A Riccati Implementation of Ideal MHD Stability Analysis

It has recently been shown that the quadratic Hamiltonian associated to the energy of ideal MHD perturbations makes the δW analysis of plasma stability into a standard Riccati problem of optimal control theory. In particular, it has been shown that the Newcomb equation for extremal plasma perturbations can be reduced to a Riccati matrix differential equation. This equivalent Riccati formulation directly solves for the stability characteristics of a plasma equilibrium--that is, the plasma response matrix--and enjoys a number of numerical advantages over the Hamiltonian solution approach. In this work, we implement and demonstrate the efficacy of this Riccati formulation, revealing it to be a viable alternative calculation method for ideal MHD stability analysis. We discuss some of the applications that such an alternative formulation affords.