Benjamin Dudson

Alternative Divertor Configurations (ADCs) often make use of high total flux expansion ( f R ) and connection length ( L ∥ ) to improve the access to and the controllability of detachment, a regime vitally important for reactor-class tokamaks such as the Spherical Tokamak for Energy Production (STEP). Achieving detachment on such high-power devices is enabled through radiation from seeded impurity species such as argon and neon, which can lead to radiative losses throughout the flux tube, altering the impact of magnetic geometry on detachment. The detachment location sensitivity (DLS) model analytically predicts detachment access and sensitivity based on upstream conditions, the magnetic geometry and seeded impurity radiation. It assumes the radiation region to have no spatial extent. In this work, we relax this assumption and introduce DLS-Extended, a new reduced 1D model which can capture the effects of the spatial distribution of impurity radiation along the field line. The prediction of radiation extent was verified against SOLPS-ITER simulations of an initial STEP design with a good match. DLS-Extended predicts that the radiation extent found in STEP weakens the detachment access benefit of f R and strengthens the benefit of L ∥ , while the detachment stability of the inner and outer legs is increased and decreased, respectively. This is due to a number of novel radiation-driven effects and has implications for the optimum strike point position in reactor-scale devices. These findings highlight the need for more experimental studies in the presence of broad-radiating impurities. DLS-Extended is distributed under the LGPL-3 open source license and is publicly available on GitHub.

We have investigated the response of detached plasmas to multi-ms timescale power transients using 1D simulations of the scrape-off layer on a scale and parameter range relevant for reactor-scale tokamaks, such as the Spherical Tokamak for Energy Production (STEP). Simulations were performed using the fluid code Hermes-3, employing the solver CVODE for robust time integration. Including or disregarding the momentum received by the neutral gas via charge exchange reactions in simulations is found to dramatically affect the detachment front’s response. In the analysis, motion of the ionisation front of a detached plasma is determined by two distinct mechanisms; a fast initial pressure-dominated response as the neutral cloud is rapidly compressed, and a slow burn-through dominated one as the cloud is ionised. The former is only observed if the momentum transfer to neutrals is kept. With transfer of momentum to the neutrals disabled, the plasma only interacts with the neutrals through ionisation and recombination. Thus, the front speed during the transient is determined by the rate of burn-through of the neutrals only. Simulations are compared to a recent semi-empirical reattachment model (Henderson et al 2024 Nucl. Fusion 64 066006), where the best qualitative agreement is seen for cases without neutral momentum and for power rises of ∼ 2 × their baseline power. The difference in these agreements are encompassed by the range of potential fits provided by model parameter choice.

Understanding parallel thermal transport in the scrape-off layer (SOL) is crucial for designing future high-powered tokamak exhaust systems. Fluid models, whilst computationally efficient, cannot accurately predict heat flux in conditions with large temperature gradients or low upstream collisionality. Here the electron mean free path becomes large and so the heat transport is non-local. The impact of non-local electron thermal transport on key detachment processes is often overlooked. The Hermes-3 multi-fluid SOL code is applied to a medium collisionality ( S _|| /λ _e ≈ 25 upstream) ITER-like scenario in 1D, comparing non-local (SNB), to classical Spitzer-H¨arm (SH) as well as flux-limited (FL) electron conduction models. A neon fixed-fraction impurity seeding model is applied at increasing percentage until detachment is observed. Competing behaviour between FL and impurity seeding on target temperatures is observed, whilst the SNB model agrees qualitatively with SH, showing earlier detachment onset compared to FL (at∼ 1% lower neon fraction). This motivates the inclusion of non-local thermal conduction models (such as the SNB model) in fluid detachment modelling of SOL plasmas.

Electrostatic flux-driven turbulence simulations with the Hermes-3 code are performed in TCV L-mode conditions in forward and reversed toroidal field configurations, and compared to the TCV-X21 reference dataset (Oliveira et al 2022 Nucl. Fusion 62 096001) qualitatively and with a quantitative methodology. Using only the magnetic equilibrium, total power across the separatrix (120 kW) and total particle flux to the targets ( 3 × 10 21 s ⁻¹ ) as inputs, the simulations produce time-averaged plasma profiles in good agreement with experiment. Shifts in the target peak location when the toroidal field direction is reversed are reproduced in simulation, including the experimentally observed splitting of the outer strike point into two density peaks. The overall normalized discrepancy between simulation and observation is better than any previously reported in the reversed field configuration, and matches the best previously reported in forward field configuration. Differences between simulation and experiment include density profiles inside the separatrix and at the inner target in forward (favorable ∇ B ) field configuration. These differences in target temperature in forward field configuration lead to differences in the balance of current to the inner and outer divertor in the private flux region. The cause of these differences is most likely the lack of neutral gas in these simulations, indicating that even in low recycling regimes neutral gas plays an important role in determining edge plasma profiles. These conclusions are consistent with findings in Oliveira et al (2022 https://github.com/SPCData/TCV-X21 ).

