Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria
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.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- DOE Contract Number:
- W-7405-ENG-26
- OSTI ID:
- 5497291
- Journal Information:
- Phys. Fluids; (United States), Vol. 26:12
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
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)