Methodology of Plasma Shape Reachability Area Estimation in D-Shaped Tokamaks

This paper suggests and develops a new methodology of estimation for a multivariable reachability region of a plasma separatrix shape on the divertor phase of a plasma discharge in D-shaped tokamaks. The methodology is applied to a spherical Globus-M/M2 tokamak, including the estimation of a controllability region of a vertical unstable plasma position on the basis of the experimental data. An assessment of the controllability region and the reachability region of the plasma is important for the design of tokamak poloidal field coils and the synthesis of a plasma magnetic control system. When designing a D-shaped tokamak, it is necessary to avoid the small controllability region of the vertically unstable plasma, because such cases occur in practice at a restricted voltage on a horizon field coil. To make the estimations mentioned above robust, PID-controllers for vertical and horizontal plasma position control were designed using the Quantitative Feedback Theory approach, which stabilizes the system and provides satisfactory control indexes (stability margins, setting time, overshoot) during plasma discharges. The controllers were tested on a series of plasma models and nonlinear models of current inverters in auto-oscillation mode as actuators for plasma position control. The estimations were made on these models, taking into account limitations on control actions, i.e., voltages on poloidal field coils. This research is the first step in the design of the plasma shape feedback control system for the operation of the Globus-M2 spherical tokamak. The developed methodology may be used in the design of poloidal field coil systems in tokamak projects in order to avoid weak achievability and controllability regions in magnetic plasma control. It was found that there is a strong cross-influence from the PF-coils currents and the CC current on the plasma shape; hence, these coils should be used to control the plasma shape simultaneously.