Solving the 3D MHD equilibrium equations in toroidal geometry by Newton's method

Journal Article · Sun Jan 01 00:00:00 EST 2006 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2005.05.007· OSTI ID:20687269

Oliver, H J ^[1]; Reiman, A H ^[1]; Monticello, D A ^[1]

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1. Princeton Plasma Physics Laboratory, Princeton University, NJ (United States)

We describe a novel form of Newton's method for computing 3D MHD equilibria. The method has been implemented as an extension to the hybrid spectral/finite-difference Princeton Iterative Equilibrium Solver (PIES) which normally uses Picard iteration on the full nonlinear MHD equilibrium equations. Computing the Newton functional derivative numerically is not feasible in a code of this type but we are able to do the calculation analytically in magnetic coordinates by considering the response of the plasma's Pfirsch-Schlueter currents to small changes in the magnetic field. Results demonstrate a significant advantage over Picard iteration in many cases, including simple finite-{beta} stellarator equilibria. The method shows promise in cases that are difficult for Picard iteration, although it is sensitive to resolution and imperfections in the magnetic coordinates, and further work is required to adapt it to the presence of magnetic islands and stochastic regions.

• OSTI ID: 20687269
• Journal Information: Journal of Computational Physics, Vol. 211, Issue 1; Other Information: DOI: 10.1016/j.jcp.2005.05.007; PII: S0021-9991(05)00264-0; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COORDINATES
EQUATIONS
GEOMETRY
MAGNETIC FIELDS
MAGNETIC ISLANDS
MAGNETOHYDRODYNAMICS
MHD EQUILIBRIUM
NEWTON METHOD
NONLINEAR PROBLEMS
STOCHASTIC PROCESSES
THREE-DIMENSIONAL CALCULATIONS