Evaluation of SPARC divertor conditions in H-mode operation using SOLPS-ITER

Modeling of carbon transport in the divertor and SOL of DIII-D during high performance plasma operation

Divertor geometry modeling with the SOLPS-ITER code for reactor concepts with liquid metal divertors

Inferring the scrape-off layer heat flux width in a divertor with a low degree of axisymmetry

The physics of parallel heat transport was tested in the scrape-off layer (SOL) plasma of the National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 40, 557 (2000); S. M. Kaye et al., Nucl. Fusion 45, S168 (2005)] tokamak by comparing the upstream electron temperature (Te) and density (ne) profiles measured by the midplane reciprocating probe to the heat flux (q⊥) profile at the divertor plate measured by an infrared camera. It is found that electron conduction explains the near SOL width data reasonably well while the far SOL, which is in the sheath limited regime, requires an ion heat flux profile broader than the electron one to be consistent with the experimental data. The measured plasma parameters indicate that the SOL energy transport should be in the conduction-limited regime for R−Rsep (radial distance from the separatrix location) <2–3cm. The SOL energy transport should transition to the sheath-limited regime for R−Rsep>2–3cm. The Te, ne, and q⊥ profiles are better described by an offset exponential function instead of a simple exponential. The conventional relation between midplane electron temperature decay length (λTe) and target heat flux decay length (λq) is λTe=7∕2λq, whereas the newly derived relation, assuming offset exponential functional forms, implies λTe=(2–2.5)λq. The measured values of λTe∕λq differ from the new prediction by 25%–30%. The measured λq values in the far SOL (R−Rsep>2–3cm) are 9–10cm, while the expected values are 2.7<λq<4.9cm (for the sheath-limited regime). We propose that the ion heat flux profile is substantially broader than the electron heat flux profile as an explanation for this discrepancy in the far SOL.

Experiments performed during strongly-shaped high-power diverted negative triangularity (NT) experiments in DIII-D achieved detached divertor conditions and a transient-free edge, showcasing the potential for application of NT to a core-edge integrated reactor-like scenario and providing the first characterization of the parametric dependencies for detachment onset. Detached divertor conditions will be required in future devices to mitigate divertor heat fluxes. Access to dissipative divertor conditions was investigated via an increase in upstream density. Detachment onset at the outer strike point was achieved with H-mode level confinement H98−y2∼1 and reactor-relevant normalized pressures βN∼2 . Confinement degradation was observed with deeper detachment, associated with the loss of an electron temperature pedestal. Differences in geometry, radial transport, impact of cross field drifts are discussed to explain differences in access to detachment in NT discharges. Higher normalized densities, with respect to equivalent discharges in positive triangularity, were necessary to achieve detachment, partially explained by the shorter parallel connection length to the targets. The effect of cross-field particle drifts (E×B, B ×∇ B) on access to detachment was demonstrated by the lower upstream density needed to access detachment with ion B ×∇ B drift directed outside of the active divertor (Greenwald fraction fGw∼ 0.9–1.0 vs fGw∼ 1.3). The upstream density at detachment onset was observed to increase linearly with plasma current with ion B ×∇ B drift into the divertor, consistent with the observed narrowing of the scrape-off layer heat flux width λ q . Edge fluid simulations capture separatrix densities needed to achieve detachment in NT plasma and their dependence on drift direction. The ability to reproduce detachment dynamics in NT plasma increases the confidence in future design studies for NT divertors.

The BOUT + + code has been used to simulate edge plasma electromagnetic (EM) turbulence and transport, and to study the role of EM turbulence in setting the scrape-off layer (SOL) heat flux width λq. More than a dozen tokamak discharges from C-Mod, DIII-D, EAST, ITER and CFETR have been simulated with encouraging success. The parallel electron heat fluxes onto the target from the BOUT + + simulations of C-Mod, DIII-D, and EAST follow the experimental heat flux width scaling of the inverse dependence on the poloidal magnetic field. Further turbulence statistics analysis shows that the blobs are generated near the pedestal pressure peak gradient region inside the separatrix and contribute to the transport of the particle and heat in the SOL region. Transport simulations indicate two distinct regimes: drift dominant regime and turbulence dominant regime. Goldston's heuristic drift-based (HD) model yields a consistent divertor heat flux width in the drift dominant regime. For C-Mod enhanced Dα H-mode discharges, drifts and turbulence are competing in setting the divertor heat flux width, possibly due to its compact machine size and good pedestal confinement.The simulations for ITER and CFETR indicate that divertor heat flux width λq of the future machines may no longer follows the 1/Bpol,OMP HD-based empirical (Eich) scalings and the HD model gives a pessimistic limit of divertor heat flux width. The simulation results show a transition from a drift dominant regime to a turbulence dominant regime from current machines to future machines such as ITER and CFETR for two reasons. (1) The magnetic drift-based radial transport decreases due to large CFETR and ITER machine sizes. (2) The SOL turbulence thermal diffusivity increases due to larger turbulent fluxes ejected from the pedestal into the SOL when operating in a different pedestal structure, from an ELM-free H-mode pedestal regime to a small and grassy ELM regime.

