Analytical solutions to the Grad–Shafranov equation for tokamak equilibrium with dissimilar source functions

TLDR

The current density profile has three free parameters, which is sufficiently flexible to describe equilibria consistent with external magnetic measurements. An efficient algorithm for least‑squares fitting of numerically obtained experimental equilibria to the exact solution functions is described and applied to the ASDEX Upgrade tokamak. Exact solutions for ideal MHD tokamak equilibria with differing pressure and poloidal current profiles are presented, showing that experimental x‑point and limiter configurations can be modeled by superpositions with a common eigenvalue and that both normal and reversed shear current profiles are permissible. Reference: IAEA, Vienna, 1993, Vol.

Abstract

Exact solutions to the Grad–Shafranov equation for ideal magnetohydrodynamic (MHD) tokamak equilibria with dissimilar functional dependences of the pressure and poloidal current source profiles are presented. The current density profile has three free parameters, which is sufficiently flexible to describe equilibria consistent with external magnetic measurements. Experimental x-point and limiter plasma configurations can be represented by a superposition of solutions with the same eigenvalue. Both normal and reversed shear current profiles are allowed. An efficient algorithm for least squares fitting of numerically obtained experimental equilibria to the exact solution functions is described and applied to the ASDEX Upgrade (axially symmetric divertor experiment) tokamak [Plasma Physics and Controlled Nuclear Fusion Research 1992 (International Atomic Energy Agency, Vienna, 1993), Vol. I, p. 127].