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

Journal Article · Fri Oct 15 00:00:00 EDT 2010 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.3491426· OSTI ID:21421262

Cicogna, G ^[1]; Pegoraro, F; Ceccherini, F ^[2]

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1. Dipartimento di Fisica, 'E.Fermi' dell'Universita di Pisa, INFN, Sez. di Pisa, Largo B.Pontecorvo 3, I-56127 Pisa (Italy)
2. Dipartimento di Fisica, 'E.Fermi' dell'Universita di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa (Italy)

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.

• OSTI ID: 21421262
• Journal Information: Physics of Plasmas, Vol. 17, Issue 10; Other Information: DOI: 10.1063/1.3491426; (c) 2010 American Institute of Physics; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY LAYERS
GRAD-SHAFRANOV EQUATION
MATHEMATICAL SOLUTIONS
PLASMA
PLASMA CONFINEMENT
SYMMETRY
CONFINEMENT
DIFFERENTIAL EQUATIONS
EQUATIONS
LAYERS
PARTIAL DIFFERENTIAL EQUATIONS