标题： 双环湍流螺旋磁流体动力学：大尺度发电机和能量谱 显示英文标题

标题： Two-Loop Turbulent Helical Magnetohydrodynamics: Large-Scale Dynamo and Energy Spectrum

摘要： 我们对不可压缩螺旋磁流体动力学（MHD）在充分发展稳态湍流中的两环场论分析进行了研究。 螺旋MHD的一个关键特征是在磁响应函数的环图中出现了一个红外不稳定的“质量类似”项。 从物理上讲，这一项对应于焦耳阻尼的相关扰动，与$\boldsymbol{\nabla} \times \boldsymbol{b}$ ($\boldsymbol{b} =$磁场) 成正比。 它的存在会使平凡基态$\langle \boldsymbol{b} \rangle = 0$不稳定，并迫使我们寻找一种稳定系统的方法。 我们表明，这种稳定可以通过两种方式实现：(i) 在感应方程中引入一个外部的质量类似参数，精确抵消这些危险的环修正（运动学区域），或者 (ii) 通过旋转对称性的自发破缺，导致具有非零大尺度磁场的新基态（湍流发电机区域）。 对于后一种情况，我们研究了自发生成的磁场的两环修正，并证明了沿阿尔芬模的类戈德斯通修正以及一些其他各向异性结构的出现。 我们的结果还证实，产生的平均磁场会导致磁能谱的斜率更陡，$-11/3 + 2\gamma_{b\star}$ （其中$\gamma_{b\star} = -0.1039 - 0.4202\rho^2$，对于$|\rho| \leqslant 1$作为螺旋度的度数），与$-11/3$的Kolmogorov速度谱相比，从而打破能量均分。 显示英文摘要

摘要： We present a two-loop field-theoretic analysis of incompressible helical magnetohydrodynamics (MHD) in fully developed stationary turbulence. A key feature of helical MHD is the appearance of an infrared-unstable ``mass-like'' term in the loop diagrams of the magnetic response function. Physically, this term corresponds to the relevant perturbation of the Joule damping, proportional to $\boldsymbol{\nabla} \times \boldsymbol{b}$ ($\boldsymbol{b} =$ magnetic field). Its presence destabilizes the trivial ground state $\langle \boldsymbol{b} \rangle = 0$ and forces us to look for a mechanism for stabilizing the system. We show that such stabilization can be achieved in two ways: (i) by introducing into induction equation an external mass-like parameter that precisely cancels these dangerous loop corrections (kinematic regime), or (ii) via spontaneous breaking of the rotational symmetry, leading to a new ground state with nonzero large-scale magnetic field (turbulent dynamo regime). For the latter case, we study the two-loop correction to the spontaneously generated magnetic field and demonstrate that Goldstone-like corrections to Alfv\'en modes along with some other anisotropic structures arise. Our results also confirm that the emergent mean magnetic field leads to a steeper slope of the magnetic energy spectrum, $-11/3 + 2\gamma_{b\star}$ (with $\gamma_{b\star} = -0.1039 - 0.4202\rho^2$, for $|\rho| \leqslant 1$ as the degree of helicity), compared to the Kolmogorov velocity spectrum of $-11/3$, thereby breaking equipartition.