skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Gyrokinetic magnetohydrodynamics and the associated equilibria

Abstract

The gyrokinetic magnetohydrodynamic (MHD) equations, related to the recent paper by W. W. Lee, and their associated equilibria properties are discussed. This set of equations consists of the time-dependent gyrokinetic vorticity equation, the gyrokinetic parallel Ohm's law, and the gyrokinetic Ampere's law as well as the equations of state, which are expressed in terms of the electrostatic potential, Φ, and the vector potential, A, and support both spatially varying perpendicular and parallel pressure gradients and the associated currents. The corresponding gyrokinetic MHD equilibria can be reached when Φ → 0 and A becomes constant in time, which, in turn, gives ∇· (J+J) = 0 and the associated magnetic islands, if they exist. Examples of simple cylindrical geometry are given. In conclusion, these gyrokinetic MHD equations look quite different from the conventional MHD equations, and their comparisons will be an interesting topic in the future.

Authors:
ORCiD logo [1];  [1];  [1]
  1. Princeton Univ., Princeton, NJ (United States). Princeton Plasma Physics Lab.
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1415462
Alternate Identifier(s):
OSTI ID: 1414982
Grant/Contract Number:  
AC02-09CHI1466
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 24; Journal Issue: 12; 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

Lee, W. W., Hudson, S. R., and Ma, C. H. Gyrokinetic magnetohydrodynamics and the associated equilibria. United States: N. p., 2017. Web. doi:10.1063/1.5008257.
Lee, W. W., Hudson, S. R., & Ma, C. H. Gyrokinetic magnetohydrodynamics and the associated equilibria. United States. doi:10.1063/1.5008257.
Lee, W. W., Hudson, S. R., and Ma, C. H. Wed . "Gyrokinetic magnetohydrodynamics and the associated equilibria". United States. doi:10.1063/1.5008257. https://www.osti.gov/servlets/purl/1415462.
@article{osti_1415462,
title = {Gyrokinetic magnetohydrodynamics and the associated equilibria},
author = {Lee, W. W. and Hudson, S. R. and Ma, C. H.},
abstractNote = {The gyrokinetic magnetohydrodynamic (MHD) equations, related to the recent paper by W. W. Lee, and their associated equilibria properties are discussed. This set of equations consists of the time-dependent gyrokinetic vorticity equation, the gyrokinetic parallel Ohm's law, and the gyrokinetic Ampere's law as well as the equations of state, which are expressed in terms of the electrostatic potential, Φ, and the vector potential, A, and support both spatially varying perpendicular and parallel pressure gradients and the associated currents. The corresponding gyrokinetic MHD equilibria can be reached when Φ → 0 and A becomes constant in time, which, in turn, gives ∇· (J∥+J⊥) = 0 and the associated magnetic islands, if they exist. Examples of simple cylindrical geometry are given. In conclusion, these gyrokinetic MHD equations look quite different from the conventional MHD equations, and their comparisons will be an interesting topic in the future.},
doi = {10.1063/1.5008257},
journal = {Physics of Plasmas},
number = 12,
volume = 24,
place = {United States},
year = {2017},
month = {12}
}

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

Figures / Tables:

FIG. 1 FIG. 1: Magnetic islands produced by equilibrium parallel pressure gradient for (a) w = 5 and (b) w = 15 in Eq. (21).

Save / Share:

Works referenced in this record:

Equilibrium potential well due to finite Larmor radius effects at the tokamak edge
journal, August 2017

  • Lee, W. W.; White, R. B.
  • Physics of Plasmas, Vol. 24, Issue 8
  • DOI: 10.1063/1.4997787

Alfvén waves in gyrokinetic plasmas
journal, August 2003


Magnetohydrodynamics for collisionless plasmas from the gyrokinetic perspective
journal, July 2016


Nonlinear, three-dimensional magnetohydrodynamics of noncircular tokamaks
journal, January 1976


Dynamics of high β tokamaks
journal, January 1977


Shear-Alfvén waves in gyrokinetic plasmas
journal, October 2001

  • Lee, W. W.; Lewandowski, J. L. V.; Hahm, T. S.
  • Physics of Plasmas, Vol. 8, Issue 10
  • DOI: 10.1063/1.1400124

    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.