A Riccati Solution for the Ideal MHD Plasma Response with Applications to Real-time Stability Control

Abstract

To effectuate near real-time feedback control of ideal MHD instabilities in a tokamak geometry, a rapid solution for stability analysis is a prerequisite. Toward this end, we reformulate the δW stability method with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the generic tokamak ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD matrix Riccati differential equation (MRDE). Since Riccati equations are prevalent in the control theory literature, such a shift in perspective brings to bear a range of numerical methods that are well-suited to the robust, fast solution of control problems. We discuss the usefulness of Riccati techniques in solving the stiff ODEs often encountered in ideal MHD stability analyses-—for example, in tokamak edge and stellarator physics. We then demonstrate the applicability of such methods to an existing 2D ideal MHD stability code—DCON—enabling its parallel operation in near real-time. Output is shown to match with high accuracy, and with wall-clock time ≪ 1s. Such speed may help enable active feedback ideal MHD stability control, especially in tokamak plasmas whose ideal MHD equilibria evolve with inductive timescale τ > 1s-—as in ITER.