MHD α-2-发电机的Krein空间相关微扰理论和恶魔点的共振开折
Krein space related perturbation theory for MHD alpha-2-dynamos and resonant unfolding of diabolical points
摘要：
研究了理想边界条件下球对称α 2发电机的谱。从具有恒定α轮廓的模型的精确解析解出发，在Krein空间方法中发展了微扰理论和Galerkin技术。在这些工具的帮助下，在频谱网格的变形中以及在位于该网格的节点处的恶魔点的展开中发现了非常明显的α共振模式。非振荡以及振荡发电机制度。基于傅立叶分量的估计技术的开发获得的临界α-配置文件的特征值进入右谱半平面与非零虚分量（在超临界振荡发电机制度的形式）。最后，Frechet导数（梯度）为基础的方法开发，适合进一步的数值研究Krein空间相关的设置，如MHD α-2-发电机或PT对称量子力学模型。
英文摘要：
The spectrum of the spherically symmetric alpha-2 dynamo is studied in the case of idealized boundary conditions. Starting from the exact analytical solutions of models with constant alpha-profiles a perturbation theory and a Galerkin technique are developed in a Krein-space approach. With the help of these tools a very pronounced alpha-resonance pattern is found in the deformations of the spectral mesh as well as in the unfolding of the diabolical points located at the nodes of this mesh. Non-oscillatory as well as oscillatory dynamo regimes are obtained. A Fourier component based estimation technique is developed for obtaining the critical alpha-profiles at which the eigenvalues enter the right spectral half-plane with non-vanishing imaginary components (at which overcritical oscillatory dynamo regimes form). Finally, Frechet derivative (gradient) based methods are developed, suitable for further numerical investigations of Krein-space related setups like MHD alpha-2-dynamos or models of PT-symmetric quantum mechanics.
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