Nitrogen (N2) gas was injected into the helium (He) plasma with a LaB6 cathode as an impurity to observe the variations of heat flux and the SOL heat flux width in the Divertor Plasma Simulator-2 (DiPS-2) device. The injection rate of N2 impurities was varied from 2.5% to 30% with a constant neutral pressure (~9 mTorr). To evaluate the plasma heat flux to a tungsten target, three diagnostic methods were used: (1) three thermocouples (TCs) were installed within the tungsten target to estimate the inner temperature of the tungsten, (2) an infrared (IR) camera detected the surface temperature of the tungsten; (3) a triple (electric) probe (TP) was used to determine the electron temperature (Te), plasma density (n0), and heat flux (q) of He plasma. With 30% N2 injection, a 20% decrease in Te and a 60% decrease in n0 were observed at the center of the plasma. The target temperature and heat flux also decreased with N2 seeding rate. The heat fluxes to the tungsten target deduced from the IR and TC methods produce higher values than those of the TP. The width of the heat flux transported from the main plasma to the scrape-off layer (SOL) heat flux width (λq) decreases with the impurity ratio; hence, the heat flux to the tungsten target.

Dependence of divertor heat flux widths on heating power, flux expansion, and plasma current in the NSTX

Empirical scalings of cross-field heat diffusivities in the scrape-off layer of Alcator C-Mod from a 2-D interpretive model

Reduced model simulations of turbulence in the edge and scrape-off-layer (SOL) region of a spherical torus or tokamak plasma are employed to address the physics of the scrape-off-layer heat-flux width. The simulation model is an electrostatic two-dimensional fluid turbulence model, applied in the plane perpendicular to the magnetic field at the outboard midplane of the torus. The model contains curvature-driven-interchange modes, sheath losses, and both perpendicular turbulent diffusive and convective (blob) transport. These transport processes compete with classical parallel transport to set the SOL width. Midplane SOL profiles of density, temperature, and parallel heat flux are obtained from the simulation and compared with experimental results from the National Spherical Torus Experiment [S. M. Kaye et al., Phys. Plasmas 8, 1977 (2001)] to study the scaling of the heat-flux width with power and plasma current. It is concluded that midplane turbulence is the main contributor to the SOL heat-flux width for the low power H-mode discharges studied, while additional physics is required to fully explain the plasma current scaling of the SOL heat-flux width observed experimentally in higher power discharges. Intermittent separatrix-spanning convective cells are found to be the main mechanism that sets the near-SOL width in the simulations. The roles of sheared flows and blob trapping versus emission are discussed.

Introduction of cross-field drifts in SOLPS-ITER simulations of connected double-null plasmas in STEP with the ion ∇B×B drift towards the upper divertors was found to enhance the detachment of the inner divertors with decreased target densities and ion and heat fluxes, while simultaneously complicating the access to detachment in the outer lower divertor by increasing the target temperature and heat loads to levels above the engineering limits. The ∇B×B drift was observed to significantly affect the radial heat transport between the core and the scrape-off layer (SOL), altering the poloidal temperature and pressure profiles and, consequently, the poloidal conductive and convective heat transport in the SOL. As a result, up-down asymmetries of 52:48 and 58:42 biased towards the outer lower and upper inner divertors, respectively, were observed to arise in the unmitigated power entering the divertor regions, breaking the up-down symmetry seen in simulations without the drift terms and contradicting with earlier experimental observations on the low-field side. Moreover, the upstream electron density was found to decrease noticeably in the core and separatrix regions following the activation of the drifts due to an increased share of the neutrals arriving from D2 injections near the upper and lower X-points ionizing already in the private flux regions.

The heat flux distributions on divertor targets in H-mode plasmas are serious concerns for future devices. We seek to simulate the tokamak boundary plasma turbulence and heat transport in the edge localized mode-suppressed regimes. The improved BOUT++ model shows that not only Ip but also the radial electric field Er plays an important role on the turbulence behavior and sets the heat flux width. Instead of calculating Er from the pressure gradient term (diamagnetic Er), it is calculated from the plasma transport equations with the sheath potential in the scrape-off layer and the plasma density and temperature profiles inside the separatrix from the experiment. The simulation results with the new Er model have better agreement with the experiment than using the diamagnetic Er model: (1) The electromagnetic turbulence in enhanced Dα H-mode shows the characteristics of quasi-coherent modes (QCMs) and broadband turbulence. The mode spectra are in agreement with the phase contrast imaging data and almost has no change in comparison to the cases which use the diamagnetic Er model; (2) the self-consistent boundary Er is needed for the turbulence simulations to get the consistent heat flux width with the experiment; (3) the frequencies of the QCMs are proportional to Er, while the divertor heat flux widths are inversely proportional to Er; and (4) the BOUT++ turbulence simulations yield a similar heat flux width to the experimental Eich scaling law and the prediction from the Goldston heuristic drift model.

