This work introduces a novel flux-surface-aligned algorithm to extend the state-of-the-art SOLEDGE3X code to non-axisymmetric magnetic configurations, and thereby addresses the growing demand for comprehensive plasma edge simulations in both tokamak and stellarator geometries. Such configurations pose significant challenges, as toroidal distortions of magnetic surfaces invalidate conventional mesh construction strategies that rely on flux-aligned meshes to handle the strong anisotropy between parallel and perpendicular transport. The proposed method transforms the existing 2D mesh into a 3D flux-aligned mesh by computing a 3D poloidal flux function, $\Psi^{3D}$, derived from vacuum coil perturbations. To accommodate the new geometry, a three-dimensional curvilinear metric formulation is introduced, where metric coefficients are evaluated at cell centers using finite-difference calculations based on the 3D mesh corner positions and are consistently integrated into all discrete operators. Verification tests using manufactured solutions confirm that the new algorithm preserves the accuracy and the robustness of the original axisymmetric version. In particular, the resulting flux surfaces are demonstrated to remain aligned with the magnetic field to first order in the perturbation amplitude. The method of manufactured solutions (MMS) also shows the second-order spatial accuracy of the transport operators. The enhanced capabilities of the solver are demonstrated through transport simulations of toroidal field ripple effects in the WEST tokamak, where heat flux patterns are consistent with experimental observations, and strong plasma asymmetries emerge in detached divertor regimes. Additionally, a proof-of-concept simulation on a stellarator-like geometry validates the algorithm’s ability to consistently model plasma transport, neutral dynamics, limiter boundary conditions, and density-control feedback in fully three-dimensional configurations with nested flux surfaces.

The WEST tokamak allows for high power steady-state plasma discharges in Lower Single-Null (LSN), Double-Null (DN) and Upper Single-Null (USN) configurations. In this contribution, first results from experimental L-mode DN discharges with 3.1 MW of additional heating in the WEST tokamak and associated modeling with the SOLEDGE-EIRENE code are presented. The goal is to investigate if the magnetic configuration could help to reduce the peak heat load on the targets, and how sensitive is the power sharing between the strike points to a change in magnetic equilibrium. This study, previously performed on other devices such as DIII-D, Alcator C-mod and MAST-U, provide new data for machines with a compact divertor configuration and tungsten walls. During the experiment, the distance between the two separatrices at the outer midplane dRsep was scanned from -32 mm (USN) to 42 mm (LSN), with the ion Bx del B drift directed towards the lower divertor. The measured power fall off length mapped at the outer midplane can vary between configurations but is centered around lambda q = 15.6 +/- 2.4 mm. In the DN configuration, Langmuir probes measurements have shown that 86 % of the power is directed towards the outer strike points. This inner/outer imbalance is consistent with the ones measured on DIII-D, Alcator C-mod and MAST-U. The influence of ballooned radial transport, that drives most of the power towards the low field side, has been reproduced in transport simulation with imposed poloidally ballooned cross-field transport. The peak heat flux measured on all strike points is reduced by half in DN compared to LSN configuration. In certain conditions of high radiations (Ohmic discharges or with ICRH), the DN configuration can trigger a MARFE on the High-Field Side (HFS) that moves in opposition to the oscillations of the plasma vertical position. This MARFE has been measured to account for 0.3 % of the particles in the plasma. Temperature and density of the core plasma are unaffected by its presence.

