Development of a reduced model for energetic particle transport by sawteeth in tokamaks

The sawtooth instability is known for inducing transport and loss of energetic particles (EPs), and for generating seed magnetic islands that can trigger tearing modes. Both effects degrade the overall plasma performance. Several theories and numerical models have been previously developed to quantify the expected EP transport caused by sawteeth, with various degrees of sophistication to differentiate the response of EPs at different energies and on different orbits (e.g. passing vs. trapped), although the analysis is frequently limited to a single time slice during a tokamak discharge. This work describes the development and initial benchmark of a framework that enables a reduced model for EP transport by sawteeth retaining the full EP phase-space information. The model, implemented in the ORBIT hamiltonian particle-following code, can be used either as a standalone post-processor taking input data from codes such as TRANSP, or as a pre-processor to compute transport coefficients that can be fed back to TRANSP for time-dependent simulations including the effects of sawteeth on EPs. The advantage of the latter approach is that the evolution of the EP distribution can be simulated quantitatively for sawtoothing discharges, thus enabling a more accurate modeling of sources, sinks and overall transport properties of EP and thermal plasma species for comprehensive physics studies that require detailed information of the fast-ion distribution function and its evolution over time.

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

Self-consistent interaction of fast particles and ICRF waves in 3D applications of fusion plasma devices

Jonathan Marc Philippe Faustin

Tokamaks and stellarators are the most promising reactor concepts using the magnetic confinement to contain the plasma fuel. Reactors capable of sustaining deuterium-tritium (D-T) fusion reactions requires the confinement of a very high temperature plasma (above 100 millions kelvin). In addition to external heating methods, the slowing down of alpha particles (helium-4 nuclei) born from D-T fusion reactions on the background plasma represents a significant source of plasma heating. The good confinement of fast particles is therefore one of the most important aspect of magnetic fusion devices. Furthermore, long plasma operation in future fusion reactors requires the control of inherent plasma instabilities. These instabilities are particularly dangerous in tokamaks because of the large plasma current necessary to establish the confining magnetic field. In this thesis we use the numerical code package SCENIC to study the application of Ion Cyclotron Range of Frequency (ICRF) waves to tokamak and stellarator devices. This numerical tool was built to self-consistently solve, in three dimensional configurations, the plasma magnetohydrodynamic (MHD) equilibrium, the ICRF wave propagation and the resonant ion distribution function. SCENIC is used to interpret how the sawtooth instability can be controlled in tokamaks by appropriate application of ICRF waves. This control method was successfully tested in the JET tokamak and it is foreseen to be applied in the future ITER tokamak. Such plasma degrading instabilities are not, however, expected in stellarators because they operate with no plasma current. The recently started stellarator Wendelstein 7-X (W7-X) must however prove experimentally that fast particles particles can be confined in an optimised quasi-isodynamic magnetic configuration. An efficient auxiliary source of fast ions is required in W7-X since it is not designed to procude alpha particles via D-T fusion reactions. In this thesis, we address the possibility of generating a significant fast ion population with ICRF waves in W7-X. SCENIC simulations are employed in order to identify relevant fast ion loss channels that may still exist in the W7-X quasi-omnigenous equilibrium. These simulations show that ICRF minority heating may not be suitable for producing fast ions in W7-X plasmas. It is found that a high energy tail is more likely to be developed if a three-ion species scheme is applied.

EPFL2017

SOLPS5 modelling of ELMing H-mode on TCV

Roland Behn, Barbora Gulejová, Jan Horacek, János Márki, Richard Pitts, Marco Wischmeier

Although ohmic H-modes have long been produced on the TCV tokamak and the effects of ELMs at the divertor targets studied in some detail [1], no attempt has yet been made to model the scrape-off layer (SOL) in these plasmas. This contribution describes details of the first such efforts to do so. Simulations with the coupled fluid-Monte Carlo SOLPS5 code are constrained by careful upstream Thomson scattering and fast reciprocating Langmuir probe profiles and the results compared w ith measurements at the divertor targets. Recent experiments with high power ECRH at the third harmonic have produced large, possibly Type I ELMs on TCV for the first time, but in standard ohmic H-modes operating close to the L-H transition threshold power, only Type III ELMs are obtained. Typical single null lower H-mode discharges have I p = 400 kA, n/n GW ~ 0.3 and steady ELMing phases with f ELM ~ 100 Hz, where each ELM exhausts only a few 100 J of plasma stored energy. As such, these ELMs cannot be compared with larger events typical elsewhere regarding the magnitude of target power fluxes etc., but their behaviou r with respect to transport in the SOL and interaction with the targets is no different. In fact, their benign nature makes the fluid plasma simulation in some ways more appropriate since the ELMs are insu fficiently large to require a true kinetic simulation and are likely to be less perturbing in the sense of parallel heat flux limits and variations in sheath heat transmission coefficients. The modelling attempts described here broadly follow the approach in [2], seeking first the closest match to upstream experimental profiles during inter-ELM phases using a step-like ansatz for the perpendicular particle and heat diffusivities (D and χ i,e ) in the edge and SOL regions, but also introducing a poloidal variation of the transport coefficients both in the main chamber and dive rtor. This is extremely important in TCV, where the unconventional divertor geometry means that care must be taken in the presence of steep H-mode edge barriers to tailor differently the transport in this region compared with the core. Similar reasoning applies even more to the ELM itself, which is known to burst into the SOL in the outboard, unfavourable curvature region and is thus extremely poloidally localised. This has also been accounted for in the simulations which, as in the earlier SOLPS5 attempts to simulate Type ELMs in JET [3], m odel the ELM as an instantaneous local increase in the transport coefficients and simulate the subsequent SOL transport in a time dependent way. Good agreement is found between code and experime nt in the inter-ELM phase. Experimentally, these Type III ELMs are too rapid for comparison on an individual ELM basis. Instead, many similar events are coherently averaged and simulation comp ared with power and par ticle flux measurements at the divertor targets and line integrated observations of recycling in the divertor volume obtained using a new fast AXUV diode camera system filtered for Lyman-alpha emission.

2006