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Title: Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria

Abstract

An energy principle is used to obtain the solution of the magnetohydrodynamic (MHD) equilibrium equation J x B-delp = 0 for nested magnetic flux surfaces that are expressed in the inverse coordinate representation x = x(rho, theta, zeta). Here, theta are zeta are poloidal and toroidal flux coordinate angles, respectively, and p = p(rho) labels a magnetic surface. Ordinary differential equations in rho are obtained for the Fourier amplitudes (moments) in the doubly periodic spectral decomposition of x. A steepest-descent iteration is developed for efficiently solving these nonlinear, coupled moment equations. The existence of a positive-definite energy functional guarantees the monotonic convergence of this iteration toward an equilibrium solution (in the absence of magnetic island formation). A renormalization parameter lambda is introduced to ensure the rapid convergence of the Fourier series for x, while simultaneously satisfying the MHD requirement that magnetic field lines are straight in flux coordinates. A descent iteration is also developed for determining the self-consistent value for lambda.

Authors:
;
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
OSTI Identifier:
5497291
DOE Contract Number:  
W-7405-ENG-26
Resource Type:
Journal Article
Journal Name:
Phys. Fluids; (United States)
Additional Journal Information:
Journal Volume: 26:12
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; MAGNETOHYDRODYNAMICS; MOMENTS METHOD; PLASMA; EQUILIBRIUM; ANALYTICAL SOLUTION; DIFFERENTIAL EQUATIONS; FUNCTIONALS; ITERATIVE METHODS; MAGNETIC FLUX; NONLINEAR PROBLEMS; RENORMALIZATION; THREE-DIMENSIONAL CALCULATIONS; EQUATIONS; FLUID MECHANICS; FUNCTIONS; HYDRODYNAMICS; MECHANICS; 700105* - Fusion Energy- Plasma Research- Plasma Kinetics-Theoretical- (-1987)

Citation Formats

Hirshman, S P, and Whitson, J C. Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria. United States: N. p., 1983. Web. doi:10.1063/1.864116.
Hirshman, S P, & Whitson, J C. Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria. United States. https://doi.org/10.1063/1.864116
Hirshman, S P, and Whitson, J C. 1983. "Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria". United States. https://doi.org/10.1063/1.864116.
@article{osti_5497291,
title = {Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria},
author = {Hirshman, S P and Whitson, J C},
abstractNote = {An energy principle is used to obtain the solution of the magnetohydrodynamic (MHD) equilibrium equation J x B-delp = 0 for nested magnetic flux surfaces that are expressed in the inverse coordinate representation x = x(rho, theta, zeta). Here, theta are zeta are poloidal and toroidal flux coordinate angles, respectively, and p = p(rho) labels a magnetic surface. Ordinary differential equations in rho are obtained for the Fourier amplitudes (moments) in the doubly periodic spectral decomposition of x. A steepest-descent iteration is developed for efficiently solving these nonlinear, coupled moment equations. The existence of a positive-definite energy functional guarantees the monotonic convergence of this iteration toward an equilibrium solution (in the absence of magnetic island formation). A renormalization parameter lambda is introduced to ensure the rapid convergence of the Fourier series for x, while simultaneously satisfying the MHD requirement that magnetic field lines are straight in flux coordinates. A descent iteration is also developed for determining the self-consistent value for lambda.},
doi = {10.1063/1.864116},
url = {https://www.osti.gov/biblio/5497291}, journal = {Phys. Fluids; (United States)},
number = ,
volume = 26:12,
place = {United States},
year = {Thu Dec 01 00:00:00 EST 1983},
month = {Thu Dec 01 00:00:00 EST 1983}
}