The onset of detachment in the ITER machine is analyzed in this work through the help of 2D-axisymmetric boundary plasma simulations with the SOLEDGE3X-EIRENE code, which features a numerical domain for the plasma solver extending up to the first wall. The plasma boundary is computed in scenarios from the first non-active phase of ITER, in pure H and at 20 MW. This set of simulations is used in two aspects: first, to study the plasma detachment in the divertor, and second, the plasma conditions, fluxes, and beryllium erosion at the first wall. Here, the code results are also compared to those obtained with the well-established SOLPS-ITER code, which includes a plasma numerical domain only covering the main SOL. Results show an increase in the SOL width lambda q with increasing density, and a detailed analysis is carried out, for the first time, on each of the different plasma-neutral interactions in the code's physics model in EIRENE. The gross beryllium erosion rates of first wall panels are estimated from 2D simulations, with the aim of assessing their sensitivity to two parameters: the divertor density regime, and the presence of density shoulders in the far-SOL formed by enhanced perpendicular transport at this location. The erosion contributions from neutrals and ions are considered in each case, and the charge-exchange atoms fluxes and energy distributions are provided, highlighting the two atom populations (cold and charge-exchange).

Even small fluctuations in the magnetic field are known to impact edge plasma turbulence and transport properties in magnetic confinement fusion devices. Magnetic induction modifies the parallel electric field, and as such, it impacts the parallel current in Ohm's law. In addition, magnetic fluctuations can induce geometrical and topological changes in the magnetic field structure, leading to parallel transport across the equilibrium magnetic surfaces. This paper presents the new drift-reduced fluid electromagnetic model implemented in SOLEDGE3X [Bufferand et al., Nuc. Fus. 2021]. Based on a domain decomposition, a specific numerical scheme is proposed using conservative second-order finite volumes associated with a semi-implicit time advancement. The coupling between the parallel current jll and the parallel electromagnetic potential All in Ohm's and Ampere's laws is treated using a new toroidally and poloidally staggered grid. While adding All doubles the size of the vorticity operator to be inverted, numerical tests show that the inclusion of the finite mass of the electrons in the new model acts as an upper limit on the parallel diffusion coefficient, thus improving the conditioning of the matrix at high plasma temperatures when the parallel resistivity rill approaches zero. The changes in the algorithm are verified using the method of manufactured solutions. The implementation is first validated with respect to theoretical linear stability results, recovering the transition from Alfv & eacute;n to thermal electron waves as the perpendicular wavenumber increased. Comparisons with available results in the literature show a qualitative agreement on a single blob propagation in a limited slab geometry. The first 3D simulations of plasma edge turbulence in TCV demonstrate the capability of the new solver to handle realistic tokamak configurations. The explicit-implicit time integration scheme enables one to compare electrostatic and electromagnetic effects using the same solver, with or without electron inertia and magnetic flutter. This ability opens the way to a better understanding of the impact of the electrostatic and electromagnetic mechanisms on the transport and turbulence properties in realistic tokamak configurations.

First principle modelling of edge plasma turbulence including neutrals and plasma recycling on the wall remains a challenge, in particular due to the long time scales necessary to simulate to reach particle balance. In this contribution, we propose a strategy to address these long time scales with the fluid code SOLEDGE, resorting to 2D reduced models for turbulence as well as 3D coarse grid simulations. The approach is applied to simulate TCV-X21 reference plasma scenario for edge turbulence modelling validation.

Experimental results from several tokamaks suggest a strong impact of divertor density regimes on turbulent transport in the edge plasma. Reciprocally, the change in transverse transport and SOL width affects the access to density regimes, making it a fundamental topic for heat exhaust issue. Such phenomenology is highly nonlinear and can only be approached quantitatively using numerical simulations treating turbulence and neutrals recycling physics self-consistently. In this study, the SOLEDGE3X edge multi-fluid code is used to investigate the mutual interaction between edge plasma turbulence and neutrals recycling. A fluid neutrals model based on the assumption of a charge-exchange-dominated plasma-neutral interaction has been implemented. Two simulations in circular geometry are compared: one without neutrals, where the particle flux is driven by a constant in flux from the core region, and the other one with neutrals recycling included in which the particle input to the system is self-consistently injected by a gas puff from the midplane. The presence of the neutrals triggers three types of perturbations on the plasma: a local and non-axisymmetric one driven by the gas puff, a global perturbation affecting both profiles and turbulence properties in the whole domain, and a local one in the vicinity of the limiter where recycling occurs. The largest effect of the inclusion of self-consistent neutrals recycling is a large-scale reorganization of the plasma profiles and turbulence properties due to the dissociation of particle and energy fluxes. These effects are expected to be more important at higher densities regimes or in diverted configuration.

