Nontrivial topology in the continuous spectrum of a magnetized plasma

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 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.

arXiv comment18 pages, 5 figures

References in corpus (15)

• Topological Insulators
• Topological Photonics
• Topological Photonics
• Topological Acoustics
• Acoustic topological insulator and robust one-way sound transport
• Topological Band Theory for Non-Hermitian Hamiltonians
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods
• Topological Origin of Equatorial Waves
• Topological waves in fluids with odd viscosity
• Alfven Waves in the Solar Atmosphere
• Topological Sound and Flocking on Curved Surfaces
• A bulk-interface correspondence for equatorial waves
• Topological Gaseous Plasmon Polariton in Realistic Plasma

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• Topological Langmuir-cyclotron wave
• Topological phase in plasma physics
• Wave topology brought to the coast
• The dispersion and propagation of topological Langmuir-cyclotron waves in cold magnetized plasmas
• Topological plasma transport from a diffusion view
• Topology of rotating stratified fluids with and without background shear flow
• Continuum damping of topologically-protected edge modes at the boundary of a magnetized plasma
• Wave Topology in Hall MHD
• Symmetry-Driven Bulk-Edge Correspondence in Electron Magnetofluids at Finite Temperature
• Topological edge states of continuous Hamiltonians