A phenomenological explanation for the anomalous ion heating observed in the JET alpha-heating experiment of 1997

In the so-called alpha-heating experiment performed on the JET tokamak during the deuterium-tritium campaign of 1997, the ion temperature was found to be far exceeding (both in absolute value and in its rise time) the level that could have been expected from direct collisional heating by the fusion-born alpha particles themselves and energy equi-partition with the electrons. To date, no explanation has been put forward for this long standing puzzle, despite much work having been performed on this subject in the early 2000s. Two analysis methods that have recently become available have been employed to re-analyse these observations of an anomalous ion heating. First, an algorithm based on the Sparse Representation of Signals has been used to analyse magnetic, reflectometry and electron cyclotron emission measurements of the turbulence spectra in the drift-wave range of frequencies. This analysis has then been complemented with turbulence simulations performed with the GENE code. We find, both experimentally and in the simulations, that the presence of a minority, but sufficiently large, population of fusion-born alpha particles that have not yet fully thermalized stabilizes the turbulence in the ion-drift direction, but practically does not affect the turbulence in the electron-drift direction. We link such stabilization of the ion-drift-wave turbulence to the increase in the ion temperature above the level achieved in similar discharges that did not have (at all or enough) alpha particles. When the fusion-born alpha particles have fully thermalized, the turbulence spectrum in the ion-drift direction re-appears at somewhat larger amplitudes, which we link to the ensuing reduction in the ion temperature. This phenomenological dynamics fully corresponds to the actual experimental observations. By taking into account an effect of the alpha particles that had not been previously considered, our new analysis finally presents a phenomenological explanation for the so-far-unexplained anomalous ion heating observed in the JET alpha-heating experiment of 1997. Through the formulation of an empirical criterion for ion-drift-wave turbulence stabilization by fusion-born alpha particles, we also show why similar observations were not made in the other deuterium-tritium experiments run so far in JET and TFTR. This allows assessing the operational domain for this stabilization mechanism for ion-drift-wave turbulence in future burning plasma experiments such as ITER, which may open a new path towards the sustainment of a high energy gain in such forthcoming devices.

Tokamak Edge Plasma Turbulence Interaction with Magnetic X-Point in 3D Global Simulations

Davide Galassi, Eric Serre

Turbulence in the edge plasma of a tokamak is a key actor in the determination of the confinement properties. The divertor configuration seems to be beneficial for confinement, suggesting an effect on turbulence of the particular magnetic geometry introduced by the X-point. Simulations with the 3D fluid turbulence code TOKAM3X are performed here to evaluate the impact of a diverted configuration on turbulence in the edge plasma, in an isothermal framework. The presence of the X-point is found, locally, to affect both the shape of turbulent structures and the amplitude of fluctuations, in qualitative agreement with recent experimental observations. In particular, a quiescent region is found in the divertor scrape-off layer (SOL), close to the separatrix. Globally, a mild transport barrier spontaneously forms in the closed flux surfaces region near the separatrix, differently from simulations in limiter configuration. The effect of turbulence-driven Reynolds stress on the formation of the barrier is found to be weak by dedicated simulations, while turbulence damping around the X-point seems to globally reduce turbulent transport on the whole flux surface. The magnetic shear is thus pointed out as a possible element that contributes to the formation of edge transport barriers.

2019

Gyrokinetic particle-in-cell global simulations of ion-temperature-gradient and collisionless-trapped-electron-mode turbulence in tokamaks

