Ricci发电机拉伸剪切等离子体流和磁能边界
Ricci dynamo stretch-shear plasma flows and magnetic energy bounds
摘要：
几何工具，用于爱因斯坦的广义相对论（GR），适用于发电机理论，以获得快速发电机行动的限制，以磁能，从杀害对称性的里奇流。磁场被证明是剪切流张量本征方向，在边缘发电机的情况下。杀死黎曼度量的对称性，以爱因斯坦空间为界，使我们能够减少计算。所使用的技术类似于索伯列夫空间中的流的应变分解，最近Nuñez [JMP \textbf{43}（2002）]使用该技术在具有等离子体电阻率的磁流体发电机的情况下对磁能进行限制。与Nuñez情况相反，我们假设发电机是运动的，并且速度流梯度被分解为膨胀、剪切和扭转。当坐标系涡度与Ricci旋转系数一致时，有效扭转消失。特征值在这里是李雅普诺夫指数。与曲率起引力作用的GR类似，这里里奇曲率似乎起扩散作用。
英文摘要：
Geometrical tools, used in Einstein's general relativity (GR), are applied to dynamo theory, in order to obtain fast dynamo action bounds to magnetic energy, from Killing symmetries in Ricci flows. Magnetic field is shown to be the shear flow tensor eigendirection, in the case of marginal dynamos. Killing symmetries of the Riemann metric, bounded by Einstein space, allows us to reduce the computations. Techniques used are similar to those strain decomposition of the flow in Sobolev space, recently used by Nuñez [JMP \textbf{43} (2002)] to place bounds in the magnetic energy in the case of hydromagnetic dynamos with plasma resistivity. Contrary to Nuñez case, we assume that the dynamos are kinematic, and the velocity flow gradient is decomposed into expansion, shear and twist. The effective twist vanishes by considering that the frame vorticity coincides with Ricci rotation coefficients. Eigenvalues are here Lyapunov exponents. In analogy to GR, where curvature plays the role of gravity, here Ricci curvature seems to play the role of diffusion.
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