Hugo Bufferand

WEST Physics Basis

With WEST (Tungsten Environment in Steady State Tokamak) (Bucalossi et al 2014 Fusion Eng. Des. 89 907-12), the Tore Supra facility and team expertise (Dumont et al 2014 Plasma Phys. Control. Fusion 56 075020) is used to pave the way towards ITER divertor procurement and operation. It consists in implementing a divertor configuration and installing ITER-like actively cooled tungsten monoblocks in the Tore Supra tokamak, taking full benefit of its unique long-pulse capability. WEST is a user facility platform, open to all ITER partners. This paper describes the physics basis of WEST: the estimated heat flux on the divertor target, the planned heating schemes, the expected behaviour of the L-H threshold and of the pedestal and the potential W sources. A series of operating scenarios has been modelled, showing that ITER-relevant heat fluxes on the divertor can be achieved in WEST long pulse H-mode plasmas.

Numerical modelling for divertor design of the WEST device with a focus on plasma?wall interactions

In the perspective of operating tungsten monoblocks in WEST, the ongoing major upgrade of the Tore Supra tokamak, a dedicated modelling effort has been carried out to simulate the interaction between the edge plasma and the tungsten wall. A new transport code, SolEdge2D–EIRENE, has been developed with the ability to simulate the plasma up to the first wall. This is especially important for steady state operation, where thermal loads on all the plasma facing components, even remote from the plasma, are of interest. Moreover, main chamber tungsten sources are thought to dominate the contamination of the plasma core. We present here in particular new developments aimed at improving the description of the interface between the plasma and the wall, namely a way to treat sheath physics in a more faithful way using the output of 1D particle in cell simulations. Moreover, different models for prompt redeposition have been implemented and are compared. The latter is shown to play an important role in the balance between divertor and main chamber sources.

The TOKAM3X code for edge turbulence fluid simulations of tokamak plasmas in versatile magnetic geometries

The new code TOKAM3X simulates plasma turbulence in full torus geometry including the open field lines of the Scrape-off Layer (SOL) and the edge closed field lines region in the vicinity of the separatrix. Based on drift-reduced Braginskii equations, TOKAM3X is able to simulate both limited and diverted plasmas. Turbulence is flux driven by incoming particles from the core plasma and no scale separation between the equilibrium and the fluctuations is assumed so that interactions between large scale flows and turbulence are consistently treated. Based on a domain decomposition, specific numerical schemes are proposed using conservative finite-differences associated to a semi-implicit time advancement. The process computation is multi-threaded and based on MPI and OpenMP libraries. In this paper, fluid model equations are presented together with the proposed numerical methods. The code is verified using the manufactured solution technique and validated through documented simple experiments. Finally, first simulations of edge plasma turbulence in X-point geometry are also introduced in a JET geometry. Modelling of the turbulent cross-field transport in tokamak edge plasma.Development of a fluid code TOKAM3X to simulate turbulence.Code verification and validation.First X-point simulations in a JET-like geometry.

Multi-scale self-organisation of edge plasma turbulent transport in 3D global simulations

The 3D global edge turbulence code TOKAM3X is used to study the properties of edge particle turbulent transport in circular limited plasmas, including both closed and open flux surfaces. Turbulence is driven by an incoming particle flux from the core plasma and no scale separation between the equilibrium and the fluctuations is assumed. Simulations show the existence of a complex self-organization of turbulence transport coupling scales ranging from a few Larmor radii up to the machine scale. Particle transport is largely dominated by small scale turbulence with fluctuations forming quasi field-aligned filaments. Radial particle transport is intermittent and associated with the propagation of coherent structures on long distances via avalanches. Long range correlations are also found in the poloidal and toroidal direction. The statistical properties of fluctuations vary with the radial and poloidal directions, with larger fluctuation levels and intermittency found in the outboard scrape-off layer (SOL). Radial turbulent transport is strongly ballooned, with 90% of the flux at the separatrix flowing through the low-field side. One of the main consequences is the existence of quasi-sonic asymmetric parallel flows driving a net rotation of the plasma. Simulations also show the spontaneous onset of an intermittent E × B rotation characterized by a larger shear at the separatrix. Strong correlation is found between the turbulent particle flux and the E × B flow shear in a phenomenology reminiscent of H-mode physics. The poloidal position of the limiter is a key player in the observed dynamics.

Ionization balance of impurities in turbulent scrape-off layer plasmas I: local ionization-recombination equilibrium

In magnetized fusion devices, cross field impurity transport is often dominated by turbulence, in particular in the scrape-off layer. In these outer regions of the plasma, fluctuations of plasma parameters can be comparable to mean values, and the way ionization and recombination sources are treated in transport codes becomes questionnable. In fact, sources are calculated using the mean density and temperature values, with no account of fluctuations. In this work we investigate the modeling uncertainties introduced by this approximation, both qualitatively and quantitatively for the local ionization equilibrium. As a first step transport effects are neglected, and their role will be discussed in a companion paper. We show that temperature fluctuations shift the ionization balance towards lower temperatures, essentially because of the very steep temperature dependence of the ionization rate coefficients near the threshold. To reach this conclusion, a thorough analysis of the time scales involved is carried out, in order to devise a proper way of averaging over fluctuations. The effects are found to be substantial only for fairly large relative fluctuation levels for temperature, that is of the order of a few tens of percents.

