固体中子星物质中轴对称磁场的霍尔漂移
Hall drift of axisymmetric magnetic fields in solid neutron-star matter
摘要：
霍尔德里夫岛例如，运动的电子对磁通量的输运产生电流，可能是导致中子星固体地壳中磁场演化的主要效应。这是一个非线性的过程，尽管作出了一些努力，仍然没有完全理解。我们使用霍尔感应方程的轴对称，以获得一些一般性质的nonevolving领域，以及分析纯环向场的演变，他们的极向扰动，和电流自由，纯极向场。我们还分析了霍尔不稳定性中的能量守恒，并给出了霍尔平衡的变分原理。我们表明，任何环形磁场的演变可以描述的伯格斯方程，如以前发现的平面平行几何。它会导致急剧的电流片，消散在霍尔时间尺度上，产生一个稳定的场配置，取决于一个单一的，适当定义的坐标。然而，这个场对于极向扰动是不稳定的，极向扰动随着它们的场线被背景电子流拉伸而增长，就像以前在数值上发现的不稳定性一样。另一方面，无电流极向配置是稳定的，可以代表一个长期存在的地壳场的流体恒星核心的电流支持。
英文摘要：
Hall drift, i. e., transport of magnetic flux by the moving electrons giving rise to the electrical current, may be the dominant effect causing the evolution of the magnetic field in the solid crust of neutron stars. It is a nonlinear process that, despite a number of efforts, is still not fully understood. We use the Hall induction equation in axial symmetry to obtain some general properties of nonevolving fields, as well as analyzing the evolution of purely toroidal fields, their poloidal perturbations, and current-free, purely poloidal fields. We also analyze energy conservation in Hall instabilities and write down a variational principle for Hall equilibria. We show that the evolution of any toroidal magnetic field can be described by Burgers' equation, as previously found in plane-parallel geometry. It leads to sharp current sheets that dissipate on the Hall time scale, yielding a stationary field configuration that depends on a single, suitably defined coordinate. This field, however, is unstable to poloidal perturbations, which grow as their field lines are stretched by the background electron flow, as in instabilities earlier found numerically. On the other hand, current-free poloidal configurations are stable and could represent a long-lived crustal field supported by currents in the fluid stellar core.
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