湍流发电机中的撕裂不稳定性和电流片破裂
Tearing instability and current-sheet disruption in the turbulent dynamo
摘要：
传导等离子体中的湍流可以放大被称为湍流或小规模发电机的种子磁场。相关的增长率和出射磁场的几何形状敏感地依赖于等离子体的材料性质，特别是雷诺数${\rm Re}$，磁雷诺数${\rm Rm}$，和它们的比率${\rm Pm}\equiv{\rm Rm}/{\rm Re}$。对于${\rm Pm} > 1$，放大的磁场逐渐排列成折叠结构，在电阻尺度方向反转，在较大的流动尺度磁力线弯曲。当平均磁能增长到与流体运动近似均分时，这种折叠结构被认为会持续下去。使用分析理论和高分辨率MHD模拟与雅典娜++代码，我们表明，这些磁褶皱变得不稳定撕裂期间的发电机的非线性阶段的${\rm Rm}\gtrsim 10^4$和${\rm Re}\gtrsim 10^3$。一个${\rm Rm}$-和${\rm Pm}$-依赖撕裂规模，在和低于折叠被破坏，理论上预测，并发现匹配以及在模拟中测量的特征场反转规模。撕裂破坏褶皱增加了粘性耗散与阻力耗散的比率。在饱和状态下，磁能谱表现出一个子撕裂尺度陡峭的斜率一致的撕裂介导的阿尔夫文湍流的预测。它的光谱峰值似乎是独立的电阻规模和可比的驱动规模的流量，而磁能驻留在一个广泛的范围内的规模延伸到现场反转规模设置撕裂。在湍流发电机的饱和状态下出现一定程度的大尺度磁相干性可能与星系团中磁场波动的观测结果和最近的实验室实验相一致。
英文摘要：
Turbulence in a conducting plasma can amplify seed magnetic fields in what is known as the turbulent, or small-scale, dynamo. The associated growth rate and emergent magnetic-field geometry depend sensitively on the material properties of the plasma, in particular on the Reynolds number ${\rm Re}$, the magnetic Reynolds number ${\rm Rm}$, and their ratio ${\rm Pm}\equiv{\rm Rm}/{\rm Re}$. For ${\rm Pm} > 1$, the amplified magnetic field is gradually arranged into a folded structure, with direction reversals at the resistive scale and field lines curved at the larger scale of the flow. As the mean magnetic energy grows to come into approximate equipartition with the fluid motions, this folded structure is thought to persist. Using analytical theory and high-resolution MHD simulations with the Athena++ code, we show that these magnetic folds become unstable to tearing during the nonlinear stage of the dynamo for ${\rm Rm}\gtrsim 10^4$ and ${\rm Re}\gtrsim 10^3$. An ${\rm Rm}$- and ${\rm Pm}$-dependent tearing scale, at and below which folds are disrupted, is predicted theoretically and found to match well the characteristic field-reversal scale measured in the simulations. The disruption of folds by tearing increases the ratio of viscous-to-resistive dissipation. In the saturated state, the magnetic-energy spectrum exhibits a sub-tearing-scale steepening to a slope consistent with that predicted for tearing-mediated Alfvénic turbulence. Its spectral peak appears to be independent of the resistive scale and comparable to the driving scale of the flow, while the magnetic energy resides in a broad range of scales extending down to the field-reversal scale set by tearing. Emergence of a degree of large-scale magnetic coherence in the saturated state of the turbulent dynamo may be consistent with observations of magnetic-field fluctuations in galaxy clusters and recent laboratory experiments.
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