论文标题
在各向异性电导率的滑动板上的发电机作用
Dynamo action in sliding plates of anisotropic electrical conductivity
论文作者
论文摘要
借助各向异性电导率的材料，可以生成具有简单速度场的发电机，这种类型被带有各向同性材料的Cowling定理所阻止的类型。在Ruderman和Ruzmaikin [1]的先前研究之后，他们考虑了均匀的剪切流量引起的发电机效应，我们确定当实心板在另一个带有各向异性电导率的固体板滑过另一个时，发电机阈值的条件。我们使用搭配Chebyshev方法获得了一类各向异性的数值解，并获得最低磁性雷诺数的条件。在各向异性和波数的特定几何形状中，我们还得出了一个分析解决方案，其中特征向量只是四个指数函数的组合。对于临界磁性雷诺数，获得了明确的分析表达。在临界磁性雷诺数上方，我们还得出了生长速率的分析表达，这表明这是一种非常快的dynamo，在Vainshtein和Zeldovich引入的“慢速”和“快速”术语上推断了[2]。
With materials of anisotropic electrical conductivity, it is possible to generate a dynamo with a simple velocity field, of the type precluded by Cowling's theorems with isotropic materials. Following a previous study by Ruderman and Ruzmaikin [1] who considered the dynamo effect induced by a uniform shear flow, we determine the conditions for the dynamo threshold when a solid plate is sliding over another one, both with anisotropic electrical conductivity. We obtain numerical solutions for a general class of anisotropy and obtain the conditions for the lowest magnetic Reynolds number, using a collocation Chebyshev method. In a particular geometry of anisotropy and wavenumber, we also derive an analytical solution, where the eigenvectors are just combinations of four exponential functions. An explicit analytical expression is obtained for the critical magnetic Reynold number. Above the critical magnetic Reynold number, we have also derived an analytical expression for the growth rate showing that this is a 'very fast' dynamo, extrapolating on the 'slow' and 'fast' terminology introduced by Vainshtein and Zeldovich [2].
