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

摘要

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