%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 }