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.

In 2021 JET exploited its unique capabilities to operate with T and D-T fuel with an ITER-like Be/W wall (JET-ILW). This second major JET D-T campaign (DTE2), after DTE1 in 1997, represented the culmination of a series of JET enhancements-new fusion diagnostics, new T injection capabilities, refurbishment of the T plant, increased auxiliary heating, in-vessel calibration of 14 MeV neutron yield monitors-as well as significant advances in plasma theory and modelling in the fusion community. DTE2 was complemented by a sequence of isotope physics campaigns encompassing operation in pure tritium at high T-NBI power. Carefully conducted for safe operation with tritium, the new T and D-T experiments used 1 kg of T (vs 100 g in DTE1), yielding the most fusion reactor relevant D-T plasmas to date and expanding our understanding of isotopes and D-T mixture physics. Furthermore, since the JET T and DTE2 campaigns occurred almost 25 years after the last major D-T tokamak experiment, it was also a strategic goal of the European fusion programme to refresh operational experience of a nuclear tokamak to prepare staff for ITER operation. The key physics results of the JET T and DTE2 experiments, carried out within the EUROfusion JET1 work package, are reported in this paper. Progress in the technological exploitation of JET D-T operations, development and validation of nuclear codes, neutronic tools and techniques for ITER operations carried out by EUROfusion (started within the Horizon 2020 Framework Programme and continuing under the Horizon Europe FP) are reported in (Litaudon et al Nucl. Fusion accepted), while JET experience on T and D-T operations is presented in (King et al Nucl. Fusion submitted).

The fluid-drift code SOLEDGE3X, developed by CEA/IRFM in collaboration with Aix-Marseille University, is a powerful tool for simulating transport and turbulence in tokamak edge plasmas with axisymmetric magnetic configurations. In tokamaks such as WEST, the pronounced toroidal magnetic ripple significantly affects plasma confinement and power exhaust, modulating both the poloidal and toroidal components of the equilibrium field. Using a discrete Biot–Savart law, the ripple field is calculated as a magnetic perturbation on the SOLEDGE3X mesh. The transport model and parallel gradient solvers have been enhanced to incorporate the new radial magnetic field component. Preliminary simulations of a WEST scenario reveal a heat deposition pattern in the divertor region consistent with observations from infrared camera experiments.

In the pedestal region, electromagnetic effects affect the evolution of micro-instabilities and plasma turbulence. The transport code Soledge3X developed by the CEA offers an efficient framework for turbulent 3D simulation on an electrostatic model with a fixed magnetic field. The physical accuracy of the model is improved with electromagnetic induction, driven by the local value of the parallel component of the electromagnetic vector potential A parallel to$$ {A}_{\parallel } $$, known from Ampere's law. It is solved implicitly in a coupled system with the vorticity equation on the electric potential phi$$ \Phi $$. The consequence is a basic electromagnetic behavior in the form of shear Alfven waves. A finite electron mass prevents unphysical speeds but requires solving for the time evolution of the parallel current density j parallel to$$ {j}_{\parallel } $$ in the generalized Ohm's law. This term can be analytically included with little computational overhead in the system on phi$$ \Phi $$ and A parallel to$$ {A}_{\parallel } $$ and improves its numerical condition, facilitating the iterative solving procedure. Simulations on a periodic slab case let us observe the predicted bifurcation of the wave propagation speed between the Alfven wave and the electron thermal wave speeds for varying perpendicular wavenumbers. The first results on a circular geometry with a limiter attest to the feasibility of turbulent electromagnetic scenarios.

