Design and simulation of extremum-seeking open-loop optimal control of current profile in the DIII-D tokamak

In a magnetic fusion reactor, the achievement of a certain type of plasma current profiles, which are compatible with magnetohydrodynamic stability at high plasma pressure, is key to enable high fusion gain and non-inductive sustainment of the plasma current for steady-state operation. The approach taken toward establishing such plasma current profiles at the DIII-D tokamak is to create the desired profile during the plasma current ramp-up and early flattop phases. The evolution in time of the current profile is related to the evolution of the poloidal flux, which is modeled in normalized cylindrical coordinates using a partial differential equation usually referred to as the magnetic diffusion equation. The control problem is formulated as an open-loop, finite-time, optimal control problem for a nonlinear distributed parameter system, and is approached using extremum seeking. Simulation results, which demonstrate the accuracy of the considered model and the efficiency of the proposed controller, are presented.