Control of sawteeth and neo-classical tearing modes in tokamaks using electron cyclotron waves

Resistive magneto-hydrodynamic instabilities are expected to limit the performance of nuclear fusion reactors. Prime examples are the sawtooth instability and the neoclassical tearing modes. The sawtooth instability will affect the refueling of the plasma core and the fast particle concentration. In reactor relevant conditions, the sawtooth can also trigger secondary instabilities. These are the neo-classical tearing modes, which can deteriorate the plasma performance or even disrupt the discharge. These modes (sawteeth and tearing modes) appear at specific locations in the tokamak plasma, associated with the distribution of the current density and the toroidal magnetic field. Localized current drive from electron cyclotron waves is foreseen as a possible actuator for the width of the tearing modes and the period of the sawteeth. Magnetic pick-up coils, electron cyclotron emission (ECE) and soft X-ray emission are the most likely sensors. A system approach for real-time detection, localisation and control of resistive magneto-hydrodynamic modes in tokamaks is presented. The system combines an ECE diagnostic for sensing of the instabilities in the same sight-line with a steerable Electron Cyclotron Resonant Heating and Current Drive (ECRH/CD) antenna. A model for the sawtooth is used to derive the linearized input-output relations (transfer functions) from the varying deposition location of high power Electron Cyclotron waves to the sawtooth period. The transfer functions are derived around a large collection of operating points. Proportional-integral-integral (PII) action can be applied to achieve fast and perfect tracking, while satisfying robustness constraints. The launcher dynamics seriously affects the closed loop performance in present-day experiments. Special emphasis is put on the issue of real-time sawtooth period detection. An algorithm based on time-scale wavelet theory and edge detection for accurate real-time sawtooth period estimation has been developed. The period is estimated by detecting subsequent crashes. The realized accuracy of the detection algorithm is well below the uncertainty of the crash period for most crashes. Multi-resolution analysis enables distinction between different sizes of sawtooth crashes due to the different sizes of wavelets (scales), resulting in an algorithm, which is robust and accurate. A methodology for fast detection of q = m/n = 2/1 tearing modes and retrieval of their location, rotation frequency and phase is presented. Set-points to establish alignment of the ECRH/CD deposition location with the centre of the tearing mode are generated in real-time and forwarded in closed-loop to the steerable launcher and as a modulation pulse train to the gyrotron.