Edge-localized modes (ELMs) eject intense bursts of heat and particles that threaten plasma-facing components in fusion reactors. Nonlinear full-torus BOUT++ simulations show that turbulence-driven zonal magnetic fields (ZMFs) play an essential role in nonlinear ELM evolution by maintaining self-consistent force balance. Zonal flows mitigate the initial crash through shear but do not prevent continued radial transport. When ZMFs are self-consistently included, turbulence-driven zonal currents modify the parallel current distribution and magnetic tension and are associated with a reduction of the axisymmetric (n=0) perturbed radial force imbalance. This coincides with a transition from convective, bursty propagation to more localized, diffusive transport. Similar behavior is observed across the regimes considered, including both resistive-ballooning and peeling-ballooning cases. Associated signatures, including radial electric field shear and parallel current redistribution, provide experimentally accessible diagnostics for present devices and ITER-relevant conditions.

Simulating magnetically confined fusion plasmas presents a uniquely challenging problem due to the nonlinear anisotropic heat conduction. We introduce the MAPS (MFEM Anisotropic Plasma Solver) tool, which uses a high-order finite element method to compute transport solutions on unstructured meshes. We show results for a set of three 2-D verification tests, two of which demonstrate the expected convergence properties for various mesh resolutions and polynomial degrees. We then discuss the convergence rate for the third test.

This paper presents a comprehensive overview of the preliminary divertor design and plasma exhaust scenario for the reactor-class Spherical Tokamak for Energy Production project. Due to the smaller size of the machine, with a major radius less than half that of most DEMO concepts, the current design features a double-null divertor geometry, comprising tightly baffled extended outer legs and shorter inner legs approaching an X-divertor. Leveraging a significant database of SOLPS-ITER simulations, the exhaust operational space is mapped out, offering valuable insights into the plasma exhaust dynamics. An approach involving the validation of simple, yet robust models capable of accurately predicting key exhaust parameters is detailed, thereby streamlining the design process. The simple models are used to simulate the entire plasma scenario from the plasma current ramp-up, through the burning phase, to the plasma current ramp-down. Notably, the findings suggest that pronounced detachment, with peak heat loads below engineering limits and electron temperatures below 5 eV, is achievable with a divertor neutral pressure between 10 Pa and 15 Pa during the burning phase, and pressures below 5 Pa during the ramp-up to maximise the auxiliary current-drive efficiency. Throughout the scenario, an Ar concentration of approximate to 3% in the scrape-off layer (SOL) is required, in combination with a core radiation fraction of 70% driven by intrinsic emission and extrinsic injection of Xe seeded fuelling pellets. However, significant uncertainties remain regarding key parameters such as the SOL heat flux width, Ar screening, and plasma kinetic effects.

Isothermal fluid turbulence simulations have been performed in the edge and scrape-off layer (SOL) of an analytic stellarator configuration with an island divertor, thereby providing numerical insight into edge turbulence in regions around islands in a stellarator. The steady-state transport follows the a curvature drive that is inverse to the major radius ( $1/R$ ) toward the outboard side, but large fluctuations are present throughout the island divertor region, with the average wavelength of similar size to the island width. The system exhibits a prominent $m=2$ , $n=5$ mode, where m is the poloidal mode number and n is the toroidal mode number, although other modes are present. The amplitude and radial extent of the density fluctuations are similar throughout the edge and SOL, but can decrease near island O-points. The fluctuations exhibit a predominantly positive skewness on the outboard midplane, indicating blob-like perturbations for the transport into the outer SOL. It is determined that a point on the separatrix is generally more correlated with regions outside of the SOL than a nearby reference point which does not lie on the separatrix.

Isothermal fluid turbulence simulations have been performed in the edge and scrape-off-layer (SOL) of an analytic stellarator configuration with an island divertor, thereby providing numerical insight into edge turbulence in regions around islands in a stellarator. The steady-state transport follows the 1/R curvature drive toward the outboard side, but large fluctuations are present throughout the island divertor region, with the average wavelength of similar size to the island width. The system exhibits a prominent m=2, n=5 mode, although other modes are present. The amplitude and radial extent of the density fluctuations are similar throughout the edge and SOL, but can decrease near island O-points. The fluctuations exhibit a predominantly positive skewness on the outboard midplane, indicating blob-like perturbations for the transport into the outer SOL. It is determined that a point on the separatrix is generally more correlated with regions outside of the SOL than a nearby reference point which does not lie on the separatrix.

