Realistic multi-machine tokamak profile simulations and numerical ramp-down optimization using the RAPTOR code

Predictive modelling of plasma profiles is an essential part of ongoing research in tokamak plasmas, required for a successful realization of future fusion reactors. This thesis focuses on upgrading the RAPTOR code to extend the area of its applicability for plasma modelling and scenario development. RAPTOR is a light and fast simulator, solving radial transport equations, developed for plasma real-time control. This thesis also demonstrates new strategy for ramp-down optimization. The RAPTOR transport model has been extended to take into account the influence of the time-varying plasma equilibrium geometry and background kinetic profiles on the evolution of the predicted plasma profiles. It allows to get more realistic predictions of the plasma state in case of rapid changes in the plasma shape and equilibrium. Also transport equations for the ion temperature and plasma particles (electrons and ions) have been implemented in the code. Benchmarks have been performed with more sophisticated transport ASTRA and CRONOS codes and with prescribed data for the particle transport in ITER. With successful benchmarks, we confirm that the new transport equations are solved correctly. A new ad-hoc transport model based on constant gradients for core and pedestal regions, that is suitable for simulations of transition between H (high) and L (low confinement) modes, has been implemented into RAPTOR. This model assumes stiffness'' of the plasma profiles in the core region, reflecting their relatively weak reaction to changes in the heat flux. Only few transport model parameters have to be prescribed. They are validated with predictive simulations of the time evolution of plasma profiles for TCV, ASDEX Upgrade and JET plasmas. We demonstrate the capabilities of RAPTOR for fast and realistic predictions of plasma state over the entire plasma discharges, i.e. from ramp-up to ramp-down. We have defined characteristic gradients in the stiff'' region for each machine and L/H confinement modes and have obtained a very good agreement with experimental measurements. We have also demonstrated several special cases, where the obtained set of the transport parameters does not work, and proposed possible solutions of the problems. An optimization procedure for the plasma ramp-down phase has been developed during this work. Nondisruptive termination scenarios are necessary for safe operation of ITER, since it can withstand only a limited amount of plasma disruptions. Automatic optimization algorithms can be applied for searching the optimal ramp-down trajectory. With RAPTOR, optimization results are obtained in a reasonable time (hours). We define the goal of the optimization as ramping down the plasma current as fast as possible while avoiding any disruptions caused by reaching physical or technical limits. Physical constraints are relevant for most tokamaks, others are technical and related to the specific tokamaks. We show how different goals and constraints can easily be included or updated in order to simulate a new machine. A proper plasma shaping during the current ramp-down can reduce significantly the plasma internal inductance, improving its vertical stability. Specific heating scenarios allow to reduce the drop in Î²pol during H-L transition, which is important for plasma MHD stability. Results of numerical and experimental ramp-down studies for TCV, AUG and JET plasmas are presented.

Real-Time Control of Tokamak Plasmas: from Control of Physics to Physics-Based Control