The critical task of inferring anomalous cross-field transport coefficients is addressed in simulations of boundary plasmas with fluid models. A workflow for parameter inference in the UEDGE fluid code is developed using Bayesian optimization with parallelized sampling and integrated uncertainty quantification. In this workflow, transport coefficients are inferred by maximizing their posterior probability distribution, which is generally multidimensional and non-Gaussian. Uncertainty quantification is integrated throughout the optimization within the Bayesian framework that combines diagnostic uncertainties and model limitations. As a concrete example, we infer the anomalous electron thermal diffusivity χ ⊥ from an interpretive 2D model describing electron heat transport in the conduction-limited region with radiative power loss. The workflow is first benchmarked against synthetic data and then tested on H-, L-, and I-mode discharges to match their midplane temperature and divertor heat flux profiles. We demonstrate that the workflow efficiently infers diffusivity and its associated uncertainty, generating 2D profiles that match 1D measurements. Future efforts will focus on incorporating more complicated fluid models and analyzing transport coefficients inferred from a large database of experimental results.

A new self-consistent 1D scrape-off layer model has been recently developed in BOUT++ framework, named SD1D, which includes equations for various particle species (e.g. main plasma, neutrals and impurities) and couples open databases like ADAS and AMJUEL. It is able to quickly and effectively simulate divertor detachment experiments. In this work, a typical detachment experiment (shot #6270) on HL-3 with neon seeding is simulated using the SD1D code. It is found that the target electron temperature and the target ion saturation current in the simulations are consistent with experimental results measured by Langmuir probes on the target plate. The variation of D α radiation intensity in the divertor is qualitatively similar to the measured D α signal. Following the experimental validations, different upstream densities are set in the simulations to study the impurity distribution under different plasma density conditions. It is found that increasing upstream density can be helpful for the control of the neon radiation front (closer to the target). In this work we also compare two detachment regimes in simulations. Based on the same initial experimental parameters (shot #6270) on HL-3, a scan of upstream density and a scan of neon seeding rate are carried out respectively. It is found that the role of atomic and molecular processes is different in the two detachment regimes. The current density roll-over is ascribed to a drop in the divertor ion source, and the variation of D α radiation intensity via different excitation channels is associated with the relevant collisional reaction sources.

This white paper contributes input from the Executive Committee of the Theory Coordinating Committee to the 2024 FESAC Decadal Plan Subcommittee. It is argued that the public Theory and Modeling program plays a critical role in the pursuit of commercial fusion energy. A new mechanism for fostering engagement between the fusion industry and the public Theory and Modeling program could provide better alignment between the goals of the public program and the needs of private industry.

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 with a scale-separated four-field reduced MHD (RMHD) model using the BOUT++ framework. In the early nonlinear phase, the small first crash is triggered by linearly unstable RDBMs, and m/n=2/1 magnetic islands are nonlinearly excited by nonlinear coupling of RDBMs as well as their higher harmonics. Here, m is the poloidal mode number, n is the toroidal mode number, the q = 2 rational surface exists near the pressure gradient peak, and q is the safety factor. Simultaneously, middle-n RDBM turbulence develops but is poloidally localized around X-points of the magnetic islands, leading to the small energy loss. The second large crash occurs in the late nonlinear phase. Higher harmonics of m/n=2/1 magnetic islands well develop around the q = 2 surface via nonlinear coupling and make the magnetic field stochastic by magnetic island overlapping. Turbulence heat transport develops at X-points of higher harmonics of m/n=2/1 magnetic islands, resulting in the turbulence spreading in the poloidal direction. The large second crash is triggered when the turbulence covers the whole poloidal region so that the magnetic island generation and magnetic field stochastization before the large crash can be interpreted as ELM precursors. It is concluded that the ELM trigger is attributed to the turbulent spreading in the poloidal direction in synchronization with the magnetic field stochastization and the crash is driven by E × B convection rather than the conventional Rechester–Rosenbluth anomalous electron heat transport.