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Title: 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 ±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 severalmore » 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.« less

Authors:
ORCiD logo; ; ORCiD logo;
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program; National Science Foundation (NSF); European Research Council (ERC); Simons Foundation; USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1661740
Alternate Identifier(s):
OSTI ID: 1764226; OSTI ID: 1811226
Report Number(s):
LA-UR-20-28556; LLNL-JRNL-804866
Journal ID: ISSN 2643-1564; PPRHAI; 033425
Grant/Contract Number:  
AC52-07NA27344; 20180756PRD4; 89233218CNA000001; PHY-1607611; D5S-DLV-786780; 662962
Resource Type:
Published Article
Journal Name:
Physical Review Research
Additional Journal Information:
Journal Name: Physical Review Research Journal Volume: 2 Journal Issue: 3; Journal ID: ISSN 2643-1564
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Mathematics; Magnetic fusion energy; Alfven waves; magnetic confinement fusion; magnetohydrodynamics; topological phases of matter; Physics - Plasma physics

Citation Formats

Parker, Jeffrey B., Burby, J. W., Marston, J. B., and Tobias, Steven M.. Nontrivial topology in the continuous spectrum of a magnetized plasma. United States: N. p., 2020. Web. https://doi.org/10.1103/PhysRevResearch.2.033425.
Parker, Jeffrey B., Burby, J. W., Marston, J. B., & Tobias, Steven M.. Nontrivial topology in the continuous spectrum of a magnetized plasma. United States. https://doi.org/10.1103/PhysRevResearch.2.033425
Parker, Jeffrey B., Burby, J. W., Marston, J. B., and Tobias, Steven M.. Wed . "Nontrivial topology in the continuous spectrum of a magnetized plasma". United States. https://doi.org/10.1103/PhysRevResearch.2.033425.
@article{osti_1661740,
title = {Nontrivial topology in the continuous spectrum of a magnetized plasma},
author = {Parker, Jeffrey B. and Burby, J. W. and Marston, J. B. and Tobias, Steven M.},
abstractNote = {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 ±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.},
doi = {10.1103/PhysRevResearch.2.033425},
journal = {Physical Review Research},
number = 3,
volume = 2,
place = {United States},
year = {2020},
month = {9}
}

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