Modeling NSTX-U Isoflux plasma shape control using the TokaMaker open-source Grad-Shafranov solver

The plama shape controller of the National Spherical Torus eXperiment - Upgrade (NSTX-U) uses the Isoflux algorithm during the main phase of plasma discharges. The algorithm finds the difference in poloidal flux between the x-point and several control points chosen along the desired plasma boundary and uses this flux difference as the error for a PID control system that adjusts the current in each coil. In this work, a Python code is developed which models this control system using the open-source time-dependent Grad-Shafranov solver, TokaMaker. The new shape control modeling workflow described here is initialized by passing parameters for an initial and final plasma shape, picking control points along intermediate steps, and checking that each of these shapes can be stably produced in NSTX-U. Then, TokaMaker is iteratively used to evolve the plasma equilibrium, allowing for calculation of the flux errors and subsequent calculation of the updated coil currents at each time step. Realistic convergence to target shapes on the tens to hundreds-of-milliseconds timescales is shown. Attempts to construct vertically asymmetric shapes in NSTX-U to drive intrinsic toroidal rotation are also discussed.