Radiative divertor operation in JET high confinement mode plasmas with the ITER-like wall has been experimentally investigated and simulated with EDGE2D-EIRENE in horizontal and vertical low field side (LFS) divertor configurations. The simulations show that the LFS divertor heat fluxes are reduced with N2-injection in similar fashion in both configurations, qualitatively consistent with experimental observations. The simulations show no substantial difference between the two configurations in the reduction of the peak LFS heat flux as a function of divertor radiation, nitrogen concentration, or pedestal Zeff. Consistently, experiments show similar divertor radiation and nitrogen injection levels for similar LFS peak heat flux reduction in both configurations. Nevertheless, the LFS strike point is predicted to detach at 20% lower separatrix density in the vertical than in the horizontal configuration. However, since the peak LFS heat flux in partial detachment in the vertical configurations is shifted towards the far scrape-off layer (SOL), the simulations predict no benefit in the reduction of LFS peak heat flux for a given upstream density in the vertical configuration relative to a horizontal one. A factor of 2 reduction of deuterium ionization source inside the separatrix is observed in the simulations when changing to the vertical configuration. The simulations capture the experimentally observed particle and heat flux reduction at the LFS divertor plate in both configurations, when adjusting the impurity injection rate to reproduce the measured divertor radiation. However, the divertor Dα-emissions are underestimated by a factor of 2–5, indicating a short-fall in radiation by the fuel species. In the vertical configuration, detachment is experimentally measured and predicted to start next to the strike point, extending towards the far SOL with increasing degree of detachment. In contrast, in the horizontal configuration, the entire divertor particle flux profile is reduced uniformly with increasing degree of detachment.

Understanding the responsible mechanisms and resulting scaling of the scrape-off layer (SOL) heat flux width is important for predicting viable operating regimes in future tokamaks and for seeking possible mitigation schemes. In this paper, we present a qualitative and conceptual framework for understanding various regimes of edge/SOL turbulence and the role of turbulent transport as the mechanism for establishing the SOL heat flux width. Relevant considerations include the type and spectral characteristics of underlying instabilities, the location of the gradient drive relative to the SOL, the nonlinear saturation mechanism, and the parallel heat transport regime. We find a heat flux width scaling with major radius R that is generally positive, consistent with the previous findings [Connor et al., Nucl. Fusion 39, 169 (1999)]. The possible relationship of turbulence mechanisms to the neoclassical orbit width or heuristic drift mechanism in core energy confinement regimes known as low (L) mode and high (H) mode is considered, together with implications for the future experiments.

The study of edge localized mode (ELM) behavior, stationary heat flux and transient heat flux during the ELM crash phase is performed for a China Fusion Engineering Test Reactor (CFETR) 1 GW hybrid mode operation scenario ( = 7.2 m, = 6.5 T, = 13.78 MA). Modeling and simulation start with a scenario obtained by multi-code integrated modeling on the one modeling framework for integrated tasks framework. Linear stability and nonlinear simulations of ELM dynamics are carried out using the BOUT++ six-field reduced magnetohydrodynamic module, which show a much smaller ELM energy loss (ΔELM ~ 0.13%) compared to that of a Type-I ELM. Parametric analysis of the weak linear growth rate and small ELM energy loss characteristics shed light on physics corresponding to a grassy ELM regime for CFETR 1 GW hybrid scenario. The transient heat flux on the divertor target during this small ELM phase is investigated using BOUT++. We found that upstream radial transport in the scrape-off-layer (SOL) induced by small ELMs is weak, which keeps it in the drift-dominated region. However, the heat flux width is still broadened to = 4.64 mm by the increase of separatrix temperature during ELM nonlinear evolution. The impact of transient peak heat load and ELM energy fluence on tungsten melting and net erosion rate of divertor target is evaluated for the first-time using physics-based transport that connects the pedestal with the SOL. Energy fluence caused by a single ELM pulse is below the tungsten melting limit, while tungsten erosion would exceed the material requirements. We conclude that external mitigation methods, such as divertor detachment and advanced divertor geometry are likely needed for the steady state operation of CFETR.