A high performance spectral code for nonlinear MHD stability

Abstract

A new spectral code, NSTAB, has been developed to do nonlinear stability and equilibrium calculations for the magnetohydrodynamic (MHD) equations in three-dimensional toroidal geometries. The code has the resolution to test nonlinear stability by calculating bifurcated equilibria directly. These equilibria consist of weak solutions with current sheets near rational surfaces and other less localized modes. Bifurcated equilibria with a pronounced current sheet where the rotational transform crosses unity are calculated for the international thermonuclear experimental reactor (ITER). Bifurcated solutions with broader resonances are found for a model of the LHD stellarator currently being built in Japan and an optimized configuration like the Wendelstein VII-X proposed for construction in Germany. The code is able to handle the many harmonics required to capture the high mode number of these instabilities. NSTAB builds on the highly successful BETAS code, which applies the spectral method to a flux coordinate formulation of the variational principle associated with the MHD equilibrium equations. A new residue condition for the location of the magnetic axis has been developed and implemented. This condition is based on the weak formulation of the equations and imposes no constraints on the inner flux surfaces. © 1994 Academic Press, Inc.