二维封闭扭曲黎曼通量管上$α^{2}$ -发电机的共振
Resonant oscillations in $α^{2}$-dynamos on a closed, twisted Riemannian 2D flux tubes
摘要：
Chicone等人[CMP（1995）]已经证明，扩散介质中的运动学快速发电机只能存在于具有常负曲率的封闭二维黎曼流形上。本文指出，当扭转磁通量管的环向和极向频率之间存在共振模式时，他们的结果不能推广到振荡$α^{2}$发电机。因此，发电机作用量可以在黎曼曲率为正的区域中得到支持。对于湍流发电机，这似乎在物理上是合理的，因为最近，[Shukurov等人PRE（2008）]已经获得了钠液体中的Moebius流带，torus Perm发电机，其中曲率也通过扩散与磁场连接。这可以通过调整相应的频率直到它们实现共振来完成。实际上，二维环面是一个零平均曲率的流形，其中存在正曲率和负曲率的区域。结果表明，黎曼孤子表面，被赋予一个稳定的$α^{2}$ -发电机从磁结构[Wilkin等人，PRL（2007）]。
英文摘要：
Chicone et al [CMP (1995)] have shown that, kinematic fast dynamos in diffusive media, could exist only on a closed, 2D Riemannian manifold of constant negative curvature. This report, shows that their result cannot be extended to oscillatory $α^{2}$-dynamos, when there are resonance modes, between toroidal and poloidal frequencies of twisted magnetic flux tubes. Thus, dynamo action can be supported in regions, where Riemannian curvature is positive. For turbulent dynamos, this seems physically reasonable, since recently, [Shukurov et al PRE (2008)] have obtained a Moebius flow strip in sodium liquid, torus Perm dynamo where curvature is also connected to the magnetic fields via diffusion. This could be done, by adjusting the corresponding frequencies till they achieved resonance. Actually 2D torus, is a manifold of zero mean curvature, where regions of positive and negative curvatures exist. It is shown that, Riemannian solitonic surface, endowed with a steady $α^{2}$-dynamo from magnetic filamentary structures [Wilkin et al,PRL (2007)].
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