论文标题
撕裂的不稳定性和湍流发电机的电流式破坏
Tearing instability and current-sheet disruption in the turbulent dynamo
论文作者
论文摘要
导电等离子体中的湍流可以扩增所谓的湍流或小规模发电机中的种子磁场。相关的生长速率和新兴磁场几何形状敏感地取决于等离子体的材料特性，尤其是雷诺数$ {\ rm re} $，磁性雷诺数$ {\ rm rm rm rm} $，其比率$ {\ rm pm} \ rm pm} \ equiv equiv repe {对于$ {\ rm pm}> 1 $，放大的磁场逐渐排列成折叠的结构，在电阻尺度上的方向逆转和磁场线在较大的流量范围内弯曲。随着平均磁能随着流体运动的近似为电气，这种折叠的结构被认为持续存在。使用雅典娜++代码的分析理论和高分辨率MHD模拟，我们表明，这些磁折叠在发电机的非线性阶段变得不稳定，以$ {\ rm rm rm} \ gtrsim 10^4 $和$ {\ rm re} \ rm re} \ gtrsim 10^3 $。 $ {\ rm rm} $ - 和$ {\ rm pm} $ - 依赖的撕裂量表，在理论上预测了折叠的折叠量，并发现在模拟中测量的特征性场反转量表很好地匹配。通过撕裂而破坏褶皱会增加粘性与抗性耗散的比率。在饱和状态下，磁能频谱表现出一个尺寸陡峭的斜率，与斜坡一致，该斜率与撕裂介导的alfvénic湍流相一致。它的光谱峰似乎与电阻尺度无关，并且与流量的驾驶量表相当，而磁能则位于广泛范围的尺度上，从而延伸到通过撕裂设置的田间反转尺度。在湍流发电机饱和状态下的一定程度的大规模磁相干性的出现可能与观察到星系簇中的磁场波动和最近的实验室实验。
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.
