Physics-based control-oriented modeling of the current density profile evolution in NSTX-Upgrade

•A physics-based, control-oriented model describing the temporal evolution of the current density profile in tokamaks is obtained by combining the magnetic diffusion equation with empirical correlations for the electron density, electron temperature, and non-inductive current drives.•The resulting first-principles-driven control-oriented model is tailored to the National Spherical Torus eXperiment-Upgrade (NSTX-U) based on the predictions of the TRANSP simulation code.•The model's prediction capabilities are illustrated by comparing simulated data to TRANSP predictions for a reference run.•Objectives and possible challenges associated with the use of the proposed model for the design of both feedforward and feedback controllers are discussed. Active control of the toroidal current density profile is among those plasma control milestones that the National Spherical Torus eXperiment-Upgrade (NSTX-U) program must achieve to realize its next-step operational goals. Motivated by the coupled, nonlinear, multivariable, distributed-parameter plasma dynamics, the first step towards control design is the development of a physics-based, control-oriented model for the current profile evolution in response to non-inductive current drives and heating systems. The evolution of the toroidal current density profile is closely related to the evolution of the poloidal magnetic flux profile, whose dynamics is modeled by a nonlinear partial differential equation (PDE) referred to as the magnetic-flux diffusion equation (MDE). The proposed control-oriented model predicts the spatial-temporal evolution of the current density profile by combining the nonlinear MDE with physics-based correlations obtained at NSTX-U for the electron density, electron temperature, and non-inductive current drives (neutral beams). The resulting first-principles-driven, control-oriented model is tailored for NSTX-U based on predictions by the time-dependent transport code TRANSP. Main objectives and possible challenges associated with the use of the developed model for the design of both feedforward and feedback controllers are also discussed.