黎曼流形中基于保角映射的拉伸快速发电机机制
Stretch fast dynamo mechanism via conformal mapping in Riemannian manifolds
摘要：
给出了黎曼流形中自感方程的两个新的解析解。第一种是等离子体天体物理学中的扭曲磁通量管或磁通绳，它表明依赖于流体的旋转，极向场从代表发电机的环向场放大。放大的值取决于管的磁轴的弗伦内扭转。实际上，这个结果说明了Zeldovich拉伸，扭曲和折叠（STF）的方法来产生发电机从直和untwisted绳。这个问题的动机是处理使用黎曼几何的扭曲磁通量绳最近开发（物理等离子体（2006）），我们研究了第二个发电机的解决方案，这是共形相关的阿诺德运动学快速发电机。在这个解决方案中，它表明，共形效应的快速发电机度规只增强Zeldovich拉伸，因此，一个新的发电机解决方案得到。在Arnold快速发电机线元中作保角变换，可得到原线元的均匀拉伸。
英文摘要：
Two new analytical solutions of self-induction equation, in Riemannian manifolds are presented. The first represents a twisted magnetic flux tube or flux rope in plasma astrophysics, which shows that the depending on rotation of the flow the poloidal field is amplified from toroidal field which represents a dynamo. The value of the amplification depends on the Frenet torsion of the magnetic axis of the tube. Actually this result illustrates the Zeldovich stretch, twist and fold (STF) method to generate dynamos from straight and untwisted ropes. Motivated by the fact that this problem was treated using a Riemannian geometry of twisted magnetic flux ropes recently developed (Phys Plasmas (2006)), we investigated a second dynamo solution which is conformally related to the Arnold kinematic fast dynamo. In this solution it is shown that the conformal effect on the fast dynamo metric only enhances the Zeldovich stretch, and therefore a new dynamo solution is obtained. When a conformal mapping is performed in Arnold fast dynamo line element a uniform stretch is obtained in the original line element.
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