Study of Magnetic Helicity Dynamics in Solar and Space Plasmas

磁螺旋度是一个物理变量，可以量化磁场通量的总连接数。由于磁螺旋度在理想磁流体动力学（MHD）过程中是一个守恒量，是磁自由能的代表，因此人们普遍认为磁螺旋度可能是理想磁流体动力学活动的示踪和驱动因素。我们研究了太阳-地球连接系统中磁螺旋度的动力学。首先，我们建立了基于磁图观测的太阳表面螺旋度通量测量方法，发现日冕的螺旋度注入与日冕的软x射线发射活动有很好的相关性。其次，我们开发了新的数值工具，从矢量磁图中重建太阳日冕的三维磁场，并将其应用于新的太阳卫星天文台HINODE提供的数据。结果表明，耀斑前阶段的磁场确实具有剪切结构，这与耀斑开始后出现的双带状削形现象很好地吻合。第三，我们创建了理想MHD方程的最先进的数值格式，称为HUD格式，并证明了hld格式的计算性能优于以往任何格式，计算的准确性，鲁棒性，效率和方便性。最后，我们将hld格式应用到日冕模拟中，日冕模拟充分考虑了球面几何，而磁层模拟则考虑了更一般的状态方程。日冕模拟表明，驱动日冕物质抛射发生的临界磁螺旋度对磁螺旋度注入的空间结构非常敏感。

Magnetic helicity is a physical variable, which can quantify the total linking number of magnetic field flux. Since magnetic helicity is a conserved quantity in the ideal magnetohydrodynamic (MHD) process, and is a proxy of magnetic free energy, it is widely believed that magnetic helicity may play a role as tracer and driver of MHD activities. We have investigated the dynamics of magnetic helicity in the Sun-Earth connection system. First, we have developed the methodology to measure magnetic helicity flux across the solar surface based on the madnetogram observation, and found that the helicity injection into the solar corona is well correlated with the soft X-ray emission activity in the solar corona. Second, we have developed the new numerical tool to reconstruct the three-dimensional magnetic field in the solar corona from vector magnetogram, and applied it to the data provided by the new solar satellite observatory HINODE.. As a result, we have revealed that magnetic field in pre-flare phase indeed has a sheared structure, which is well consistent with the paring of two-ribbon appearing after the onset of flare. Third, we created the state-of-the-art numerical scheme for ideal MHD equation, called HUD scheme, and have demonstrated that the computational performance of HLLD scheme is better than any previous schemes for the accuracy, robustness, efficiency and handiness of computation. Finally, we have applied the HLLD scheme to the solar coronal simulation, which fully includes the spherical geometry, as well as to the magnetospheric simulation, in which more generic equation of state is taken into account. The solar coronal simulation has revealed that the critical magnetic helicity to drive the onset of coronal mass ejection (CME) is sensitive to the spatial structure of magnetic helicity injection.