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Title: The Relationship between Flux Coordinates and Equilibrium-based Frames of Reference in Fusion Theory

Abstract

The properties of two local reference frames based on the magnetic field and the current density are investigated for magnetized plasmas in toroidal geometry with symmetric angle. The magnetic field-based local frame of reference has been well-studied for example by Dewar and colleagues [Phys. Fluids 27, 1723 (1984)] An analogous frame based on the current density vector is possible because it is also divergence free and perpendicular to the gradient of the poloidal flux. The concept of straightness of a vector is introduced and used to elucidate the Boozer and Hamada coordinate systems. The relationship of these local frames to the more well-known Frenet frame of reference, which specifies a curve in terms of curvature and torsion, is given. As an example of the usefulness of the these formal relationships, we briefly review the ideal MHD theory and their use. We also present a new annihilation operator, useful for eliminating shorter time scales than the time scale of interest, for deriving the inner layer equations of Glasser, Greene, and Johnson [Phys. Fluids 18, 875 (1975)]. Compared to the original derivation that is based on the local frame of reference in terms of the magnetic field, the new annihilation operator thatmore » is based on the local frame of reference in terms of the current density simplifies the derivation.« less

Authors:
 [1]
  1. Tech-X Corp., Boulder, CO (United States)
Publication Date:
Research Org.:
Tech-X Corp., Boulder, CO (United States); Tech-X Corporation, Boulder, CO (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
OSTI Identifier:
1557796
Alternate Identifier(s):
OSTI ID: 1543141
Grant/Contract Number:  
SC0019067
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 26; Journal Issue: 8; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Kruger, S. E. The Relationship between Flux Coordinates and Equilibrium-based Frames of Reference in Fusion Theory. United States: N. p., 2019. Web. doi:10.1063/1.5098313.
Kruger, S. E. The Relationship between Flux Coordinates and Equilibrium-based Frames of Reference in Fusion Theory. United States. doi:10.1063/1.5098313.
Kruger, S. E. Mon . "The Relationship between Flux Coordinates and Equilibrium-based Frames of Reference in Fusion Theory". United States. doi:10.1063/1.5098313. https://www.osti.gov/servlets/purl/1557796.
@article{osti_1557796,
title = {The Relationship between Flux Coordinates and Equilibrium-based Frames of Reference in Fusion Theory},
author = {Kruger, S. E.},
abstractNote = {The properties of two local reference frames based on the magnetic field and the current density are investigated for magnetized plasmas in toroidal geometry with symmetric angle. The magnetic field-based local frame of reference has been well-studied for example by Dewar and colleagues [Phys. Fluids 27, 1723 (1984)] An analogous frame based on the current density vector is possible because it is also divergence free and perpendicular to the gradient of the poloidal flux. The concept of straightness of a vector is introduced and used to elucidate the Boozer and Hamada coordinate systems. The relationship of these local frames to the more well-known Frenet frame of reference, which specifies a curve in terms of curvature and torsion, is given. As an example of the usefulness of the these formal relationships, we briefly review the ideal MHD theory and their use. We also present a new annihilation operator, useful for eliminating shorter time scales than the time scale of interest, for deriving the inner layer equations of Glasser, Greene, and Johnson [Phys. Fluids 18, 875 (1975)]. Compared to the original derivation that is based on the local frame of reference in terms of the magnetic field, the new annihilation operator that is based on the local frame of reference in terms of the current density simplifies the derivation.},
doi = {10.1063/1.5098313},
journal = {Physics of Plasmas},
number = 8,
volume = 26,
place = {United States},
year = {2019},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Figures / Tables:

TABLE I: Part 1 TABLE I: Part 1: Summary of the flux and helical-angle coordinate systems with the demonstration of the special cases.

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Works referenced in this record:

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  • Greene, John M.; Johnson, John L.
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    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.