A new open source tool for fluid simulation of multi-component plasmas is presented, based on a flexible software design that is applicable to scientific simulations in a wide range of fields. This design enables the same code to be configured at run-time to solve systems of partial differential equations in 1D, 2D or 3D, either for transport (steady-state) or turbulent (time-evolving) problems, with an arbitrary number of ion and neutral species. To demonstrate the capabilities of this tool, applications relevant to the boundary of tokamak plasmas are presented: 1D simulations of diveror plasmas evolving equations for all charge states of neon and deuterium; 2D transport simulations of tokamak equilibria in single-null X-point geometry with plasma ion and neutral atom species; and simulations of the time-dependent propagation of plasma filaments (blobs). Hermes-3 is publicly available on Github under the GPL-3 open source license. The repository includes documentation and a suite of unit, integrated and convergence tests.

Future tokamak devices that aim to create conditions relevant to power plant operations must consider strategies for mitigating damage to plasma facing components in the divertor. One of the goals of MAST-U tokamak operations is to inform these considerations by researching advanced divertor configurations that aid stable plasma detachment. Machine design, scenario planning and detachment control would all greatly benefit from tools that enable rapid calculation of scenario-relevant quantities given some input parameters. This paper presents a method for generating large, simulated scrape-off layer data sets, which was applied to generate a data set of steady-state Hermes-3 simulations of the MAST-U tokamak. A machine learning model was constructed using a Bayesian approach to hyperparameter optimisation to predict diagnosable output quantities given control-relevant input features. The resulting best-performing model, which is based on a feedforward neural network, achieves high accuracy when predicting electron temperature at the divertor target and carbon impurity radiation front position and runs in around 1 ms in inference mode. Techniques for interpreting the predictions made by the model were applied, and a high-resolution parameter scan of upstream conditions was performed to demonstrate the utility of rapidly generating accurate predictions using the emulator. This work represents a step forward in the design of machine learning-driven emulators of tokamak exhaust simulation codes in operational modes relevant to divertor detachment control and plasma scenario design.

We report a two-stage crash process in edge localized mode (ELM) driven by resistive drift-ballooning modes (RDBMs) numerically simulated in a full annular torus domain. In the early nonlinear phase, the first crash is triggered by linearly unstable RDBMs and m/n = 2/1 magnetic islands are nonlinearly excited via nonlinear couplings of RDBMs. Simultaneously, middle-n RDBM turbulence develops but is poloidally localized around X-points of the magnetic islands, leading to the small energy loss. Here m is the poloidal mode number, n is the toroidal mode number, the q = 2 rational surface exists at the pressure gradient peak, and q is the safety factor, respectively. The second crash occurs in the late nonlinear phase. Low-n magnetic islands are also excited around the q = 2 surface via nonlinear couplings among the middle-n turbulence. Since the turbulence develops from the X-points of higher harmonics of m/n = 2/1 magnetic islands, it expands out poloidally. The second crash is triggered when the turbulence covers the whole poloidal region. A scan of toroidal wedge number N, where full torus is divided into N segments in the toroidal direction, also reveals that the first crash process becomes more prominent with the higher toroidal wedge number where the RDBMs play a dominant role. These results indicate that nonlinear interactions of all channels in the full torus domain can significantly affect the trigger dynamics of ELMs driven by the RDBMs.

We propose to build a Flexible Stellarator Physics Facility to explore promising regions of the vast parameter space of disruption-free stellarator solutions for Fusion Pilot Plants (FPPs).

Fusion power plants will require detachment to mitigate sputtering and keep divertor heat fluxes at tolerable levels. Controlling detachment on these devices may require the use of real-time scrape-off-layer modeling to complement the limited set of available diagnostics. In this work, we use the configurable Hermes-3 edge modeling framework to perform time-dependent, fixed-fraction-impurity 1D detachment simulations. Although currently far from real-time, these simulations are used to investigate time-dependent effects and the minimum physics set required for control-relevant modeling. We show that these simulations reproduce the expected rollover of the target ion flux — a typical characteristic of detachment onset. We also perform scans of the input heat flux and impurity concentration and show that the steady-state results closely match the scalings predicted by the 0D time-independent Lengyel-Goedheer model. This allows us to indirectly compare to SOLPS simulations, which find a similar scaling but a lower value for the impurity concentration required for detachment for given upstream conditions. We use this result to suggest a series of improvements for the Hermes simulations, and finally show simulations demonstrating the impact of time-dependence.

