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This paper deals with the distribution of sources, transport, and exhaust of particles in a tokamak. Knowledge and understanding of all the physical phenomena involved in the global particle buildup are necessary to study and predict density regimes and subsequently to develop optimized scenarios for tokamak operation in order to control heat and particle exhaust. Neutral particles and their interactions with plasma are central in this perspective. This paper discusses the impact of varying the intensity of particle fueling in 2D transport simulations of a WEST discharge. Simulations are performed with an updated version of SOLEDGE-HDG that allows a more realistic transport of neutrals using a self-consistent diffusive model based on charge exchange and ionization processes. New code capabilities allow the entire WEST poloidal cross section to be simulated in a realistic configuration for both geometry and the range of control parameters. A gas puff scan illustrates the main features of the sheath-limited, high-recycling, and detached regimes, such as the buildup of the temperature gradient and the pressure drop in the scrape-off layer (SOL), the target temperature falling to 1 eV, and the ionization source moving away from the targets, as well as the particle flux rollover. A crude estimate of wall erosion is also provided, showing the respective role of each plasma wall component in each of these regimes.

In its first phase of exploitation, JT-60SA will be equipped with an inertially cooled divertor, which can sustain heat loads of 10 MW/m2 on the targets for a few seconds, which is much shorter than the intended discharge duration. Therefore, in order to maximize the duration of discharges, it is crucial to develop operational scenarios with a high radiated fraction in the plasma edge region without unacceptably compromising the scenario performance. In this study, the core and edge conditions of unseeded and neon-seeded deuterium H-mode scenarios in JT-60SA were investigated using METIS and SOLEDGE3X–EIRENE codes. The aim was to determine whether, and under which operational conditions, it would be possible to achieve heat loads at the targets significantly lower than 10 MW/m2 and potentially establish a divertor-detached regime while keeping favorable plasma core conditions. In first analysis, an investigation of the edge parameter space of unseeded scenarios was carried out. Simulations at an intermediate edge power of 15 MW indicate that, without seeded impurities, the heat loads at the targets are higher than 10 MW/m2 in attached cases, and achieving detachment is challenging, requiring upstream electron densities at least above 4 × 1019 m−3. This points toward the need for impurity injection during the first period of exploitation of the machine. Therefore, neon seeding simulations were carried out, performing a seeding rate scan and an injected power scan while keeping the upstream electron density at the separatrix at 3 × 1019 m−3. They show that at 15 MW of power injected into the edge plasma, the inner target is easily detached and presents low heat loads when neon is injected. However, at the outer target, the heat fluxes are not lowered below 10 MW/m2, even when the power losses in the edge plasma are equal to 50% of the power crossing the separatrix. Therefore, the tokamak will probably need to be operated in a deep detached regime in its first phase of exploitation for discharges longer than a few seconds. In the framework of core–edge integrated modeling, using METIS, the power radiated in the core was computed for the most interesting cases.

A central problem in magnetized fusion plasmas is to understand whether the plasma edge sustains a turbulent state and transitions to improved confinement. The authors simulate the detailed organization of turbulence from the primitive flux-driven kinetic equations including plasma-solid interaction and identify basic mechanisms which allow to cure the oft-reported shortfall of turbulence power in the plasma edge and to describe spontaneous onset of a transport barrier.

