磁场重联中的Hall电流效应及地球磁尾通量绳结构的模拟研究
摘要
磁场重联是磁能转化为等离子体动能和热能的有效机制，也是日地能量耦合系统中的基本过程。研究表明广义欧姆定律中的非电阻项对于磁场重联动力学具有重要影响。本文以多步隐格式为基础，发展形成具有良好精度与稳定性的USTC Hall MHD格式，应用该格式研究磁场重联中的Hall电流效应。现分章介绍如下：
第三章研究具有不同特征尺度的驱动重联过程，考察Hall电流效应对于初始电流片厚度L_c与离子惯性长d_i之比(L_c／d_i)的依赖关系。对于电流片厚度与离子惯性长相比拟，即L_c／d_i≤1.0的算例，数值结果展示了Hall MHD重联的特征：具有短电流片的单X线准稳态重联在均匀低电阻等离子体中得以实现，在重联X中性线附近，Hall电流产生了平面外磁场分量B_y的四极结构。重联达稳态后，X中性线处的重联率(?)A／(?)t|_(st)大于0.11．L_c／d_i＞1.0的算例结果表明，随着L_c／d_i增大，Hall电流效应减弱，Hall MHD重联逐渐过渡为电阻MHD重联
本文第四章研究具有不同等离子体β值(β为等离子体热压与磁压之比)的HallMHD重联过程。结果表明在引导场B_(y0)=0时，重联动力学由Hall效应控制，各向同性电子压强梯度项是可以忽略的。并且磁分界线以及对应的B_y，四极结构的夹角随β增大而明显增大，当β＞2.0时，B_y，等值线图中出现具有相反极性的小结构。模拟结果表明，随着等离子体β增大，电子速度的变化比离子速度的要大的多，电子与离子运动的解耦在大于d_i的尺度内发生。由电子和离子相对运动产生的反向电流导致在出流区B_y等值线图中小结构的出现，与此相对应，B_y分量剖面图呈波形变化。Cluster Ⅱ卫星在地球磁层高β外极尖区探测到的波活动增强可能与本文模拟发现的磁场重联中的Hall效应有关。
Wind，Cluster和Polar卫星分别在地球磁尾和磁层顶探测到了等离子体密度降低，本文第五章研究磁场重联中的密度降低。在d_i／L_c≥1.0的算例中，Hall MHD重联准稳态的数值结果，不仅展示了沿着磁分界线的密度降低，也展示了X中性线附近的低密度区。具有不同Hall效应的数值实验证明，磁重联中的密度降低是具有强Hall效应(d_i／L_c≥1.0，亦即初始电流片厚度与离子惯性长相比拟)算例所特有的性质。并且，沿着磁分界线的密度降低对应于磁压增强的区域．对于d_i／L_c=2.0的算例，密度ρ沿z的剖面图与Cluster探测基本相符，位于分界线的密度降低与K_H／ρ(J×B)_z～z曲线的峰值和谷值相对应，表明Hall效应对于沿磁分界线的密度降低层的形成起了重要作用。将
Magnetic reconnection is an effective mechanism for converting magnetic energy into kinetic and thermal energies of plasma, and plays an essential role in the energy coupling system between the Sun and the Earth. Recent research has indicated that the non-resistivity terms in the generalized Ohm's law have important effects on the reconnection dynamics. In this thesis, the Hall effect in magnetic reconnection is investigated using an USTC Hall MHD scheme with an adequate computational accuracy and numerical stability, which was derived from multi-step implicit scheme.
In the driven reconnection process with various scales the effect of Hall current is studied numerically in chapter 3. In the cases with L_c/d_i≤1.0 (L_c is the half-thickness of initial current sheet layer, d_i is the ion inertial length), the features of Hall MHD reconnection are shown as follows: a quasi-steady single X-line reconnection is obtained, the B_y component with a quadrupolar structure is generated and the maximum reconnection rate is larger than 0.11. For the cases with L_c/d_i>1.0, the effect of Hall current on the reconnection dynamics weakens and Hall MHD reconnection is gradually transformed into resistive MHD reconnection as L_c/d_i increases.
Magnetic reconnection with various plasma β (the ratio of plasma pressure to the magnetic pressure) is studied numerically in chapter 4. It is demonstrated by the comparing studies that the reconnection dynamics is controlled by the Hall effect and the effect of scalar electron pressure gradient is negligible in the generalized Ohm's law for the cases with a zero guide field (i.e., B_(y0)=0 at t=0). It is also found that the openness of the magnetic separatrices and associated quadrupolar B_y structure is enlarged as β increases. When β>2.0 fine structures of B_y contours with reversed sign emerge. The numerical results indicate that the variations in electron velocity V_e are greater than those in ion velocity V_i and the decoupling of electron and ion occurs in a larger scale lengths than d_i as β increases. Clearly, the reversed current, which is associated with the relative motion between electrons and ions, generates the fine structures of B_y contours in the outflow region. Then the corresponding profile of B_y component exhibits a wave signature. Enhanced wave activities observed during a Cluster crossing of the high-β exterior cusp region might be related to the Hall effects of magnetic reconnection shown in the present simulation.
