自相似阶段磁环的相对论展开
Relativistic Expansion of Magnetic Loops at the Self-similar Stage
摘要：
我们得到了考虑方位磁场的相对论膨胀磁环的自相似解。我们忽略恒星自转，并假设轴对称和一个纯粹的径向流。当磁环扩展时，初始偶极磁场被拉伸到径向方向。当膨胀速度接近光速时，位移电流减小了环形电流，并改变了从中心恒星抬升的等离子体的分布。由于这些自相似解描述了磁环的自由膨胀，即，$Dv/Dt=0$，运动方程类似于静态相对论磁流体力学。这使我们能够通过应用维里定理来估计存储在磁环中的总能量。这种能量与在磁星中观察到的巨大耀斑的能量相当。
英文摘要：
We obtained self-similar solutions of relativistically expanding magnetic loops taking into account the azimuthal magnetic fields. We neglect stellar rotation and assume axisymmetry and a purely radial flow. As the magnetic loops expand, the initial dipole magnetic field is stretched into the radial direction. When the expansion speed approaches the light speed, the displacement current reduces the toroidal current and modifies the distribution of the plasma lifted up from the central star. Since these self-similar solutions describe the free expansion of the magnetic loops, i.e., $Dv/Dt=0$, the equations of motion are similar to those of the static relativistic magnetohydrodynamics. This allows us to estimate the total energy stored in the magnetic loops by applying the virial theorem. This energy is comparable to that of the giant flares observed in magnetars.
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