The mission of WEST (tungsten-W Environment in Steady-state Tokamak) is to explore long pulse operation in a full tungsten (W) environment for preparing next-step fusion devices (ITER and DEMO) with a focus on testing the ITER actively cooled W divertor in tokamak conditions. Following the successful completion of phase 1 (2016-2021), phase 2 started in December 2022 with the lower divertor made entirely of actively cooled ITER-grade tungsten mono-blocks. A boronization prior the first plasma attempt allowed for a smooth startup with the new divertor. Despite the reduced operating window due to tungsten, rapid progress has been made in long pulse operation, resulting in discharges with a pulse length of 100 s and an injected energy of around 300 MJ per discharge. Plasma startup studies were carried out with equatorial boron nitride limiters to compare them with tungsten limiters, while Ion Cyclotron Resonance Heating assisted startup was attempted. High fluence operation in attached regime, which was the main thrust of the first campaigns, already showed the progressive build up of deposits and appearance of dust, impacting the plasma operation as the plasma fluence increased. In total, the cumulated injected energy during the first campaigns reached 43 GJ and the cumulated plasma time exceeded 5 h. Demonstration of controlled X-Point Radiator regime is also reported, opening a promising route for investigating plasma exhaust and plasma-wall interaction issues in more detached regime. This paper summarises the lessons learned from the manufacturing and the first operation of the ITER-grade divertor, describing the progress achieved in optimising operation in a full W environment with a focus on long pulse operation and plasma wall interaction.

The interaction between a plasma and a solid surface is studied in a (1D–1V) kinetic framework using a localized particle and convective energy source. Matching the quasineutral plasma region and sheath horizon is addressed in the fluid framework with a zero heat flux closure. It highlights non-polytropic nature of the physics of parallel transport. Shortfalls of this approach compared to a reference kinetic simulation highlight the importance of the heat flux as the measure of kinetic effects. Non-collisional closure and higher moment closure are used to determine the sound velocity. Within these frameworks, no gain in the fluid predictive capability is obtained. The kinetic constraint at the sheath horizon is discussed and modified to account for conditions that are actually met in simulations, namely quasineutrality with a small but finite charge density. Analyzing the distribution functions shows that collisional transfer is mandatory to achieve steady-state self-organization on the open field lines.

The interaction between a plasma and a solid surface is studied in a (1D-1V) kinetic approach using immersed boundary conditions and penalization to model the wall. Two solutions for the penalized wall region are investigated that either allow currents to flow within the material boundary or not. Essential kinetic aspects of sheath physics are recovered in both cases and their parametric dependencies investigated. Importantly, we show how the two approaches can be reconciled when accounting for relevant kinetic effects. Non-Maxwellian features of the ion and electron distribution functions are essential to capture the value of the potential drop in the sheath. These features lead to a sheath heat transmission factor for ions 60% larger than usually predicted and 35% for electrons. The role of collisions is discussed and means of incorporating minimally-relevant kinetic sheath physics in the gyrokinetic framework are discussed.

This paper deals with the distribution of sources, transport, and exhaust of particles in a tokamak. Knowledge and understanding of all the physical phenomena involved in the global particle buildup are necessary to study and predict density regimes and subsequently to develop optimized scenarios for tokamak operation in order to control heat and particle exhaust. Neutral particles and their interactions with plasma are central in this perspective. This paper discusses the impact of varying the intensity of particle fueling in 2D transport simulations of a WEST discharge. Simulations are performed with an updated version of SOLEDGE-HDG that allows a more realistic transport of neutrals using a self-consistent diffusive model based on charge exchange and ionization processes. New code capabilities allow the entire WEST poloidal cross section to be simulated in a realistic configuration for both geometry and the range of control parameters. A gas puff scan illustrates the main features of the sheath-limited, high-recycling, and detached regimes, such as the buildup of the temperature gradient and the pressure drop in the scrape-off layer (SOL), the target temperature falling to 1 eV, and the ionization source moving away from the targets, as well as the particle flux rollover. A crude estimate of wall erosion is also provided, showing the respective role of each plasma wall component in each of these regimes. [ABSTRACT FROM AUTHOR]

