Computationally advantageous expressions for 3-D MHD stability

Numerically accurate expressions are critical for the evaluation of 3-D MHD plasma stability, as the conventional formulas generally suffer from large numerical problems. In this work, we present new expressions for the quantities of interest, namely the parallel current density sigma, the local shear S and the normal and geodesic components of the curvature kappa. High accuracy is achieved in these expressions by employing strategies such as avoiding as much as possible the computation of derivatives in the direction normal to the flux surfaces, and avoiding cancellation errors by subtracting large numbers. The result is a set of equations that have been found to be important for the calculation of MHD stability of axisymmetric equilibria, and essential for the assessment of 3-D ones. (C) 2019 Published by Elsevier B.V.