Symmetries, weak symmetries, and related solutions of the Grad-Shafranov equation

Cicogna, G.; Pegoraro, F.; Ceccherini, F.
October 2010
Physics of Plasmas;Oct2010, Vol. 17 Issue 10, p102506
Academic Journal
We discuss a new family of solutions of the Grad-Shafranov (GS) equation that describes D-shaped toroidal plasma equilibria with sharp gradients at the plasma edge. These solutions have been derived by exploiting the continuous Lie symmetry properties of the GS equation and in particular a special type of 'weak' symmetries. In addition, we review the continuous Lie symmetry properties of the GS equation and present a short but exhaustive survey of the possible choices for the arbitrary flux functions that yield GS equations admitting some continuous Lie symmetry. Particular solutions related to these symmetries are also discussed.


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