Loureiro Nuno F, Boldyrev Stanislav
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Department of Physics, University of Wisconsin at Madison, Madison, Wisconsin 53706, USA.
Phys Rev Lett. 2017 Jun 16;118(24):245101. doi: 10.1103/PhysRevLett.118.245101.
The current understanding of magnetohydrodynamic (MHD) turbulence envisions turbulent eddies which are anisotropic in all three directions. In the plane perpendicular to the local mean magnetic field, this implies that such eddies become current-sheetlike structures at small scales. We analyze the role of magnetic reconnection in these structures and conclude that reconnection becomes important at a scale λ∼LS_{L}^{-4/7}, where S_{L} is the outer-scale (L) Lundquist number and λ is the smallest of the field-perpendicular eddy dimensions. This scale is larger than the scale set by the resistive diffusion of eddies, therefore implying a fundamentally different route to energy dissipation than that predicted by the Kolmogorov-like phenomenology. In particular, our analysis predicts the existence of the subinertial, reconnection interval of MHD turbulence, with the estimated scaling of the Fourier energy spectrum E(k_{⊥})∝k_{⊥}^{-5/2}, where k_{⊥} is the wave number perpendicular to the local mean magnetic field. The same calculation is also performed for high (perpendicular) magnetic Prandtl number plasmas (Pm), where the reconnection scale is found to be λ/L∼S_{L}^{-4/7}Pm^{-2/7}.
目前对磁流体动力学（MHD）湍流的理解认为，湍流涡旋在所有三个方向上都是各向异性的。在垂直于局部平均磁场的平面内，这意味着这些涡旋在小尺度下会变成电流片状结构。我们分析了磁重联在这些结构中的作用，并得出结论：在尺度λ∼LSL-4/7时，重联变得重要，其中SL是外尺度（L）伦德奎斯特数，λ是垂直于磁场的涡旋尺寸中最小的那个。这个尺度大于由涡旋的电阻扩散所设定的尺度，因此意味着能量耗散的途径与类柯尔莫哥洛夫现象学所预测的有根本不同。特别是，我们的分析预测了MHD湍流的亚惯性重联区间的存在，其傅里叶能量谱E(k⊥)∝k⊥-5/2，其中k⊥是垂直于局部平均磁场的波数。对于高（垂直）磁普朗特数等离子体（Pm）也进行了同样的计算，其中发现重联尺度为λ/L∼SL-4/7Pm-2/7。
