一维等离子体发电机谱的Anosov分支
Anosov branches of dynamo spectra in one dimensional plasmas
摘要：
最近，Guenther等人在平均场介质中全局对角化的$α^{2}$发电机算子谱[J Phys A 2007]，及其Krein空间相关微扰理论[J Phys A 2006]。早些时候，Gilbert给出了拉伸剪切和褶皱Anosov映射中快速发电机的一个例子[PRSA [1993]）。本文给出了电阻等离子体中一般湍流发电机细丝的解析解。当湍流扩散系数存在而动力学螺旋度为零时，得到了一个快速发电机模式，并得到了Anosov本征值。磁场沿着嵌入在3D流中的细丝放置在Frenet 2平面上。曲率对快速发电机的影响也进行了研究。在弱曲率细丝的情况下，等离子体中的一维流形呈现快速发电机作用。Chicone等人在二维紧致负常曲率黎曼流形（称为Anosov空间）中的快速发电机谱的情况下得到了一个平行的结果。虽然嵌入问题可能会出现在他们的情况下，在这里没有嵌入问题出现，因为一维弯曲等离子体是嵌入在三维欧几里得空间。在这里考虑的示例中，考虑了磁场分量的法向分量和副法向分量之间的均分。在相反的情况下，非Anosov振荡，纯虚，分支的频谱中发现发电机流形。负常曲率非紧凑$\textbf{H}^{2}$流形，也已被Fantoni和Tellez用于单组分电子2D等离子体（Stat. Phys，（2008））
英文摘要：
Recently Guenther et al the globally diagonalized $α^{2}$ dynamo operator spectrum [J Phys A 2007) in mean field media, and its Krein space related perturbation theory [J Phys A 2006). Earlier, an example of fast dynamos in stretch shear and fold Anosov maps have been given by Gilbert [PRSA [1993)). In this paper, analytical solutions representing general turbulent dynamo filaments are obtained in resistive plasmas. When turbulent diffusivity is present and kinetic helicity vanishes, a fast dynamo mode is obtained, and the Anosov eigenvalue obtained. The magnetic field lays down on a Frenet 2 plane along the filaments embedded in a 3D flow. Curvature effects on fast dynamo are also investigate. In case of weak curvature filaments the one dimensional manifolds in plasmas present a fast dynamo action. A parallel result has been obtained by Chicone et al [Comm Math Phys), in the case fast dynamo spectrum in two dimensional compact Riemannian manifolds of negative constant curvature, called Anosov spaces. While problems of embedding may appear in their case here no embedding problems appear since the one dimensional curved plasmas are embedded in three dimensional Euclidean spaces. In the examples considered here, equipartion between normal and binormal components of the magnetic field components is considered. In the opposite case, non Anosov oscillatory, purely imaginary, branches of the spectrum are found in dynamo manifold. Negative constant curvature non-compact $\textbf{H}^{2}$ manifold, has also been used in one-component electron 2D plasma by Fantoni and Tellez (Stat. Phys, (2008))
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