Resonant Axisymmetric Modes

Axisymmetric modes in shaped tokamak plasmas are normally associated with vertical displacement events. However, not enough attention has been given to the fact that these modes can be resonant in two different ways. Firstly, for a plasma bounded by a divertor separatrix, a generic n=0 ideal-MHD perturbation, ξ, is singular at the divertor X- point(s), where Beq · ∇ξ = 0, with Beq the equilibrium magnetic field. As a consequence, n=0 perturbations can give rise to current sheets localized along the divertor separatrix. Secondly, a feedback-stabilized n=0 mode tends to acquire an Alfv ́enic oscillation frequency. As a result, a resonant interaction with energetic particle orbits can lead to a new type of fast ion instability

Study of External Kink Modes in Shaped HBT-EP Plasmas

The first study of magnetohydrodynamic (MHD) equilibria and external kink modes in shaped plasmas on the High Beta Tokamak - Extended Pulse (HBT-EP) is described. A new poloidal field coil and high-current, low-voltage capacitive power supply was designed and installed. The new coil significantly modifies the shape of the plasma cross section and provides a new research tool for the study of kink mode structure and control. When fully energized, the coil creates a magnetic separatrix, which defines the boundary between confined and unconfined plasma. The separatrix is set by a poloidal field null called an “X-point”, which is on the inboard side of the torus, above the midplane. Several arrays of magnetic sensors observe and characterize the plasma equilibrium and the MHD fluctuations from kink modes. Free-boundary plasma equilibria are reconstructed using standard methods that minimize the mean-square error between the numerically reconstructed equilibria and various measurements. Reconstructions of shaped plasma equilibria show the creation of fully diverted plasmas with shaped outer boundaries. The reconstructions are confirmed by direct measurements using arrays of magnetic sensors and a moveable Langmuir probe to measure the outermost closed flux surface. Measurements of individual kink modes are obtained from the magnetic fluctuations using a technique known as biorthogonal decomposition. External kink modes that naturally arise in shaped plasmas are observed and described. The poloidal structure of modes in shaped plasmas are found to be similar to those that arise in circular plasmas, except near the X-point. The magnetic signature of kink modes on the surface of the plasma are calculated using the ideal MHD code DCON. For plasmas with an X-point, DCON shows a short-wavelength, low amplitude structure near the X-point. The code VALEN is used to calculate the perturbed magnetic field measured at the sensors due to the DCON mode at the plasma surface. VALEN includes the effects of sensor/plasma separation and eddy currents induced in conducting structures by rotation of the modes. Good agreement is found between the measured mode structures and the ideal kink mode structures calculated at the sensors by VALEN. A distributed array of forty active control coils was used to perturb the plasma equilibria, and for both shaped and circular equilibria, the structure of the response to the perturbation was found to be the same as the that of the dominant naturally occurring mode in that equilibrium. Finally, the magnitude of the plasma’s response to applied magnetic perturbations was found to be comparable between shaped and unshaped plasmas, even though separation between the sensors and the boundary of the shaped plasmas increases relative to circular plasmas with the same plasma current and radial positions. In addition to demonstrating a new research tool for study of kink modes on HBT-EP, this research demonstrates the importance of accurate electromagnetic calculations, including eddy currents, when comparing measured and predicted mode structure

Model predictive control of resistive wall mode for ITER

Active feedback stabilization of the dominant resistive wall mode (RWM) for an ITER H-mode scenario at high plasma pressure using infinite-horizon model predictive control (MPC) is presented. The MPC approach is closely-related to linear-quadratic-Gaussian (LQG) control, improving the performance in the vicinity of constraints. The control-oriented model for MPC is obtained with model reduction from a high-dimensional model produced by CarMa code. Due to the limited time for on-line optimization, a suitable MPC formulation considering only input (coil voltage) constraints is chosen, and the primal fast gradient method is used for solving the associated quadratic programming problem. The performance is evaluated in simulation in comparison to LQG control. Sensitivity to noise, robustness to changes of unstable RWM dynamics, and size of the domain of attraction of the initial conditions of the unstable modes are examined.Comment: Original manuscript as submitted to Fusion Engineering and Desig

Modelling for JET Vertical Stabilization System

Nuclear fusion is, in a sense, the opposite of nuclear fission. Fission, which is a mature technology, produces energy through the splitting of heavy atoms like uranium in controlled chain reactions. Unfortunately, the by-products of fission are highly radioactive and long lasting. On the other hand, fusion is the process by which the nuclei of two light atoms such as hydrogen are fused together to form a heavier (helium) nucleus, with energy produced as a by-product. Although controlled fusion is extremely technologically challenging, a fusion-power reactor would offer significant advantages over existing energy sources. This thesis is devoted to the control of tokamaks, magnetic confinement devices constructed in the shape of a torus (or doughnut). Tokamaks are the most promising of several proposed magnetic confinement devices. The need to improve the performance of modern tokamak operations has led to a further development of the plasma shape and position control systems. In particular, extremely elongated plasmas, with high vertical-instability growth rate, are envisaged to reach the required performance for ignition. This request for better performance from the experimentalists’ side has motivated the development of the new vertical-stabilization (VS) system at the JET tokamak, which has been proposed within the Plasma Control Upgrade project. This thesis presents the activity carried out to increase the capability of the VS system and to understand the operational limits in order to assess what can be done to improve the overall performance with the existing hardware and control system so as to minimize the impact on JET operation. The first objective of this work is the analysis of the new diagnostic system and the influence of the mechanical structure on the magnetic measurements used as diagnostics by the VS controller; the main focus is on the influence on the controller performance in the presence of large perturbations. The second objective is to design a new controlled variable to increase the performance of the VS system. The third objective is to provide an equivalent model of an ELM (Edge Localized Mode), in terms of internal plasma profile parameters via best fit of the vertical velocity estimation. The last objective is to obtain a reliable and accurate model of the overall system, based on the new platform MARTe, developed at JET and useful also for other devices

Towards practical reinforcement learning for tokamak magnetic control

Reinforcement learning (RL) has shown promising results for real-time control systems, including the domain of plasma magnetic control. However, there are still significant drawbacks compared to traditional feedback control approaches for magnetic confinement. In this work, we address key drawbacks of the RL method; achieving higher control accuracy for desired plasma properties, reducing the steady-state error, and decreasing the required time to learn new tasks. We build on top of \cite{degrave2022magnetic}, and present algorithmic improvements to the agent architecture and training procedure. We present simulation results that show up to 65\% improvement in shape accuracy, achieve substantial reduction in the long-term bias of the plasma current, and additionally reduce the training time required to learn new tasks by a factor of 3 or more. We present new experiments using the upgraded RL-based controllers on the TCV tokamak, which validate the simulation results achieved, and point the way towards routinely achieving accurate discharges using the RL approach