Federico Alberto Alfredo Felici

Stable, high-performance operation of a tokamak requires several plasma control problems to be handled simultaneously. Moreover, the complex physics which governs the tokamak plasma evolution must be studied and understood to make correct choices in controller design. In this thesis, the two subjects have been merged, using control solutions as experimental tool for physics studies, and using physics knowledge for developing new advanced control solutions. The TCV tokamak at CRPP-EPFL is ideally placed to explore issues at the interface between plasma physics and plasma control, by combining a state-of-the-art digital real-time control system with a flexible and powerful set of actuators, in particular the electron cyclotron heating and current drive system (ECRH/ECCD). This unique experimental platform has been used to develop and test new control strategies for three important and reactor-relevant tokamak plasma physics instabilities, including the sawtooth, the edge localized mode (ELM) and the neoclassical tearing mode (NTM). These control strategies offer new possibilities for fusion plasma control and at the same time facilitate studies of the physics of the instabilities with greater precision and detail in a controlled environment. The period of the sawtooth crash, a periodic MHD instability in the core of a tokamak plasma, can be varied by localized deposition of ECRH/ECCD near the q = 1 surface, where q is the safety factor. Exploiting this known physical phenomenon, a sawtooth pacing controller was developed which is able to precisely control the time of appearance of the next sawtooth crash. It was also shown that each individual sawtooth period can be controlled in real-time. A similar scheme is applied to H-mode plasmas with type-I ELMs, where it is shown that pacing regularizes the ELM period. The regular, reproducible and therefore predictable sawtooth crashes obtained by the sawtooth pacing controller have been used to study the relationship between sawteeth and NTMs. It is known that post-crash MHD activity can provide the "seed" island for an NTM, which then grows under its neoclassical bootstrap drive. Experiments are shown which demonstrate that the seeding of 3/2 NTMs by long sawtooth crashes can be avoided by preemptive, crash-synchronized EC power injection pulses at the q = 3/2 rational surface location. NTM stabilization experiments in which the ECRH deposition location is moved in real-time with steerable mirrors have shown effective stabilization of both 3/2 and 2/1 NTMs, and have precisely localized the deposition location that is most effective. Studies of current-profile driven destabilization of tearing modes in TCV plasmas with significant amounts of ECCD show a great sensitivity to details of the current profile, but failed to identify a stationary region in the parameter space in which NTMs are always destabilized. This suggests that transient effects intrinsically play a role. Next to instability control, the simultaneous control of magnetic and kinetic plasma profiles is another key requirement for advanced tokamak operation. While control of kinetic plasma profiles around an operating point can be handled using standard linear control techniques, the strongly nonlinear physics of the coupled profiles complicates the problem significantly. Even more, since internal magnetic quantities are difficult to measure with sufficient spatial and temporal resolution —even after years of diagnostic development— routine control of tokamak plasma profiles remains a daunting and extremely challenging task. In this thesis, a model-based approach is used in which physics understanding of plasma current and energy transport is embedded in the control solution. To this aim, a new lightweight transport code has been derived focusing on simplicity and speed of simulation, which is compatible with the demands for real-time control. This code has been named RAPTOR (RApid Plasma Transport simulatOR). In a first-of-its-kind application, the partial differential equation for current diffusion is solved in real-time during a plasma shot in the TCV control system using RAPTOR. This concept is known in control terms as a state observer, and it is applied experimentally to the tokamak current density profile problem for the first time. The real-time simulation gives a physics-model-based estimate of key plasma quantities, to be controlled or monitored in real-time by different control systems. Any available diagnostics can be naturally included into the real-time simulation providing additional constraints and removing measurement uncertainties. The real-time simulation approach holds the advantage that knowledge of the plasma profiles is no longer restricted to those points in space and time where they are measured by a diagnostic, but that an estimate for any quantity can be computed at any time. This includes estimates of otherwise unmeasurable quantities such as the loop voltage profile or the bootstrap current distribution. In a first closed-loop experiment, an estimate of the internal inductance resulting from the real-time simulation is feedback controlled, independently from the plasma central temperature, by an appropriate mix of co- and counter- ECCD. As a tokamak plasma evolves from one state to another during plasma ramp-up or ramp-down, the profile trajectories must stay within a prescribed operational envelope delimited by physics instabilities and engineering constraints. Determining the appropriate actuator command sequence to navigate this operational space has traditionally been a trial-and-error procedure based on experience of tokamak physics operators. A computational technique is developed based on the RAPTOR code which can calculate these trajectories based on the profile transport physics model, by solving an open-loop optimal control problem. The solution of this problem is greatly aided by the fact that the code returns the plasma state trajectory sensitivities to input trajectory parameters, a functionality which is unique to RAPTOR. This information can also be used to construct linearized models around the optimal trajectory, and to determine the active constraint, which can be used for time-varying closed-loop controller design. This physics-model-based approach has shown excellent results and holds great potential for application in other tokamaks worldwide as well as in future devices.

