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.