The SOLPS-ITER code has been utilised to study the movement of the detachment front location from target towards the X-point for MAST-U Super-X plasmas. Two sets of detached steady state solutions are obtained by either varying the deuterium ( D 2 ) fuelling rate or the nitrogen ( N ) seeding rate to scan the corresponding ‘control’ parameters of outboard midplane density, n u , and the divertor impurity concentration, f I . At seeding and fuelling rates ∼10× and ∼5× that required to start detachment at the divertor target, the detachment front only reaches ∼50% of the poloidal distance to the X-point, l p o l , corresponding to a region of strong parallel gradients in the total magnetic field B . The region of strong total field gradients correlates with where the detachment front location becomes less sensitive to control parameter variation. This result is qualitatively consistent with the predictions of a simple, analytic detachment location sensitivity (DLS) model (Lipschultz et al 2016 Nucl. Fusion 56 056007) which is based in a scaled parallel-to- B space, z . While the DLS model predictions are in agreement with SOLPS-ITER results in terms of where the front location becomes less sensitive to controls (i.e. in the region of strong parallel gradients in B ), the DLS model predicts a higher sensitivity in the region of weak parallel gradients in B downstream as compared to the simulation results. Potential sources of differences between the SOLPS-ITER and DLS model predictions were explored: The DLS model does not include energy sinks beyond radiation from a single impurity nor cross-field energy transport. Momentum and particle balance are also not included in the DLS model. The tight opening into the divertor for flux surfaces could lead to variations in plasma-neutral pressure balance as the detachment front reaches that region, exactly how this affects the front movement needs further investigation.

For tokamak edge plasma simulation, a plasma simulation framework BOUT++ employs a dual coordinate system to simulate moderate- n and high- n plasma instability with reasonable computational cost, where n is the toroidal mode number. This coordinate system however limits the computational domain to the toroidal wedge (full torus divided into N parts in the toroidal direction) for computational efficiency and the use of flute-ordering approximation in the field solver calculating the flow potential from the vorticity which may not be valid for low- n modes. Improving numerical treatment of low- n modes is however indispensable to address simulations of low- n current-driven edge localized mode (ELM), ELM control by resonant magnetic perturbations (RMPs), edge turbulence with RMPs and so on. In this work, BOUT++ is extended to simulate the interplay between n = 0 , low- n and high- n plasma components in a full annular tokamak edge domain through hybrid modeling of the flow potential and the vorticity. Low- n modes of flow potential are calculated in an orthogonal flux surface coordinate and high- n modes in the dual coordinate system separately in Fourier space. The proposed scheme can capture an interplay between n = 1 global modes and high- n turbulence during pedestal collapse in a full annular torus domain with a circular cross section.

The role of ion-molecule ( D + − D 2 ) elastic collisions in strongly detached divertor conditions has been studied in the MAST-U Super-X configuration using SOLPS-ITER. Two strongly detached steady state solutions were compared, one obtained through a main-ion fuelling scan and the other through a nitrogen seeding scan at fixed fuelling rate. A significant difference in the electron–ion recombination (EIR) levels was observed; significant EIR in strongly detached conditions in the fuelling scan and negligible EIR throughout the seeding scan. This is partly because the fuelling scan achieves electron temperatures ( T e ) as low as 0.2 eV near the divertor target, compared to 0.8 eV in the seeding scan (EIR increases strongly below T e ≈ 1 eV), and partly due to higher divertor plasma densities achieved in fuelling scan. Features of the strongly detached seeded cases, i.e. higher temperatures and negligible EIR, are recovered in the fuelling scan by turning off D + − D 2 elastic collisions. Analysis suggests that dissipation mechanisms like line radiation and charge exchange (important for detachment initiation) become weak when T e falls below 1 eV, and that D + − D 2 elastic collisions are necessary for further heat dissipation and access to strongly recombining conditions in the fuelling scan. In the seeding scan, heat dissipation through D + − D 2 elastic collisions is weak. This could be because our nitrogen seeding simulations do not include interactions between nitrogen ions and neutrals, and the strongly detached cases contain high levels of N + in the divertor. As a result, the N + acts like a reservoir of energy and momentum which appears to weaken the impact of D + − D 2 elastic collisions on the divertor plasma energy and momentum balance, making it more difficult to access recombining conditions. This suggests that some of the differences between seeding and fuelling scans could be because energy and momentum exchange between impurities and neutrals is not sufficiently captured in our simulations.