论文标题
在与理想磁流体动力学不稳定性相关的两个维度的不可压缩粘性磁重新连接的甜蜜模型上
On the Sweet-Parker model for incompressible visco-resistive magnetic reconnection in two dimensions associated to ideal magnetohydrodynamic instabilities
论文作者
论文摘要
我们在二维不可压缩的磁性水力动力学的框架中重新审视了众所周知的甜食模型（SP）模型。通过磁性prandtl编号$ p_m $考虑非零粘度，可以重新衍生稳态解决方案。此外，与原始SP模型相反，特别注意流入磁场$ b_e $和当前层$ L $的长度不一定是固定的，并且可能取决于耗散参数。使用两个不同理想的不稳定设置形成当前表，即倾斜和聚结模式，我们在磁重新连接期间以电阻率$η$ $η$ $η$ $ p_m $ $ p_m $进行数值探索缩放关系，并与广义的稳态SP理论解决方案相比。 The usual Sweet-Parker relations are recovered in the limit of small $P_m$ and $η$ values, with in particular the normalized reconnection rate being simply $S^{-1/2} (1 + P_m)^{-1/4}$, where $S$ represents the Lundquist number $S = LV_A/η$ ($V_A$ being the characteristic Alfvén speed).在较高$ p_m $和/或$η$值的相反极限中，根据考虑的设置，根据所考虑的设置，可以通过复杂的依赖$ b_e（η，p_m）$获得显着偏差。我们讨论了这些结果的重要性，以便正确解释文献中发表的众多指数增长的数值研究，目的是解释在太阳能电晕中观察到的爆发现象。
We revisit the well known Sweet-Parker (SP) model for magnetic reconnection in the framework of two dimensional incompressible magnetohydrodynamics. The steady-state solution is re-derived by considering a non zero viscosity via the magnetic Prandtl number $P_m$. Moreover, contrary to the original SP model, a particular attention is paid to the possibility that the inflowing magnetic field $B_e$ and the length of the current layer $L$ are not necessarily fixed and may depend on the dissipation parameters. Using two different ideally unstable setups to form the current sheet, namely the tilt and coalescence modes, we numerically explore the scaling relations with resistivity $η$ and Prandtl number $P_m$ during the magnetic reconnection phase, and compare to the generalized steady-state SP theoretical solution. The usual Sweet-Parker relations are recovered in the limit of small $P_m$ and $η$ values, with in particular the normalized reconnection rate being simply $S^{-1/2} (1 + P_m)^{-1/4}$, where $S$ represents the Lundquist number $S = LV_A/η$ ($V_A$ being the characteristic Alfvén speed). In the opposite limit of higher $P_m$ and/or $η$ values, a significant deviation from the SP model is obtained with a complex dependence $B_e (η, P_m)$ that is explored depending on the setup considered. We discuss the importance of these results in order to correctly interpret the numerous exponentially increasing numerical studies published in the literature, with the aim of explaining eruptive phenomena observed in the solar corona.