In its first phase of exploitation, JT-60SA will be equipped with an inertially cooled divertor, which can sustain heat loads of 10 MW/m[sup 2] on the targets for a few seconds, which is much shorter than the intended discharge duration. Therefore, in order to maximize the duration of discharges, it is crucial to develop operational scenarios with a high radiated fraction in the plasma edge region without unacceptably compromising the scenario performance. In this study, the core and edge conditions of unseeded and neon-seeded deuterium H-mode scenarios in JT-60SA were investigated using METIS and SOLEDGE3X-EIRENE codes. The aim was to determine whether, and under which operational conditions, it would be possible to achieve heat loads at the targets significantly lower than 10 MW/m[sup 2] and potentially establish a divertordetached regime while keeping favorable plasma core conditions. In first analysis, an investigation of the edge parameter space of unseeded scenarios was carried out. Simulations at an intermediate edge power of 15 MW indicate that, without seeded impurities, the heat loads at the targets are higher than 10 MW/m[sup 2] in attached cases, and achieving detachment is challenging, requiring upstream electron densities at least above 4 χ 10[sup 19] m[sup -3]. This points toward the need for impurity injection during the first period of exploitation of the machine. Therefore, neon seeding simulations were carried out, performing a seeding rate scan and an injected power scan while keeping the upstream electron density at the separatrix at 3 χ 10[sup 19] m[sup -3]. They show that at 15 MW of power injected into the edge plasma, the inner target is easily detached and presents low heat loads when neon is injected. However, at the outer target, the heat fluxes are not lowered below 10 MW/m[sup 2], even when the power losses in the edge plasma are equal to 50% of the power crossing the separatrix. Therefore, the tokamak will probably need to be operated in a deep detached regime in its first phase of exploitation for discharges longer than a few seconds. In the framework of core-edge integrated modeling, using METIS, the power radiated in the core was computed for the most interesting cases. [ABSTRACT FROM AUTHOR]

Turbulence in hot magnetized plasmas is shown to generate permeable localized transport barriers that globally organize into the so-called "ExB staircase" [G. Dif-Pradalier et al., Phys. Rev. E, 82, 025401(R) (2010)]. Its domain of existence and dependence with key plasma parameters is discussed theoretically. Based on these predictions, staircases are observed experimentally in the Tore Supra tokamak by means of high-resolution fast-sweeping X-mode reflectometry. This observation strongly emphasizes the critical role of mesoscale self-organization in plasma turbulence and may have far-reaching consequences for turbulent transport models and their validation.

Radial transport in scrape off layer is commonly attributed to the intermittent convection of plasma filaments. These filaments are observed in experiments, and commonly reproduced by turbulent simulations. These simulations are able to reproduce both filament velocities and main scrape off layer (SOL) widths measured in circular plasma geometries. In this contribution a comprehensive model of transport is derived, predicting the absolute amplitude of radial flux and SOL widths from interchange turbulence. This spectral filament model (SF model) describes the contribution to the radial flux of an assembly of poloidal waves representing plasma filaments. A model of density and potential spectra is detailed, leading to a simple expression of the time average turbulent radial flux and SOL width. The model shows a quantitative agreement with flux-driven simulations, as well as experimental measurements over a wide range of conditions. Predictions for ITER start-up conditions also recover the extrapolations from multi-machine databases. The SF model is derived for circular plasma shapes with weak flow shear, and gives a SOL width that varies mainly with the poloidal magnetic field, weakly with the toroidal magnetic field, and weakly but positively with the plasma major radius. Interestingly, this sensitivity with main control parameters is qualitatively close to what is found for diverted conditions in both L and H mode. Keywords: Tokamak, Scrape off layer, Transport, Turbulence, Model

A reduced model for radial anomalous transport of plasma in tokamaks, inspired by the Reynolds-Averaged Navier–Stokes (RANS) approach, is presented assuming diffusion as governing mechanism. In order to self-consistently calculate transport coefficients, an empirical equation is built for the turbulent kinetic energy and the system is closed via the scaling law of global confinement. In such way the SOL width appears to recover experimental dependencies with respect to machine parameters and interestingly, when the model is implemented in a 2D transport code for a realistic study-case, mean fields retrieve some features already observed in 1st-principle turbulent codes. Keywords: Anomalous transport, Reduced model, κ−ε

