A similarity reduction of the Grad-Shafranov equation

Journal Article · Thu Jul 15 04:00:00 EDT 2010 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.3456519· OSTI ID:21389156

Litvinenko, Yuri E ^[1]

---

1. Department of Mathematics, University of Waikato, P.O. Box 3105, Hamilton 3240 (New Zealand)

A direct method for finding similarity reductions of partial differential equations is applied to a specific case of the Grad-Shafranov equation. As an illustration of the method, the frequently used Solov'ev equilibrium is derived. The method is employed to obtain a new family of exact analytical solutions, which contain both the classical and nonclassical group-invariant solutions of the Grad-Shafranov equation and thus greatly extends the range of the available analytical solutions. All the group-invariant solutions based on the classical Lie symmetries are shown to be particular cases in the new family of solutions.

• OSTI ID: 21389156
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 7 Vol. 17; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ANALYTICAL SOLUTION
CLOSED PLASMA DEVICES
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID MECHANICS
GRAD-SHAFRANOV EQUATION
HYDRODYNAMICS
LIE GROUPS
MAGNETOHYDRODYNAMICS
MATHEMATICAL SOLUTIONS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
SYMMETRY GROUPS
THERMONUCLEAR DEVICES
TOKAMAK DEVICES