Exact solutions of the Grad-Shafranov equation via similarity reduction and applications to magnetically confined plasmas

Abstract

We derive exact solutions of a linear form of the Grad-Shafranov (GS) equation, including incompressible equilibrium flow, using ansatz-based similarity reduction methods. The linearity of the equilibrium equation allows linear combinations of solutions in order to obtain axisymmetric MHD equilibria with closed and nested magnetic surfaces which are favorable for the effective confinement of laboratory plasmas. In addition, employing the same reduction methods we obtain analytical solutions for several non-linear forms of the GS equation. In this context analytic force-free solutions in both linear and nonlinear regimes are also derived.

5 pages, 3 figures

References in corpus (3)

• Axisymmetric equilibria with pressure anisotropy and plasma flow
• MHD equilibria with incompressible flows: symmetry approach
• Comment on the paper "An analytic functional form for characterization and generation of axisymmetric plasma boundaries", PPCF 55 (2013) 095009

Cited by in corpus (2)

• A similarity reduction of the generalized Grad-Shafranov equation
• New axisymmetric equilibria with flow from an expansion about the generalized Solov'ev solution