With ITER, the largest tokamak ever built, and the growing number of fusion energy startups in the world, the need for numerical simulations has never been more crucial to progress towards the successful operation of fusion reactors. From fundamental plasma physics to engineering, a hierarchy of models exists from high-fidelity (gyro-)kinetic models in (5D) 6D to 0D fluid transport models. In this paper, we review the state-of-the-art of 3D turbulence fluid simulations in edge tokamak configurations. The widely used drift-reduced Braginskii equations are introduced together with the dedicated boundary conditions modelling plasma wall interactions. If until recently most of the models were focused on electrostatic turbulence driven by interchange-like instabilities, in recent years models have incorporated electromagnetic effects allowing fluctuations of the magnetic field. Specific features of the edge plasma configurations, which make these equations specially challenging to resolve and stressful for the numerical methods, are detailed. In particular, the strong anisotropy of the flow as well as the complex geometric characteristics lead to the development of dedicated discretization schemes and meshing, which are implemented in state-of-the-art codes reviewed here. It appears that the latter can be differentiated by their mesh construction as well by the manner in which they handle parallel gradients (aligned or not along the magnetic field). The review shows that no consensus on the optimal combination between meshing and discretization schemes, if it exists, has been found. Finally, examples of recent achievements show that 3D turbulence simulations of medium-sized tokamaks are currently achievable, but that ITER-size tokamaks and thermonuclear plasmas still require significant progress.

Within the 9th European Framework programme, since 2021 EUROfusion is operating five tokamaks under the auspices of a single Task Force called ‘Tokamak Exploitation’. The goal is to benefit from the complementary capabilities of each machine in a coordinated way and help in developing a scientific output scalable to future largre machines. The programme of this Task Force ensures that ASDEX Upgrade, MAST-U, TCV, WEST and JET (since 2022) work together to achieve the objectives of Missions 1 and 2 of the EUROfusion Roadmap: i) demonstrate plasma scenarios that increase the success margin of ITER and satisfy the requirements of DEMO and, ii) demonstrate an integrated approach that can handle the large power leaving ITER and DEMO plasmas. The Tokamak Exploitation task force has therefore organized experiments on these two missions with the goal to strengthen the physics and operational basis for the ITER baseline scenario and for exploiting the recent plasma exhaust enhancements in all four devices (PEX: Plasma EXhaust) for exploring the solution for handling heat and particle exhaust in ITER and develop the conceptual solutions for DEMO. The ITER Baseline scenario has been developed in a similar way in ASDEX Upgrade, TCV and JET. Key risks for ITER such as disruptions and run-aways have been also investigated in TCV, ASDEX Upgrade and JET. Experiments have explored successfully different divertor configurations (standard, super-X, snowflakes) in MAST-U and TCV and studied tungsten melting in WEST and ASDEX Upgrade. The input from the smaller devices to JET has also been proven successful to set-up novel control schemes on disruption avoidance and detachment.

Reactor relevant fusion devices will use tungsten (W) for their plasma facing components (PFCs) due to its thermomechanical properties and low tritium retention. However, W introduces high-Z impurities into the plasma, degrading its performance. Different wall conditioning methods have been developed to address this issue, including coating of W PFCs with layers of low-Z material. Wall conditioning by boron (B) powder injection using an impurity powder dropper (IPD) is being studied in WEST. Two series of experiments were conducted since the installation of the new ITER grade full W divertor. During the first series in 2023 similar to 1 g of B powder was injected in total at a maximum rate of similar to 58 mg/s, both of which are three times greater than respective values in the initial WEST powder injection experiments. The second series of experiments included injection of B and BN powders for comparison of their effects on plasma performance. The presence of an instantaneous conditioning effect is suggested by visible spectroscopy measurements of low-Z impurity lines and a rollover of total radiated power past an injection rate of similar to 20 mg/s was observed. Presence of B coating layer formation is supported by the evolution of the average radiance of visible lines of B, W and oxygen (O). To understand B transport, an interpretative modeling workflow is employed, utilizing the SOLEDGE-EIRENE fluid boundary plasma code and the Dust Injection Simulator (DIS) code. Parameters like B perpendicular diffusivity and recycling coefficients are varied to match experimental results to see if the initial assumption of B sticking to the PFCs immediately after the contact with the wall is adequate for correctly modelling its distribution on the PFCs.

