An ideal MHD W stability analysis that bypasses the Newcomb equation

In the following work, we demonstrate the efficacy of a Riccati delta W ideal MHD stability analysis that bypasses the numerically intractable integration of the Newcomb equation. By transforming the linear Newcomb equation into a quadratic Riccati equation, an accurate and equivalent delta W analysis is performed that is shown to enjoy some numerical advantages. We demonstrate that the Riccati approach is better conditioned than its Newcomb counterpart at the magnetic axis, and we apply dynamical systems insights to examine its behavior at singular points. We further discuss the constraints involved in solving for the extremal admissible perturbations of a delta W analysis. Published under license by AIP Publishing.