The density depletions were detected by Wind, Cluster and Polar spacecrafts in the
第三章研究具有不同特征尺度的驱动重联过程，考察Hall电流效应对于初始电流片厚度L_c与离子惯性长d_i之比(L_c／d_i)的依赖关系。对于电流片厚度与离子惯性长相比拟，即L_c／d_i≤1.0的算例，数值结果展示了Hall MHD重联的特征：具有短电流片的单X线准稳态重联在均匀低电阻等离子体中得以实现，在重联X中性线附近，Hall电流产生了平面外磁场分量B_y的四极结构。重联达稳态后，X中性线处的重联率(?)A／(?)t|_(st)大于0.11．L_c／d_i＞1.0的算例结果表明，随着L_c／d_i增大，Hall电流效应减弱，Hall MHD重联逐渐过渡为电阻MHD重联
本文第四章研究具有不同等离子体β值(β为等离子体热压与磁压之比)的HallMHD重联过程。结果表明在引导场B_(y0)=0时，重联动力学由Hall效应控制，各向同性电子压强梯度项是可以忽略的。并且磁分界线以及对应的B_y，四极结构的夹角随β增大而明显增大，当β＞2.0时，B_y，等值线图中出现具有相反极性的小结构。模拟结果表明，随着等离子体β增大，电子速度的变化比离子速度的要大的多，电子与离子运动的解耦在大于d_i的尺度内发生。由电子和离子相对运动产生的反向电流导致在出流区B_y等值线图中小结构的出现，与此相对应，B_y分量剖面图呈波形变化。Cluster Ⅱ卫星在地球磁层高β外极尖区探测到的波活动增强可能与本文模拟发现的磁场重联中的Hall效应有关。
Wind，Cluster和Polar卫星分别在地球磁尾和磁层顶探测到了等离子体密度降低，本文第五章研究磁场重联中的密度降低。在d_i／L_c≥1.0的算例中，Hall MHD重联准稳态的数值结果，不仅展示了沿着磁分界线的密度降低，也展示了X中性线附近的低密度区。具有不同Hall效应的数值实验证明，磁重联中的密度降低是具有强Hall效应(d_i／L_c≥1.0，亦即初始电流片厚度与离子惯性长相比拟)算例所特有的性质。并且，沿着磁分界线的密度降低对应于磁压增强的区域．对于d_i／L_c=2.0的算例，密度ρ沿z的剖面图与Cluster探测基本相符，位于分界线的密度降低与K_H／ρ(J×B)_z～z曲线的峰值和谷值相对应，表明Hall效应对于沿磁分界线的密度降低层的形成起了重要作用。将
Magnetic reconnection is an effective mechanism for converting magnetic energy into kinetic and thermal energies of plasma, and plays an essential role in the energy coupling system between the Sun and the Earth. Recent research has indicated that the non-resistivity terms in the generalized Ohm's law have important effects on the reconnection dynamics. In this thesis, the Hall effect in magnetic reconnection is investigated using an USTC Hall MHD scheme with an adequate computational accuracy and numerical stability, which was derived from multi-step implicit scheme.
In the driven reconnection process with various scales the effect of Hall current is studied numerically in chapter 3. In the cases with L_c/d_i≤1.0 (L_c is the half-thickness of initial current sheet layer, d_i is the ion inertial length), the features of Hall MHD reconnection are shown as follows: a quasi-steady single X-line reconnection is obtained, the B_y component with a quadrupolar structure is generated and the maximum reconnection rate is larger than 0.11. For the cases with L_c/d_i>1.0, the effect of Hall current on the reconnection dynamics weakens and Hall MHD reconnection is gradually transformed into resistive MHD reconnection as L_c/d_i increases.
Magnetic reconnection with various plasma β (the ratio of plasma pressure to the magnetic pressure) is studied numerically in chapter 4. It is demonstrated by the comparing studies that the reconnection dynamics is controlled by the Hall effect and the effect of scalar electron pressure gradient is negligible in the generalized Ohm's law for the cases with a zero guide field (i.e., B_(y0)=0 at t=0). It is also found that the openness of the magnetic separatrices and associated quadrupolar B_y structure is enlarged as β increases. When β>2.0 fine structures of B_y contours with reversed sign emerge. The numerical results indicate that the variations in electron velocity V_e are greater than those in ion velocity V_i and the decoupling of electron and ion occurs in a larger scale lengths than d_i as β increases. Clearly, the reversed current, which is associated with the relative motion between electrons and ions, generates the fine structures of B_y contours in the outflow region. Then the corresponding profile of B_y component exhibits a wave signature. Enhanced wave activities observed during a Cluster crossing of the high-β exterior cusp region might be related to the Hall effects of magnetic reconnection shown in the present simulation.
The density depletions were detected by Wind, Cluster and Polar spacecrafts in the
引文
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