Conditions for a massless plasma analysis to predict stabilization of the tokamak plasma vertical instability

This paper describes the problem of feedback control for stabilization of the plasma vertical instability in a tokamak. Such controllers are typically designed based on a model that assumes the plasma mass m is identically zero. However, the assumption of m = 0 can lead to a controller C that appears to be stabilizing according to the massless analysis but in fact will increase the instability of the physical system. In this work, we consider the most commonly used type of controller, a proportional-derivative controller. Suppose C is a PD controller which stabilizes the vertical instability with plasma mass assumed to be zero. We give easy-to-check necessary and sufficient conditions for C to also stabilize the physical system, in which the plasma actually has a small mass.