Classification of matter through topological phases and topological edge states between distinct materials has been a subject of great interest recently. While lattices have been the main setting for these studies, a relatively unexplored realm for this physics is that of continuum fluids. In the typical case of a fluid model with a point spectrum, nontrivial topology and associated edge modes have been observed previously. However, another possibility is that a continuous spectrum can coexist with the point spectrum. Here we demonstrate that a fluid plasma model can harbor nontrivial topology within its continuous spectrum, and that there are boundary modes at the interface between topologically distinct regions. We consider the ideal magnetohydrodynamics (MHD) model. In the presence of magnetic shear, we find nontrivial topology in the Alfvén continuum. For strong shear, the Chern number is $\pm 1$, depending on the sign of the shear. If the magnetic shear changes sign within the plasma, a topological phase transition occurs, and bulk-boundary correspondence then suggests a mode localized to the layer of zero magnetic shear. We confirm the existence of this mode numerically. Moreover, this reversed-shear Alfvén eigenmode (RSAE) is well known within magnetic fusion as it has been observed in several tokamaks. In examining how the MHD model might be regularized at small scales, we also consider the electron limit of Hall MHD. We show that the whistler band, which plays an important role in planetary ionospheres, has nontrivial topology. More broadly, this work raises the possibility that fusion devices could be carefully tailored to produce other topological states with potentially useful behavior.

中文翻译：

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磁化等离子体连续光谱中的非平凡拓扑

通过不同材料之间的拓扑阶段和拓扑边缘状态对物质进行分类是近来引起人们极大兴趣的主题。尽管晶格是这些研究的主要背景，但该物理学的一个相对未曾探索的领域是连续流体。在具有点谱的流体模型的典型情况下，先前已经观察到非平凡的拓扑结构和关联的边缘模式。但是，另一种可能性是连续光谱可以与点光谱共存。在这里，我们证明了流体等离子体模型可以在其连续光谱中包含非平凡的拓扑，并且在拓扑上不同的区域之间的界面处存在边界模式。我们考虑理想的磁流体动力学（MHD）模型。在电磁剪切作用下 我们在Alfvén连续体中发现非平凡的拓扑。对于强剪切，切恩数为$\pm \mathrm{1个}$，取决于剪切的符号。如果磁切变改变了等离子体中的正负号，则会发生拓扑相变，并且体-边界对应关系表明存在于零磁切变层中的模式。我们通过数字确认该模式的存在。此外，这种反向剪切的Alfvén本征模（RSAE）在磁聚变中是众所周知的，因为它已经在多个托卡马克中被观察到。在研究如何以小规模对MHD模型进行正则化时，我们还考虑了Hall MHD的电子极限。我们表明，在行星电离层中起重要作用的惠斯勒带具有非平凡的拓扑结构。从更广泛的意义上讲，这项工作提出了一种可能性，即可以仔细定制融合设备以产生具有潜在有用行为的其他拓扑状态。