Modeling of plasma rotation control for NSTX and NSTX-U

Abstract

This thesis studies some applications of feedback control design for plasma physics, specifically plasma drift waves and plasma toroidal rotation and covers two major steps: reduced-order modeling and controller design.

This dissertation focuses mainly on the toroidal plasma rotation but begins with the Hasegawa-Wakatani (HW) problem, a classic model of plasma drift waves zonal flows coupling, as a preliminary case study where the basic methodology of reduced-order modeling and control is applied to demonstrate the effectiveness and applicability of the approach.

First, the development of a model-based feedback control that stabilizes an unstable equilibrium in the HW equations is studied: a balanced truncation (a model reduction technique) is applied to obtain a low-dimensional model of the linearized HW equations. Then a model-based feedback controller is designed for the reduced order model using a Linear Quadratic Estimator (LQE) which only requires a small set of sensors. Results show that this controller applied to the original non-reduced nonlinear HW equations stabilizes the equilibrium and suppresses the transition to drift-waves instabilities.

Then the thesis dives into the core subject which is the control of plasma toroidal rotation in tokamaks. It uses experimental measurements from the National Spherical Torus Experiment (NSTX) and is aimed at controlling plasma rotation using two different types of actuation: momentum from injected neutral beams and neoclassical toroidal viscosity generated by three-dimensional applied magnetic fields. Based on the data-driven model obtained, a feedback controller is designed, and predictive simulations using the TRANSP plasma transport code show that the controller is able to attain desired plasma rotation profiles given practical constraints on the actuators and the available measurements of rotation.

The last part studies the rotation control on the upgraded device NSTX-U. The major change comes from the addition of a second neutral beam injector which adds three more actuators to the designed controller and thus gives us considerably more flexibility, at the expense of added complexity in the modeling and control of simultaneously the toroidal rotation and the stored energy.

Because NSTX-U modeling is a model-based design (we rely heavily on model predictions and sensors measurements) and experimental data from NSTX-U are not available, a study of the robustness of our controller to some parameters uncertainties in particular the perpendicular momentum diffusivity profile and the confinement time is developed.