Boundary plasma simulations are essential to estimate expected divertor and first wall (FW) heat and particle loads on ITER during burning plasma operation. A key missing feature of existing SOLPS simulations (Pitts et al., 2019) is the absence of a plasma solution out to the main chamber walls, essential to self-consistently estimate the gross sputtering of wall material. Here, SOLEDGE3X is applied for the first time to obtain up-to-the wall burning plasma solutions of the ITER boundary plasma at the nominal PSOL = 100 MW of the main SOLPS database simulations, including He ash, Ne seeding but without fluid drifts. Compared with the most recent SOLPS-ITER simulations, our simulations show differences in the exact impurity distribution, but the key results for divertor and wall heat flux remain consistent. In the context of the ITER re-baselining exercise (Pitts, 2024), in which the Be FW armour is proposed to be exchanged for tungsten (W), estimates of W wall sources are key to the assessment of likely core contamination and hence impact on fusion gain. We compare the W gross erosion rates due to the different species excluding W self-sputtering. For the cases simulated spanning 0.27%–0.47% separatrix-averaged Ne concentration and 7.5×1022s−1−1.95×1023s−1 D fuelling, Ne8+ remains the largest contributor to the sputtering flux with the largest source being the outer divertor and baffle. The species-wise contribution to W sputtering changes with fuelling with sputtering due to lower Ne charge states being significant at low D fuelling. In general, the gross W sputtering source is found to decrease with increase in D fuelling and increase with increased Ne seeding.

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.

This work explores the Limiter–Divertor transition (L–D) during the current ramp-up of ITER’s Q = 10 baseline plasma scenario at various central line-integrated density nli values. The analysis, based on transport simulations performed with the latest version of SoleEdge-HDG, focuses on the time evolution of heat and ion particle fluxes, revealing regions of elevated temperature on the inner wall and plasma-facing components (PFCs) despite moderate loads. The investigation also delves into the effects of perpendicular convection flux terms on density build-up, comparing different formulations and their interplay with auxiliary heating sources. Furthermore, the paper shows the impact of taking into account the evolution of the parallel neutral momentum on plasma and neutral density at the targets in the context of an ITER steady-state scenario.

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.

Corrigendum for the manuscript (Raghunathan et al 2022 Plasma Phys. Control. Fusion 64 045005).

Plasma discharges in the tungsten (W) Environment Steady-state Tokamak (WEST) are strongly impacted by W contamination. In WEST experiments, due to W contamination, the power radiated in the plasma ( P _Rad ) is on average, around 50% of the total power injected into the plasma ( P _TOT ). Furthermore, this radiated power fraction ( f _Rad ) is almost insensitive to plasma conditions. The causes behind this experimental trend are not fully understood. In this contribution, a 3D numerical model is used to analyze the W migration in the WEST boundary plasma in different plasma scenarios. The WEST experimental database is sampled to obtain a scan of simulation input parameters. These parameters mimic the WEST plasma conditions over a chosen experimental campaign. The simulation results are compared to WEST diagnostics measurements (reflectometry, Langmuir probes, and visible spectroscopy) to verify that the simulated plasma conditions are representative of the WEST database. The W contamination trend is analyzed: the W density ( n _W ) strongly decreases when the radial distance between the separatrix and WEST antennas (Radial Outer Gap, ROG) increases. On the other hand, at a given ROG, n _W increases proportionally with the power entering the scrape-off layer ( P _SOL ). P _Rad is estimated with a simple 0D model. For a fixed ROG, f _Rad is not sensitive to plasma conditions. These trends are qualitatively and, at times, quantitatively comparable to what is observed in WEST experiments: the simulated trends are related to the poorly screened W influx caused by the erosion of the main chamber Plasma-Facing Components. Thus, this numerical analysis suggests a possible interpretation of WEST experimental trends.