Abstract Details
| status: | file name: | submitted: | by: |
|---|---|---|---|
| approved | grad_shafranov.pdf | 2017-05-12 09:17:41 | Flavio Crisanti |
Abstracts
Author: Flavio Crisanti
Requested Type: Poster
Submitted: 2017-03-10 03:54:53
Co-authors:
Contact Info:
ENEA for EUROfusion
via E. Fermi 45
Frascati, 00046
Italy
Abstract Text:
The MHD equilibrium equation, ∇P=JxB, is one of the most assessed equations in plasma physics. Along the Fusion energy achievement path, the analytical solution of the toroidal axis symmetric Grad Shafranov equation was at the basis of the break through Tokamak configuration. In axis symmetry the Grad Shafranov equation coincides with the Laplace equation of the toroidal component of the vector potential. The analytical solution of the related Laplace equation, in several different geometries, was deeply studied during the second half of the XIX century and during the last century the problem was solved for a large class of these geometries. Unluckily, so far, the analytical solution of the Grad Shafranov equation had been worked out only for the standard circular shaped and for the elliptical oblate toroidal geometries. Both these geometries are not suitable for the present Tokamak experiments, all of them based on an elliptical prolate geometry. In the present paper the mathematical problem is summarized and the analytical solution of the Grad Shafranov equation is worked out for the elongated prolate toroidal Cap-Cyclides coordinate system and the analytical solution is written out in terms of the Wangerin functions.
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