A penalization technique to model plasma facing components in a tokamak with temperature variations

To properly address turbulent transport in the edge plasma region of a tokamak, it is mandatory to describe the particle and heat outflow on wall components, using an accurate representation of the wall geometry. This is challenging for many plasma transport codes, which use a structured mesh with one coordinate aligned with magnetic surfaces. We propose here a penalization technique that allows modeling of particle and heat transport using such structured mesh, while also accounting for geometrically complex plasma-facing components. Solid obstacles are considered as particle and momentum sinks whereas ionic and electronic temperature gradients are imposed on both sides of the obstacles along the magnetic field direction using delta functions (Dirac). Solutions exhibit plasma velocities (M=1) and temperatures fluxes at the plasma-wall boundaries that match with boundary conditions usually implemented in fluid codes. Grid convergence and error estimates are found to be in agreement with theoretical results obtained for neutral fluid conservation equations. The capability of the penalization technique is illustrated by introducing the non-collisional plasma region expected by the kinetic theory in the immediate vicinity of the interface, that is impossible when considering fluid boundary conditions. Axisymmetric numerical simulations show the efficiency of the method to investigate the large-scale transport at the plasma edge including the separatrix and in realistic complex geometries while keeping a simple structured grid.

A table of Balmer γ line shapes for the diagnostic of magnetic fusion plasmas

A new table of Stark-Zeeman line shapes is provided for plasma diagnostics in the framework of magnetic fusion research. Spectral profiles of Dα, Dβ, Dγ, Dδ, and Dε have been calculated using computer simulations in conditions relevant to tokamak edge and divertor plasmas. After a brief presentation of the calculation method, we propose an interpolation formula and we give a routine for diagnostic applications. Analyses of experimental and synthetic spectra are performed as an illustration.

Magnetic sheath effect on the gross and net erosion rates due to impurities

Simulations of impurity trajectories in deuterium plasmas in the vicinity of the surface are performed by taking into account the magnetic sheath in conditions relevant for ITER and WEST. We show that the magnetic sheath has a strong effect on the average impact angle of impurities in divertor conditions and that it can lead to an increase of at the gross erosion maximum for neon (Ne+4) compared to the case when only the cyclotron motion is considered. The evaluation of the net erosion has been undertaken by retaining local redeposition of tungsten (W). We investigate how it is affected by the sheath magnetic potential profile. The largest effect is however observed when an energy distribution is considered. In this case the number of particles that manage to exit the sheath is larger as it is dominated by the more energetic particles. The comparison with other work is also discussed. The application to a scenario of the WEST project is finally performed, which exhibits a moderate, however non negligible, erosion of the plasma facing components.

Magnetic geometry and particle source drive of supersonic divertor regimes

We present a comprehensive picture of the mechanisms driving the transition from subsonic to supersonic flows in tokamak plasmas. We demonstrate that supersonic parallel flows into the divertor volume are ubiquitous at low density and governed by the divertor magnetic geometry. As the density is increased, subsonic divertor plasmas are recovered. On detachment, we show the change in particle source can also drive the transition to a supersonic regime. The comprehensive theoretical analysis is completed by simulations in ITER geometry. Such results are essential in assessing the divertor performance and when interpreting measurements and experimental evidence. The generation of large-scale flows in laboratory plasma is a highly non-linear problem. In a standard fashion it is considered that the flows remain subsonic away from the wall, the occurrence of supersonic flows being singular. We show here that the geometrical features of key configurations for fusion plasma can lead to supersonic flows.

Assessment of the effects of scrape-off layer fluctuations on first wall sputtering with the TOKAM-2D turbulence code

Plasma material interactions on the first wall of future tokamaks such as ITER and DEMO are likely to play an important role, because of turbulent radial transport. The latter results to a large extent from the radial propagation of plasma filaments through a tenuous background. In such a situation, mean field descriptions (on which transport codes rely) become questionable. First wall sputtering is of particular interest, especially in a full W machine, since it has been shown experimentally that first wall sources control core contamination. In ITER, beryllium sources will be one of the important actors in determining the fuel retention level through codeposition. In this work, we study the effect of turbulent fluctuations on mean sputtering yields and fluxes, relying on a new version of the TOKAM-2D code which includes ion temperature fluctuations. We show that fluctuations enhance sputtering at sub-threshold impact energies, by more than an order of magnitude when fluctuation levels are of order unity.