Sébastien Jolliet

The goal of thermonuclear fusion research is to provide power plants, that will be able to produce one gigawatt of electricity. Among the different ways to achieve fusion, the tokamak, based on magnetic confinement, is the most promising one. A gas is heated up to hundreds of millions of degrees and becomes a plasma, which is maintained – or confined – in a toroidal vessel by helical magnetic field lines. Then, deuterium and tritium are injected and fuse to create an α particle and an energetic neutron. In order to have a favorable power balance, the power produced by fusion reactions must exceed the power needed to heat the plasma and the power losses. This can be cast in a very simple expression which stipulates that the product of the density, the temperature and the energy confinement time must exceed some given value. Unfortunately, present-days tokamaks are not able to reach this condition, mostly due to plasma turbulence. The latter phenomenon enhances the heat losses and degrades the energy confinement time, which cannot be predicted by analytical theories such as the so-called neoclassical theory in which the heat losses are caused by Coulomb collisions. Therefore, numerical simulations are being developed to model plasma turbulence, mainly caused by the Ion and Electron Temperature-Gradient and the Trapped-Electron-Mode instabilities. The plasma is described by a distribution function which evolves according to the Vlasov equation. The electromagnetic fields created by the particles are self-consistently obtained through Maxwell's equations. The resulting Vlasov-Maxwell system is greatly simplified by using the gyrokinetic theory, which consists, through an appropriate ordering, of eliminating the fast gyromotion (compared to the typical frequency of instabilities). Nevertheless, it is still extremely difficult to solve this system numerically due to the large range of time and spatial scales to be resolved. In this thesis, the Vlasov-Maxwell system is solved in the electrostatic and collisionless limit with the Particle-In-Cell (PIC) ORB5 code in global tokamak geometry. This Monte-Carlo approach suffers from statistical noise which unavoidably degrades the quality of the simulation. Consequently, the first part of this work has been devoted to the optimization of the code with a view to reduce the numerical noise. The code has been rewritten in a new coordinate system which takes advantage of the anisotropy of turbulence, which is mostly aligned with the magnetic field lines. The overall result of the optimization is that for a given accuracy, the CPU time has been decreased by a factor two thousand, the total memory has been decreased by a factor ten and the numerical noise has been reduced by a factor two hundred. In addition, the scaling of the code with respect to plasma size is presently optimal, suggesting that ORB5 could compute heat transport for future fusion devices such as ITER. The second part of this thesis presents the validation of the code with numerical convergence tests, linear (including dispersion relations) and nonlinear benchmarks. Furthermore, the code has been applied to important issues in gyrokinetic theory. It is shown for the first time that a 5D global delta-f PIC code can achieve a thermodynamic steady state on the condition that some dissipation is present. This is a fundamental result as the main criticism against delta-f PIC codes is their inability to deal with long time simulations. Next, the role of the parallel nonlinearity is studied and it is demonstrated in this work that this term has no real influence on turbulence, provided the numerical noise is sufficiently low. This result should put an end to the controversy that recently occurred, in which gyrokinetic simulations using different numerical approaches yielded contradictory results. Finally, thanks to the optimization of the code, the gyrokinetic model has been extended to include the kinetic response of trapped-electrons, in place to the usual adiabatic (Boltzmann) approximation. For the first time, global TEM nonlinear simulations are presented, and the role of the zonal flow on heat transport is analyzed. This study will help in acquiring some knowledge on the less-known TEM turbulence (as compared to ITG). In conclusion, this thesis is one of the main steps of the development of ORB5, which is now a state-of-the-art gyrokinetic code for collisionless ITG and TEM turbulence, and has brought several contributions to the understanding of these phenomena.

EPFL2009

Validation of edge turbulence codes against the TCV-X21 diverted L-mode reference case

Claudia Colandrea, Hugo De Oliveira, Davide Galassi, Maurizio Giacomin, Nicola Offeddu, Holger Reimerdes, Paolo Ricci, Eric Serre, Christian Gabriel Theiler, Cedric Kar-Wai Tsui, Nicola Vianello

Self-consistent full-size turbulent-transport simulations of the divertor and scrape-off-layer (SOL) of existing tokamaks have recently become feasible. This enables the direct comparison of turbulence simulations against experimental measurements. In this work, we perform a series of diverted ohmic L-mode discharges on the tokamak a configuration variable (TCV) tokamak, building a first-of-a-kind dataset for the validation of edge turbulence models. This dataset, referred to as TCV-X21, contains measurements from five diagnostic systems from the outboard midplane (OMP) to the divertor targets-giving a total of 45 one- and two-dimensional comparison observables in two toroidal magnetic field directions. The experimental dataset is used to validate three flux-driven 3D fluid-turbulence models-GBS, GRILLIX and TOKAM3X. With each model, we perform simulations of the TCV-X21 scenario, individually tuning the particle and power source rates to achieve a reasonable match of the upstream separatrix value of density and electron temperature. We find that the simulations match the experimental profiles for most observables at the OMP-both in terms of profile shape and absolute magnitude-while a comparatively poorer agreement is found towards the divertor targets. The match between simulation and experiment is seen to be sensitive to the value of the resistivity, the heat conductivities, the power injection rate and the choice of sheath boundary conditions. Additionally, despite targeting a sheath-limited regime, the discrepancy between simulations and experiment also suggests that the neutral dynamics should be included. The results of this validation show that turbulence models are able to perform simulations of existing devices and achieve reasonable agreement with experimental measurements. Where disagreement is found, the validation helps to identify how the models can be improved. By publicly releasing the experimental dataset and validation analysis, this work should help to guide and accelerate the development of predictive turbulence simulations of the edge and SOL.