MHD equilibria with incompressible flows: symmetry approach

Abstract

We identify and discuss a family of azimuthally symmetric, incompressible, magnetohydrodynamic plasma equilibria with poloidal and toroidal flows in terms of solutions of the Generalized Grad Shafranov (GGS) equation. These solutions are derived by exploiting the incompressibility assumption, in order to rewrite the GGS equation in terms of a different dependent variable, and the continuous Lie symmetry properties of the resulting equation and in particular a special type of "weak" symmetries.

arXiv commentAccepted for publication in Phys. Plasmas

References in corpus (5)

• Hamiltonian magnetohydrodynamics: symmetric formulation, Casimir invariants, and equilibrium variational principles
• Ideal magnetohydrodynamic equilibria with helical symmetry and incompressible flows
• Symmetries, weak symmetries and related solutions of the Grad-Shafranov equation
• Applications of Symmetry Methods to the Theory of Plasma Physics
• On the notion of conditional symmetry of differential equations

Cited by in corpus (4)

• Kinetic equilibrium of two-dimensional force-free current sheets
• Exact solutions of the Grad-Shafranov equation via similarity reduction and applications to magnetically confined plasmas
• Equilibria with incompressible flows from symmetry analysis
• Electric current filamentation induced by 3D plasma flows in the solar corona