On Lyapunov boundary control of unstable magnetohydrodymanic plasmas

TL;DR

This paper extends Lyapunov boundary control methods to unstable magnetohydrodynamic plasmas, demonstrating that appropriate control can stabilize such systems despite inherent instabilities.

Contribution

It introduces a novel Lyapunov-based boundary control approach for unstable MHD plasmas, building on a simple mechanical model and extending it to complex plasma dynamics.

Findings

Control can stabilize marginally stable models.

Extension to linearized MHD energy principle.

External control actions may be challenging to implement.

Abstract

Starting from a simple marginally stable model considered for Lyapunov based boundary control of flexible mechanical systems, we add a term driving an instability and prove that for an appropriate control condition the system can become Lyapunov stable. A similar approximate extension is found for the general energy principle of linearized magnetohydrodynamics. The implementation of such external instantaneous actions may, however, impose challenging constraints for fusion plasmas.