A variational method is developed to find approximate solutions to the Grad-Shafranov equation. The surfaces of the constant poloidal magnetic flux $\psi(R, Z)$ are obtained by solving a few ordinary differential equations, which are moments of the Grad-Shafranov equation, for the Fourier amplitudes of the inverse mapping $R(\psi,\vartheta)$ and $Z(\psi,\vartheta)$. Analytic properties and solutions of the moment equations are considered. Specific calculations using the Impurity Study Experiment (ISX-B) and the Engineering Test Facility (ETF)/International Tokamak Reactor (INTOR) geometries are performed numerically, and the results agree well with those calculated using standard two-dimensional equilibrium codes. The main advantage of the variational moment method is that it significantly reduces the computational time required to determine two-dimensional equilibria without sacrificing accuracy.
Описание
Finds the map from flux coordinates by solving moments of the GS equation, providing the basis for the VMEC code.
%0 Journal Article
%1 lao.1981
%A Lao, L. L.
%A Hirshman, S. P.
%A Wieland, R. M.
%D 1981
%I AIP
%J Physics of Fluids
%K equilibrium i-mhd nested tokamak vmec
%N 8
%P 1431-1440
%R 10.1063/1.863562
%T Variational moment solutions to the Grad--Shafranov equation
%U http://link.aip.org/link/?PFL/24/1431/1
%V 24
%X A variational method is developed to find approximate solutions to the Grad-Shafranov equation. The surfaces of the constant poloidal magnetic flux $\psi(R, Z)$ are obtained by solving a few ordinary differential equations, which are moments of the Grad-Shafranov equation, for the Fourier amplitudes of the inverse mapping $R(\psi,\vartheta)$ and $Z(\psi,\vartheta)$. Analytic properties and solutions of the moment equations are considered. Specific calculations using the Impurity Study Experiment (ISX-B) and the Engineering Test Facility (ETF)/International Tokamak Reactor (INTOR) geometries are performed numerically, and the results agree well with those calculated using standard two-dimensional equilibrium codes. The main advantage of the variational moment method is that it significantly reduces the computational time required to determine two-dimensional equilibria without sacrificing accuracy.
@article{lao.1981,
abstract = {A variational method is developed to find approximate solutions to the Grad-Shafranov equation. The surfaces of the constant poloidal magnetic flux $\psi(R, Z)$ are obtained by solving a few ordinary differential equations, which are moments of the Grad-Shafranov equation, for the Fourier amplitudes of the inverse mapping $R(\psi,\vartheta)$ and $Z(\psi,\vartheta)$. Analytic properties and solutions of the moment equations are considered. Specific calculations using the Impurity Study Experiment (ISX-B) and the Engineering Test Facility (ETF)/International Tokamak Reactor (INTOR) geometries are performed numerically, and the results agree well with those calculated using standard two-dimensional equilibrium codes. The main advantage of the variational moment method is that it significantly reduces the computational time required to determine two-dimensional equilibria without sacrificing accuracy.},
added-at = {2009-03-04T17:13:57.000+0100},
author = {Lao, L. L. and Hirshman, S. P. and Wieland, R. M.},
biburl = {https://www.bibsonomy.org/bibtex/221248d3b460301f73012eb9ab6da220c/prodrigues},
description = {Finds the map from flux coordinates by solving moments of the GS equation, providing the basis for the VMEC code.},
doi = {10.1063/1.863562},
interhash = {a1699a701fffc1fe3fd8dfb9e46fb068},
intrahash = {21248d3b460301f73012eb9ab6da220c},
journal = {Physics of Fluids},
keywords = {equilibrium i-mhd nested tokamak vmec},
month = {August},
number = 8,
pages = {1431-1440},
publisher = {AIP},
timestamp = {2009-03-04T17:13:58.000+0100},
title = {Variational moment solutions to the Grad--Shafranov equation},
url = {http://link.aip.org/link/?PFL/24/1431/1},
volume = 24,
year = 1981
}