Overview of the RFX fusion science program

This paper summarizes the main achievements of the RFX fusion science program in the period between the 2008 and 2010 IAEA Fusion Energy Conferences. RFX-mod is the largest reversed field pinch in the world, equipped with a system of 192 coils for active control of MHD stability. The discovery and understanding of helical states with electron internal transport barriers and core electron temperature > 1.5 keV significantly advances the perspectives of the configuration. Optimized experiments with plasma current up to 1.8 MA have been realized, confirming positive scaling. The first evidence of edge transport barriers is presented. Progress has been made also in the control of first-wall properties and of density profiles, with initial first-wall lithization experiments. Micro-turbulence mechanisms such as ion temperature gradient and micro-tearing are discussed in the framework of understanding gradient-driven transport in low magnetic chaos helical regimes. Both tearing mode and resistive wall mode active control have been optimized and experimental data have been used to benchmark numerical codes. The RFX programme also provides important results for the fusion community and in particular for tokamaks and stellarators on feedback control of MHD stability and on three-dimensional physics. On the latter topic, the result of the application of stellarator codes to describe three-dimensional reversed field pinch physics will be 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

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.

EPFL2017

MHD stability limits in the TCV tokamak

Holger Reimerdes

Magnetohydrodynamic (MHD) instabilities can limit the performance and degrade the confinement of tokamak plasmas. The Tokamak à Configuration Variable (TCV), unique for its capability to produce a variety of poloidal plasma shapes, has been used to analyse various instabilities and compare their behaviour with theoretical predictions. These instabilities are perturbations of the magnetic field which usually extend to the plasma edge where they can be detected with magnetic pick-up coils as magnetic fluctuations. A spatially dense set of magnetic probes, installed inside the TCV vacuum vessel, allows for a fast observation of these fluctuations. The structure and temporal evolution of coherent modes is extracted using several numerical methods. In addition to the setup of the magnetic diagnostic and the implementation of analysis methods, the subject matter of this thesis focuses on four instabilities which impose local and global stability limits. Al1 of these instabilities are relevant for the operation of a fusion reactor and a profound understanding of their behaviour is required in order to optimise the performance of such a reactor. Sawteeth, which are central relaxation oscillations common to most standard tokamak scenarios, have a significant effect on central plasma parameters. In TCV, systematic scans of the plasma shape have revealed a strong dependence of their behaviour on elongation κ, and triangularity δ, with high κ and low δ leading to shorter sawteeth with smaller crashes. This shape dependence is increased by applying central electron cyclotron heating (ECH), which increases or decreases the sawtooth period, depending on the plasma shape. The response to additional heating power is determined by the role of ideal or resistive MHD in triggering the sawtooth crash. For plasma shapes where additional heating and consequently, a faster increase of the central pressure shortens the sawteeth, the low experimental limit of the pressure gradient within the q = 1 surface is consistent with ideal MHD predictions. The observed decrease of this limit with elongation is also in qualitative agreement with ideal MHD theory. Edge localised modes (ELMs), occurring in TCV Ohmic high-confinement mode discharges, were observed to be preceded by coherent magnetic oscillations. The precursors prior to small ELMs, believed to be of type III, and prior to larger ELMs, previously referred to as TCV large ELMs, show the same characteristics, which allows for an identification of both ELMs to be of type III according to the usual classification scheme. The detected poloidal and toroidal mode structures are consistent with a resonant flux surface close to the plasma edge. Unlike conventional MHD modes, these precursors start at a random toroidal location and then grow in amplitude and toroidal extent until they encompass the whole toroidal circumference. Thus, the asymmetry causing and maintaining the toroidal localisation of the ELM precursor, must be intrinsic to the plasma. Soft X-ray measurements show that the localised precursor always coincides with a central m = 1 mode, which can usually be associated with the sawtooth pre- or postcursor mode. A comparison of the phases indicates a correlation with the maximum of the central mode preceding the toroidal location of the ELM precursor and, therefore, a hitherto unobserved coupling between central modes and ELMs. Highly elongated plasmas promise several advantages, among them higher current and beta limits. During TCV experiments dedicated to an increasing of the plasma elongation, a new disruptive current limit, at values well below the conventional current limit corresponding to qa >2, was encountered for κ >2.3. This limit, which is preceded by a kink-type mode, is found to be consistent with ideal MHD stability calculations. The TCV observations, therefore, provide the first experimental confirmation of a deviation of the linear Troyon-scaling of the ideal beta limit with normalised current at high elongation, which was predicted over 10 years ago. In addition to the ideal beta limit, several other MHD events are observed in highly elongated plasmas. The axisymmetric mode causes vertical displacement events and thereby, imposes a lower current limit. This operational limit is in good agreement with theoretical predictions of the growth rate of the axisymmetric mode. Furthermore, minor disruption are occasionally observed. They are caused by bursts of tearing modes located close to the q = 1 surface, which are destabilised by flat central current profiles, typical for highly elongated plasmas. Neoclassical tearing modes (NTMs), which have been observed to limit the achievable beta in a number of tokamaks, arise from a helical perturbation of the bootstrap current caused by an existing seed island. Neoclassical m/n = 2/1 tearing modes have been identified in TCV discharges which are characterised by a low electron collisionality νe*, a medium ion collisionality ν*, a medium value of beta and strongly peaked pressure and current profiles. In contrast to other tokamak experiments, where sawteeth, fishbones or ELMs generate the seed island, the required seed island is provided by a conventional tearing mode. The island clearly shows a conventional and a neoclassical growth phase. The TCV results provide the first clear observations of such a trigger mechanism which could also explain the occurrence of "triggerless" NTMs observed in other experiments. The slowly growing seed island also allows a measurement of the critical seed island width ωcrit, which is observed to increase with increasing density. In conclusion, several local and a global stability limits are analysed. These instabilities can limit the pressure gradient and thereby, the performance of the plasma. The presented results reveal several previously unobserved features of commonly observed instabilities. Since the most of the new observations can be explained by theory, they improve the predictive capabilities with respect to new experiments. The experiments have also shown some new interactions among different instabilities, which add to the already crowded complexities of MHD phenomena in fusion plasmas.

EPFL2001