流霍尔级联所淹没，最初通过选择背景场来避免，但很快就由不断增长的本征模之间的非线性相互作用产生。霍尔级联显示在这里，并由几个作者在其他地方，是在这个系统中的主导机制。
英文摘要：
The Hall effect is an important nonlinear mechanism affecting the evolution of magnetic fields in neutron stars. Studies of the governing equation, both theoretical and numerical, have shown that the Hall effect proceeds in a turbulent cascade of energy from large to small scales. We investigate the small-scale Hall instability conjectured to exist from the linear stability analysis of Rheinhardt and Geppert. Identical linear stability analyses are performed to find a suitable background field to model Rheinhardt and Geppert's ideas. The nonlinear evolution of this field is then modelled using a three-dimensional pseudospectral numerical MHD code. Combined with the background field, energy was injected at the ten specific eigenmodes with the greatest positive eigenvalues as inferred by the linear stability analysis. Energy is transferred to different scales in the system, but not into small scales to any extent that could be interpreted as a Hall instability. Any instabilities are overwhelmed by a late-onset turbulent Hall cascade, initially avoided by the choice of background field, but soon generated by nonlinear interactions between the growing eigenmodes. The Hall cascade is shown here, and by several authors elsewhere, to be the dominant mechanism in this system.
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