球对称alpha2-dynamo及其谱特性
The spherically symmetric alpha2-dynamo and some of its spectral peculiarities
摘要：
简要综述了最近关于球对称MHD α 2发电机谱特性的研究结果。特别是，与物理上现实的边界条件（BC）（周围真空）和理想化的BC（超导环境）的球体限制的流体或等离子体配置的光谱进行了讨论。这些问题包括谱的三阶分支点，Krein空间中发电机算子的自伴性以及恶魔点的共振开折。它是勾画出如何某些类的发电机与一个强本地化的α-剖面嵌入在一个导电的周围可以通过对角化的发电机运营商矩阵的模式解耦。的发电机本征值问题的量子力学哈密顿与能量相关的潜力的映射是用来获得有关的光谱行为的定性信息。链接到超对称量子力学和狄拉克方程表示。
英文摘要：
A brief overview is given over recent results on the spectral properties of spherically symmetric MHD alpha2-dynamos. In particular, the spectra of sphere-confined fluid or plasma configurations with physically realistic boundary conditions (BCs) (surrounding vacuum) and with idealized BCs (super-conducting surrounding) are discussed. The subjects comprise third-order branch points of the spectrum, self-adjointness of the dynamo operator in a Krein space as well as the resonant unfolding of diabolical points. It is sketched how certain classes of dynamos with a strongly localized alpha-profile embedded in a conducting surrounding can be mode decoupled by a diagonalization of the dynamo operator matrix. A mapping of the dynamo eigenvalue problem to that of a quantum mechanical Hamiltonian with energy dependent potential is used to obtain qualitative information about the spectral behavior. Links to supersymmetric Quantum Mechanics and to the Dirac equation are indicated.
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