Towards integrated control of tokamak plasmas: physics-based control of neoclassical tearing modes in the TCV tokamak

Neoclassical tearing modes (NTMs), magnetic islands located at rational $q$ surfaces, are an important class of resistive magnetohydrodynamics (MHD) instabilities in tokamak plasmas, with $q$ the safety factor. NTMs are one of the main constraints of the achievable plasma pressure by increasing the local radial transport and NTMs can lead to plasma disruptions. It is therefore crucial to understand the physics of NTMs and ensure their reliable control.

This thesis explores the physics and control of NTMs, by means of dedicated experiments in the TCV tokamak and interpretative simulations with the modified Rutherford equation (MRE), a model widely used in interpreting island width evolutions. Triggerless NTMs originating from unstable tearing modes (TMs, stability index $\Delta'>0$) and saturating under the effects of the perturbed bootstrap current are the main focus of this thesis.

In TCV, triggerless NTMs are reproducibly observed in low-density discharges with strong near-axis electron cyclotron current drive (ECCD), providing an excellent opportunity of studying these modes. Instead of direct computations of $\Delta'$, a model for $\Delta'$ is developed based on extensive experiments and interpretative simulations. This model facilitates the clarification of the complete evolution of triggerless NTMs, from onset as TMs to saturation as NTMs. Our $\Delta'$ model also explains an unexpected density dependence of the onset of NTMs, where NTMs only occur with a certain range of density that broadens with increasing near-axis ECCD power and with lower plasma current. The density range is found to result from the density and plasma current dependence of the stability of ohmic plasmas and the density dependence of ECCD efficiency.

Given its high localization and flexibility, off-axis ECH/ECCD will be used for NTM control in future tokamaks. Comprehensive experimental and numerical studies of the dynamics of NTMs are carried out in this thesis, concerning both the stabilization of existing NTMs and the prevention of NTMs by means of preemptive off-axis ECCD. It is shown and predicted that the prevention of NTMs is much more efficient than NTM stabilization in terms of EC power. Interpretative simulations of the complex set of experiments constrain well the coefficients in the MRE and quantify NTM evolutions. The prevention effects from off-axis ECCD are found to result from local ECH/ECCD instead of a change of $\Delta'$.

A key element of a reliable real-time (RT) control of NTMs is the alignment of EC beams with the target mode location. A small sinusoidal sweeping of the deposition location of EC beams around the target location proves to be effective for both NTM stabilization and prevention, making it a promising technique. Integrated control of NTMs, plasma pressure and model-estimated $q$ profiles is demonstrated on TCV, including advanced plasma state reconstruction, monitoring, supervision and actuator management. A RT-capable MRE module, based on our validated MRE, is developed for the first time and tested by extensive offline simulations for TCV and AUG. It provides a more intelligent physics-based NTM controller, aware of the EC power it requires to stabilize or prevent a given NTM. The information from the RT-MRE is also valuable for RT actuator allocations and decision-making in view of the overall integrated control, in particular for future long-pulse tokamaks like ITER and DEMO.