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Analytical solution of the Grad Shafranov equation in an elliptical prolate geometry

Published online by Cambridge University Press:  05 April 2019

F. Crisanti
F. Crisanti*
Affiliation:
ENEA for EUROfusion, via E. Fermi 45, 00044 Frascati (Rome), Italy
*
†Email address for correspondence: flavio.crisanti@enea.it
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Abstract

The analytical solution in toroidal coordinates of the Grad Shafranov equation has been at the origin of the tokamak breakthrough in the fusion development. Unfortunately, the standard toroidal coordinates have a circular poloidal section, which does not fit the elongated cross-section of the present tokamak experiments. In axisymmetry, the vacuum Grad Shafranov equation coincides with the Laplace equation for the toroidal component of the vector potential. In the present paper the solutions for the Laplace equation and that for the vacuum Grad Shafranov equation are tackled in the elliptical prolate toroidal cap-cyclide coordinates framework. The following report of the geometrical properties and of the metric of these coordinates allows us to work out the analytical solution of both equations in terms of the Wangerin functions.

Keywords

fusion plasmaplasma confinement
Type
Research Article
Information
Journal of Plasma Physics , Volume 85 , Issue 2 , April 2019 , 905850210
Copyright
© Cambridge University Press 2019 

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