Nontrivial topology in the continuous spectrum of a magnetized plasma. (arXiv:1909.07910v4 [physics.plasm-ph] UPDATED)

<a href="http://arxiv.org/find/physics/1/au:+Parker_J/0/1/0/all/0/1">Jeffrey B. Parker</a>, <a href="http://arxiv.org/find/physics/1/au:+Burby_J/0/1/0/all/0/1">J. W. Burby</a>, <a href="http://arxiv.org/find/physics/1/au:+Marston_J/0/1/0/all/0/1">J. B. Marston</a>, <a href="http://arxiv.org/find/physics/1/au:+Tobias_S/0/1/0/all/0/1">Steven M. Tobias</a>

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.

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.

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