Tokamak equilibria with toroidal current reversal: properties and computational issues

Abstract

Several properties of axisymmetric plasma equilibria with toroidal-current reversal (TCR) are discussed using some unifying concepts from catastrophe theory. Namely, those of structural stability of functions near critical points, singularity unfolding by small perturbations, and model parameter-space division by bifurcation sets are found to be of particular usefulness. Magnetic configurations displaying, simultaneously, TCR and nested flux surfaces are thence shown to be necessarily degenerate and structurally unstable, meaning that they are easily transformed into non-nested ones by small perturbations in the model parameter set. This should lead to a new paradigm when discussing TCR equilibria, as most of present knowledge relies mainly on the properties of nested solutions, which is expected to favor the study of the broader class of non-nested configurations that recently attracted a considerable discussion in the fusion community. In addition, it is also shown how TCR imposes some constraints on plasma profiles, and how these may be dealt with computationally while keeping the ability to manipulate the shape of the inner island system.

Summary of the magnetic confinement theory and modelling

“…It suggests that that the difference of the pellet injections between the high field and the low field sides is reduced in helical plasmas. Rodrigues presents the solutions of the Grad-Shafranov equation with current hole in JT-60 and compares them with experimental data [48]. These solutions are obtained with a newly developed numerical scheme allowing toroidalcurrent reversed equilibria constrained by experimental data to be computed.…”