Nontrivial topology in the continuous spectrum of a magnetized plasma

TL;DR

This paper demonstrates that magnetized plasma models can exhibit nontrivial topological properties within their continuous spectra, leading to boundary modes that could be harnessed in fusion and space plasma applications.

Contribution

It reveals the existence of topological phases in the continuous spectrum of ideal MHD and Hall MHD models, including boundary modes at interfaces with changing magnetic shear.

Findings

Nontrivial topology found in the Alfvén continuum with magnetic shear.

Boundary modes localized at zero magnetic shear layers confirmed numerically.

The whistler band in Hall MHD also exhibits nontrivial topological properties.

Abstract

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 Alfv\'{e}n 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 Alfv\'{e}n 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.