The relationship between flux coordinates and equilibriumbased 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 fieldbased local frame of reference has been wellstudied 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 wellknown 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 »
 Authors:

 TechX Corporation, Boulder, CO (United States)
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Publication Date:
 Research Org.:
 TechX Corporation, Boulder, CO (United States); TechX Corp., Boulder, CO (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Fusion Energy Sciences (FES)
 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 1070664X
 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., and Greene, John M. The relationship between flux coordinates and equilibriumbased frames of reference in fusion theory. United States: N. p., 2019.
Web. doi:10.1063/1.5098313.
Kruger, S. E., & Greene, John M. The relationship between flux coordinates and equilibriumbased frames of reference in fusion theory. United States. https://doi.org/10.1063/1.5098313
Kruger, S. E., and Greene, John M. Tue .
"The relationship between flux coordinates and equilibriumbased frames of reference in fusion theory". United States. https://doi.org/10.1063/1.5098313. https://www.osti.gov/servlets/purl/1557796.
@article{osti_1557796,
title = {The relationship between flux coordinates and equilibriumbased frames of reference in fusion theory},
author = {Kruger, S. E. and Greene, John M.},
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 fieldbased local frame of reference has been wellstudied 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 wellknown 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 = {8}
}
Figures / Tables:
Works referenced in this record:
Resistive instabilities in general toroidal plasma configurations
journal, January 1975
 Glasser, A. H.; Greene, J. M.; Johnson, J. L.
 Physics of Fluids, Vol. 18, Issue 7
Timedependent drift Hamiltonian
journal, January 1984
 Boozer, Allen H.
 Physics of Fluids, Vol. 27, Issue 10
Nonlinear magnetohydrodynamics simulation using highorder finite elements
journal, March 2004
 Sovinec, C. R.; Glasser, A. H.; Gianakon, T. A.
 Journal of Computational Physics, Vol. 195, Issue 1
Steepestdescent moment method for threedimensional magnetohydrodynamic equilibria
journal, January 1983
 Hirshman, S. P.
 Physics of Fluids, Vol. 26, Issue 12
Resistive interchanges and the negative V " criterion
journal, January 1967
 Johnson, J. L.; Greene, J. M.
 Plasma Physics, Vol. 9, Issue 5
Ideal MHD stability calculations in axisymmetric toroidal coordinate systems
journal, January 1983
 Grimm, R. C.; Dewar, R. L.; Manickam, J.
 Journal of Computational Physics, Vol. 49, Issue 1
Generalized reduced magnetohydrodynamic equations
journal, December 1998
 Kruger, S. E.; Hegna, C. C.; Callen, J. D.
 Physics of Plasmas, Vol. 5, Issue 12
Hydromagnetic equilibria and their proper coordinates
journal, January 1962
 Hamada, Shigeo
 Nuclear Fusion, Vol. 2, Issue 12
The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma
journal, July 2016
 Glasser, A. H.
 Physics of Plasmas, Vol. 23, Issue 7
Magnetic coordinates for equilibria with a continuous symmetry
journal, January 1984
 Dewar, R. L.; Monticello, D. A.; Sy, W. N. C.
 Physics of Fluids, Vol. 27, Issue 7
The second region of stability against ballooning modes
journal, April 1981
 Greene, J. M.; Chance, M. S.
 Nuclear Fusion, Vol. 21, Issue 4
Stability Criterion for Arbitrary Hydromagnetic Equilibria
journal, January 1962
 Greene, John M.; Johnson, John L.
 Physics of Fluids, Vol. 5, Issue 5
Resistive instabilities in a diffuse linear pinch
journal, June 1966
 Coppi, Bruno; Greene, John M.; Johnson, John L.
 Nuclear Fusion, Vol. 6, Issue 2
Local threedimensional magnetostatic equilibria
journal, January 2000
 Hegna, C. C.
 Physics of Plasmas, Vol. 7, Issue 10
Plasma equilibrium with rational magnetic surfaces
journal, January 1981
 Boozer, Allen H.
 Physics of Fluids, Vol. 24, Issue 11
A new form of the magnetohydrodynamic potential energy
journal, January 1996
 Greene, John M.
 Physics of Plasmas, Vol. 3, Issue 1
Stability Criterion for Arbitrary Hydromagnetic Equilibria
journal, December 1961
 Greene, John M.; Johnson, John L.
 Physical Review Letters, Vol. 7, Issue 11
Figures / Tables found in this record: