Efficient magnetic fields for supporting toroidal plasmas
Here, the magnetic field that supports tokamak and stellarator plasmas must be produced by coils well separated from the plasma. However, the larger the separation, the more difficult it is to produce a given magnetic field in the plasma region, so plasma configurations should be chosen that can be supported as efficiently as possible by distant coils. The efficiency of an externally generated magnetic field is a measure of the field's shaping component magnitude at the plasma compared to the magnitude near the coils; the efficiency of a plasma equilibrium can be measured using the efficiency of the required external shaping field. Counterintuitively, plasma shapes with low curvature and spectral width may have low efficiency, whereas plasma shapes with sharp edges may have high efficiency. Two precise measures of magnetic field efficiency, which correctly identify such differences in difficulty, will be examined. These measures, which can be expressed as matrices, relate the externally produced normal magnetic field on the plasma surface to the either the normal field or current on a distant control surface. A singular value decomposition (SVD) of either matrix yields an efficiency ordered basis for the magnetic field distributions. Calculations are carried out for both tokamak andmore »
 Authors:

^{[1]}
;
^{[2]}
 Univ. of Maryland, College Park, MD (United States)
 Columbia Univ., New York, NY (United States)
 Publication Date:
 Grant/Contract Number:
 FG0293ER54197; FC0208ER54964; FG0295ER54333; AC0205CH11231
 Type:
 Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 23; Journal Issue: 3; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Research Org:
 Univ. of Maryland, College Park, MD (United States); Columbia Univ., New York, NY (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC24)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
 OSTI Identifier:
 1470315
 Alternate Identifier(s):
 OSTI ID: 1241566
Landreman, Matt, and Boozer, Allen H. Efficient magnetic fields for supporting toroidal plasmas. United States: N. p.,
Web. doi:10.1063/1.4943201.
Landreman, Matt, & Boozer, Allen H. Efficient magnetic fields for supporting toroidal plasmas. United States. doi:10.1063/1.4943201.
Landreman, Matt, and Boozer, Allen H. 2016.
"Efficient magnetic fields for supporting toroidal plasmas". United States.
doi:10.1063/1.4943201. https://www.osti.gov/servlets/purl/1470315.
@article{osti_1470315,
title = {Efficient magnetic fields for supporting toroidal plasmas},
author = {Landreman, Matt and Boozer, Allen H.},
abstractNote = {Here, the magnetic field that supports tokamak and stellarator plasmas must be produced by coils well separated from the plasma. However, the larger the separation, the more difficult it is to produce a given magnetic field in the plasma region, so plasma configurations should be chosen that can be supported as efficiently as possible by distant coils. The efficiency of an externally generated magnetic field is a measure of the field's shaping component magnitude at the plasma compared to the magnitude near the coils; the efficiency of a plasma equilibrium can be measured using the efficiency of the required external shaping field. Counterintuitively, plasma shapes with low curvature and spectral width may have low efficiency, whereas plasma shapes with sharp edges may have high efficiency. Two precise measures of magnetic field efficiency, which correctly identify such differences in difficulty, will be examined. These measures, which can be expressed as matrices, relate the externally produced normal magnetic field on the plasma surface to the either the normal field or current on a distant control surface. A singular value decomposition (SVD) of either matrix yields an efficiency ordered basis for the magnetic field distributions. Calculations are carried out for both tokamak and stellarator cases. For axisymmetric surfaces with circular crosssection, the SVD is calculated analytically, and the range of poloidal and toroidal mode numbers that can be controlled to a given desired level is determined. If formulated properly, these efficiency measures are independent of the coordinates used to parameterize the surfaces.},
doi = {10.1063/1.4943201},
journal = {Physics of Plasmas},
number = 3,
volume = 23,
place = {United States},
year = {2016},
month = {3}
}