The effect of turbulent fluctuations on the transport of neutral particles (atoms, molecules) in tokamak plasmas is investigated with the 3D global turbulence code TOKAM3X-EIRENE in limiter geometry. The statistical properties of turbulent fields relevant to this work are discussed, including the recycling flux. The neutral particle transport is recalculated on the mean field plasma, and compared to the mean neutral particle density/flows obtained from the turbulent simulation, so as to assess the effects of the fluctuations, in particular on the ionization balance. The latter effects are remarkably modest in the simulation presented here, but are expected to become more and more pronounced as the high recycling regime is approached, in particular because the plasma temperature becomes low enough so that ionization is strongly non-linear. However, the turbulent fluctuations in the SOL do have a substantial effect on the neutral densities on the low field side of the limiter, including in the confined plasma. These effects are traced back to non-linearities in the plasma flux at the wall, and the fluctuations in the latter are identified as an important contributor both to neutral particle density fluctuations and to deviations from mean neutral particle density/flows in the turbulent simulation with respect to the same quantities recalculated on the mean plasma fields. Key words: Turbulent fluctuations, Neutral particle transport, Non-linearity, Ionization

A 3D multispecies fluid model has been implemented in the SOLEDGE-TOKAM suite of codes to address Scrape-off layer turbulent impurity transport. Zhdanov closure is used to address multi-component plasma modeling without any mass ordering or trace impurity assumption. Thanks to immersed boundary conditions, up to the wall simulations with non-axisymmetric plasma facing components are performed, in particular in the WEST configuration. A first proof of principle of interchange turbulence simulation of a Deuterium+Carbon plasma is also reported. Keywords: Edge plasma, Turbulence, Fluid modelling, Impurity transport

The dynamical interaction between eddies and shear flow is investigated through a simplified model of vorticity conservation with tilted eddies. Energy is transferred either to the flow or to eddies, depending on the eddy tilt with respect to the flow shear. When eddies are tilted in the shear direction, the system is favorable to shear increase: tilt instability (TI) or the negative viscosity phenomenon. When eddies are tilted in the opposite direction, the shear flow is damped via a Kelvin-Helmholtz (KH) process. The TI generally dominates the interaction on the largest radial scale, but a fraction of the energy cascades to smaller radial scales through the alternation of tilting and KH dynamics. Within this eddy description, we show that the symmetry breaking required to generate a net residual stress is set by the intrinsic eddy tilt. We recall that magnetic shear can provide an intrinsic tilt to ballooning modes at the edge of tokamak plasmas, with an orientation which depends on flux surface geometry. In L-mode weak shear regimes, this residual stress can dominate the Reynolds stress. Coupled to momentum sources acting in the scrape-off layer, it can induce a significant difference of the edge radial electric field between lower single null and upper single null geometries. A comparison with experimental profiles measured across the edge of Tore Supra L-mode plasmas is discussed. © 2013 IOP Publishing Ltd.

Flux-driven global gyrokinetic codes are now mature enough to make predictions in terms of turbulence and transport in tokamak plasmas. Some of the recent breakthroughs of three such codes, namely GYSELA, ORB5 and XGC1, are reported and compared wherever appropriate. In all three codes, turbulent transport appears to be mediated by avalanche-like events, for a broad range of ρ* = ρi/a values, ratio of the gyro-radius over the minor radius. Still, the radial correlation length scales with ρi, leading to the gyro-Bohm scaling of the effective transport coefficient below ρ* ≈ 1/300. The possible explanation could be due to the fact that avalanches remain meso-scale due to the interaction with zonal flows, whose characteristic radial wavelength appears to be almost independent of the system size. As a result of the radial corrugation of the turbulence driven zonal and mean flows, the shear of the radial electric field can be significantly underestimated if poloidal rotation is assumed to be governed by the neoclassical theory, especially at low collisionality. Indeed, the turbulence contribution to the poloidal rotation increases when collisionality decreases. Finally, the numerical verification of toroidal momentum balance shows that both neoclassical and turbulent contributions to the Reynolds' stress tensor play the dominant role. The phase space analysis further reveals that barely passing supra-thermal particles mostly contribute to the toroidal flow generation, consistently with quasi-linear predictions.