EPFL2011

Simulation of profile evolution from ramp-up to ramp-down and optimization of tokamak plasma termination with the RAPTOR code

Federico Alberto Alfredo Felici, Doohyun Kim, Antoine Pierre Emmanuel Alexis Merle, Olivier Sauter, Anna Teplukhina

The present work demonstrates the capabilities of the transport code RAPTOR as a fast and reliable simulator of plasma profiles for the entire plasma discharge, i.e. from ramp-up to ramp-down. This code focuses, at this stage, on the simulation of electron temperature and poloidal flux profiles using prescribed equilibrium and some kinetic profiles. In this work we extend the RAPTOR transport model to include a time-varying plasma equilibrium geometry and verify the changes via comparison with ATSRA code simulations. In addition a new ad hoc transport model based on constant gradients and suitable for simulations of L-H and H-L mode transitions has been incorporated into the RAPTOR code and validated with rapid simulations of the time evolution of the safety factor and the electron temperature over the entire AUG and TCV discharges. An optimization procedure for the plasma termination phase has also been developed during this work. We define the goal of the optimization as ramping down the plasma current as fast as possible while avoiding any disruptions caused by reaching physical or technical limits. Our numerical study of this problem shows that a fast decrease of plasma elongation during current ramp-down can help in reducing plasma internal inductance. An early transition from H-to L-mode allows us to reduce the drop in poloidal beta, which is also important for plasma MHD stability and control. This work shows how these complex nonlinear interactions can be optimized automatically using relevant cost functions and constraints. Preliminary experimental results for TCV are demonstrated.

2017

Exploration of candidate fusion reactor regimes by real time control of tokamak plasma shape

Himank Anand

The potential of nuclear fusion to provide a practically inexhaustible source of energy has motivated scientists to work towards developing nuclear fusion tokamak power plants. Stable operation of a tokamak at high performance requires simultaneous treatment of several plasma control problems. Moreover, the complex physics which governs the tokamak plasma evolution must be studied and understood to make correct choices in controller design. This mutual inter-dependence has informed this thesis, using control solutions as an experimental tool for physics studies, and using physics knowledge for developing new advanced control solutions. The TCV tokamak at SPC-EPFL is ideally placed to explore issues at the interface between plasma physics and plasma control, by combining a state-of-the-art digital real time control system with a flexible and diverse set of actuators including a full set of independently powered shaping coils. The recent deployment of the real time version of the Grad-Shafranov equilibrium reconstruction code LIUQE, with a sub-ms cycle time in the digital control system, has facilitated the design of a new generalised plasma position and shape controller, based on the information on poloidal flux and magnetic field provided by the real-time Grad-Shafranov solver. The first issue addressed in the thesis is the development and experimental testing of a new real time control strategy to construct a generalised control algorithm for not only controlling the position of the plasma but also to aid in the precise control of higher order shape moments, X-points and strike points, particularly in advanced plasma configurations such as negative-triangularity plasmas, snowflake and super-X divertors, and doublets. A controller formulation ensuring flexibility through an ordering of controlled variables from the most easily to the least easily controlled, while respecting the hardware limits on the poloidal field coil currents, is developed. The successful experimental implementation of the control algorithm has been demonstrated for both fixed and time varying plasma position and shape for limiter and divertor plasma discharges. In addition, the controller has provided satisfactory performance with respect to plasma scenarios involving complex changes in the plasma shape and position. The second issue addressed in the thesis is the application of the generalised plasma position and shape controller to a snowflake plasma configuration. A comparison between the optimised generalised plasma position and shape controller with the performance of the TCV hybrid controller for a given reference snowflake plasma discharge showed a marked improvement in various geometrical properties of the snowflake plasma configuration in the vicinity of the null point. However, strong control of the poloidal magnetic field at the two X-points resulted in a tradeoff on the upper part of the plasma boundary, where the overall precision was comparable to that of the legacy controller. In the experimental time available, the snowflake shots developed exhibited a boundary that was too close to the inner wall of the vessel, modifying the edge plasma behaviour (studied with infrared cameras and Langmuir probes) and making it difficult to study the physics properties of the exact snowflake. However, further optimisation should well be possible.