Identification of models for current profile modification in ASDEX upgrade

Control of the shape of the current density profile is essential to improve the confinement and the stability in the plasma, particularly for advanced tokamak scenarios with internal transport barriers. For real-time control of the current density profile, it is necessary to identify a model that describes the time evolution of the current density profile when additional current is driven by external current drive tools. This paper focuses on the identification of such models in ASDEX Upgrade. Neutral beam injection is planned as a tool to control the current density profile in ASDEX Upgrade. The possibility of modifying the current density profile using neutral beam injection is investigated by the ASTRA code simulations using the Weiland transport model. It is difficult to derive a physics-based model for the current profile modification with neutral beam injection because it is nonlinear and multivariable. Therefore, a numerical model, a statespace model suited for systems with many input and output signals, is employed for the modeling. The matrices of the state-space model are estimated using a database by a standard prediction error method that minimizes the difference between the model output and the reference output. The database consists of a set of perturbed input signals and simulated output signals. The input signals are the variations of neutral beam power from different beam sources, and the output signals are the variations of the total plasma pressure and the current density profile. The ASTRA code with the Weiland transport model is used for the simulations to create the database since experimental data are currently not available at ASDEX Upgrade. A test of identified models is carried out using another database, also produced by ASTRA, applying a step response pattern to the input signals. It is found that the models obtained predict the output of this database with high accuracies. It is possible to apply the approach developed here to other actuators in a similar way for the current profile control in existing and future experiments.