Treatment of binary Coulomb collisions when the full gyrokinetic distribution function is evolved is discussed here. A spectrum of different collision operators is presented, differing through both the physics that can be addressed and the numerics they are based on. Eulerian-like (semi-Lagrangian) and particle in cell (PIC) (Monte-Carlo) schemes are successfully cross-compared, and a detailed confrontation to neoclassical theory is shown.

A systematic, constructive and self-consistent procedure to quantify nonlocal, nondiffusive action at a distance in plasma turbulence is exposed and applied to turbulent heat fluxes computed from the state-of-the-art full- f, flux-driven gyrokinetic GYSELA and XGC1 codes. A striking commonality is found: heat transport below a dynamically selected mesoscale has the structure of a Lévy distribution, is strongly nonlocal, nondiffusive, scale-free, and avalanche mediated; at larger scales, we report the observation of a self-organized flow structure which we call the " E × B staircase" after its planetary analog.

This paper analyzes the properties of a two-field critical gradient model that couples a heat equation to an evolution equation for the turbulence intensity. It is shown that the dynamics of a perturbation is ballistic or diffusive depending on the shape of the pulse and also on the distance of the temperature gradient to the instability threshold. This dual character appears in the linear response of this model for a wave packet. It is recovered when investigating the nonlinear solutions of this system. Both self-similar diffusive fronts and ballistic fronts are shown to exist. When the propagation is ballistic, it is found that the front velocity is the geometric mean between the turbulent diffusion coefficient and a microinstability growth rate. © 2007 American Institute of Physics.

Motivated by Radio Frequency (RF) heating studies, the response of the plasma of tokamaks to the presence of a locally polarized limiter is studied. In a first part, we use the TOKAM3X3D global edge turbulence code to analyse the impact of such biasing in a realistic geometry. Key features of experimental observations are qualitatively recovered, especially the extension of a potential and density perturbation on long, but finite, distances along connected field lines. The perturbation is also found to extend in the transverse direction. Both observations demonstrate the influence of perpendicular current loops on the plasma confirming the need for an accurate description in reduced models. In a second part, we use the TOKAM2D slab turbulence code to determine the validity of using a transverse Ohm's law for this purpose. Results indicate that a local Ohm's law with a constant and uniform perpendicular resistivity appears at least as an oversimplified description of perpendicular charge transport in a turbulent Scrape-Off Layer. Keywords: Tokamaks, Scrape-Off Layer, RF sheath, Turbulence, Transverse resistivity

Transport codes are the main workhorses for global edge studies and modern divertor design. These tools do not resolve turbulent fluctuations responsible for the bulk of cross-field transport in the Scrape-off Layer (SOL), and solve mean field equations instead. Turbulent fluxes are modelled by diffusive transport along the gradients of the mean fields. Improvements of this description, on the basis of approaches developed in computational fluid dynamics are discussed, broadening the outlook given in Bufferand et al. (2016) [10]. This contribution focuses on additional closure issues related to non-linearities in sources/sinks from plasma-wall interactions, here sputtered fluxes from the plasma facing components. “Fluctuation dressed” sputtering yields Yeff are introduced and calculated from turbulence simulations. Properly taking fluctuations into account is shown to lead to higher sputtering at sub-threshold energies compared to mean field predictions. As a first step towards an implementation in a transport code, the possibility of parametrizing Yeff in terms of the mean fields is tentatively investigated. Keywords: Transport code, Mean field description, Turbulent flux closure, Sputtering

In order to improve cross-field transport description, drifts and currents have been implemented in SOLEDGE2D–EIRENE. The derivation of an equation for the electric potential is recalled. The resolution of current equation is tested in a simple slab case. WEST divertor simulations in forward-B and reverse-B fields are also discussed. A significant increase of ExB shear is observed in the forward-B configuration that could explain a favorable L-H transition in this case. Keywords: Edge modeling, Edge plasma, Drifts