Disentangling core and edge mechanisms of the density limit in DIII-D negative triangularity plasmas

Reduced radial transport, short midplane-to-target parallel connection lengths, and a strong effect of cross-field drifts were responsible for the higher densities required for detachment in strong negative triangularity configurations in DIII-D. Dissipative divertor conditions were achieved in negative triangularity discharges at different triangularity, injected power, plasma current, and toroidal field direction. Differences between negative and positive triangularity discharges are analyzed in this paper to understand the requirements for access to detached divertor conditions: power balance, geometry, radial transport and effect of cross-field particle drifts. Parametric dependencies of access to detachment on plasma current and power flowing into the scrape-off layer remained similar in negative and positive triangularity and impurity seeding was observed to reduce the density needed to detach by up to 30$\%$ at the expense of core impurity dilution. The impact of triangularity on core-edge integration was tested varying bottom triangularity at fixed top triangularity. The high density needed to detach was not intrinsic to the negative triangularity edge as shapes with positive lower triangularity and negative upper triangularity were able to detach at lower upstream densities while maintaining an ELM-free negative triangularity edge. Confinement degradation at deeper detachment levels was however observed in all negative triangularity shapes, often associated with radiation instabilities.

Tokamak à configuration variable (TCV), recently celebrating 30 years of near-continual operation, continues in its missions to advance outstanding key physics and operational scenario issues for ITER and the design of future power plants such as DEMO. The main machine heating systems and operational changes are first described. Then follow five sections: plasma scenarios. ITER Base-Line (IBL) discharges, triangularity studies together with X3 heating and N2 seeding. Edge localised mode suppression, with a high radiation region near the X-point is reported with N2 injection with and without divertor baffles in a snowflake configuration. Negative triangularity (NT) discharges attained record, albeit transient, β N ∼ 3 with lower turbulence, higher low-Z impurity transport, vertical stability and density limits and core transport better than the IBL. Positive triangularity L-Mode linear and saturated ohmic confinement confinement saturation, often-correlated with intrinsic toroidal rotation reversals, was probed for D, H and He working gases. H-mode confinement and pedestal studies were extended to low collisionality with electron cyclotron heating obtaining steady state electron iternal transport barrier with neutral beam heating (NBH), and NBH driven H-mode configurations with off-axis co-electron cyclotron current drive. Fast particle physics. The physics of disruptions, runaway electrons and fast ions (FIs) was developed using near-full current conversion at disruption with recombination thresholds characterised for impurity species (Ne, Ar, Kr). Different flushing gases (D2, H2) and pathways to trigger a benign disruption were explored. The 55 kV NBH II generated a rich Alfvénic spectrum modulating the FI fas ion loss detector signal. NT configurations showed less toroidal Alfvén excitation activity preferentially affecting higher FI pitch angles. Scrape-off layer and edge physics. gas puff imaging systems characterised turbulent plasma ejection for several advanced divertor configurations, including NT. Combined diagnostic array divertor state analysis in detachment conditions was compared to modelling revealing an importance for molecular processes. Divertor physics. Internal gas baffles diversified to include shorter/longer structures on the high and/or low field side to probe compressive efficiency. Divertor studies concentrated upon mitigating target power, facilitating detachment and increasing the radiated power fraction employing alternative divertor geometries, optimised X-point radiator regimes and long-legged configurations. Smaller-than-expected improvements with total flux expansion were better modelled when including parallel flows. Peak outer target heat flux reduction was achieved (>50%) for high flux-expansion geometries, maintaining core performance (H 98 > 1). A reduction in target heat loads and facilitated detachment access at lower core densities is reported. Real-time control. TCV’s real-time control upgrades employed MIMO gas injector control of stable, robust, partial detachment and plasma β feedback control avoiding neoclassical tearing modes with plasma confinement changes. Machine-learning enhancements include trajectory tracking disruption proximity and avoidance as well as a first-of-its-kind reinforcement learning-based controller for the plasma equilibrium trained entirely on a free-boundary simulator. Finally, a short description of TCV’s immediate future plans will be given.

The density limit in strongly-shaped negative triangularity (NT) discharges is studied experimentally in the DIII-D tokamak. Record-high Greenwald fractions f G are obtained, using gas puff injection only, with values up to near 2, where f G is defined as the ratio of the line-averaged density over n G = I p / ( π a 2 ) , with Ip [MA] the plasma current and a[m] the plasma minor radius. A clear higher operational limit with higher auxiliary power is also demonstrated, with the ohmic density limit about two times lower than with additional neutral beam injection heating. The evolution of the electron density, temperature and pressure profiles are analyzed as well. The core density can be up to twice the Greenwald density and keeps increasing, while the value at the separatrix remains essentially constant and slightly below n G . The edge temperature gradient collapses to near zero and NT plasmas are shown to be resilient to such profiles in terms of disruptivity. We also present the time evolution of the inverse electron pressure scale length with the value at the last closed flux surface (LCFS) decreasing below the value at the normalized radius 0.9 near the density limit, demonstrating the clear drop of confinement starting from the edge. This inverse scale length ‘collapse’ at the LCFS also defines well the characteristic behavior of the kinetic profiles approaching a density limit.

In recent years, negative triangularity (NT) has emerged as a potential high-confinement L-mode reactor solution. In this work, detachment is investigated using core density ramps in lower single null Ohmic L-mode plasmas across a wide range of upper, lower, and average triangularity (the mean of upper and lower triangularity: δ) in the TCV tokamak. It is universally found that detachment is more difficult to access for NT shaping. The outer divertor leg of discharges with δ≈−0.3 could not be cooled to below 5 eV through core density ramps alone. The behavior of the upstream plasma and geometrical divertor effects (e.g. a reduced connection length with negative lower triangularity) do not fully explain the challenges in detaching NT plasmas. Langmuir probe measurements of the target heat flux widths (λ q ) were constant to within 30% across an upper triangularity scan, while the spreading factor S was lower by up to 50% for NT, indicating a generally lower integral scrape-off layer width, λ int. The line-averaged core density was typically higher for NT discharges for a given fuelling rate, possibly linked to higher particle confinement in NT. Conversely, the divertor neutral pressure and integrated particle fluxes to the targets were typically lower for the same line-averaged density, indicating that NT configurations may be closer to the sheath-limited regime than their PT counterparts, which may explain why NT is more challenging to detach.

Negative triangularity (NT) has received renewed interest as a fusion reactor regime due to its beneficial power-handling properties, including low scrape-off layer power and a larger divertor wetted area that facilitates simple divertor integration. NT experiments have also demonstrated core performance on par with positive triangularity (PT) high confinement mode (H-mode) without edge-localized modes (ELMs), encouraging further study of an NT reactor core. In this work, we use integrated modeling to scope the operating space around two NT reactor strategies. The first is the high-field, compact fusion pilot plant concept Modular, Adjustable, NT ARC (MANTA) (The MANTA Collaboration et al 2024 Plasma Phys. Control. Fusion 66 105006) and the second is a low field, high aspect ratio concept based on work by Medvedev et al (Medvedev et al 2015 Nucl. Fusion 55 063013). By integrating equilibrium, core transport, and edge ballooning instability models, we establish a range of operating points with less than 50 MW scrape-off layer power and fusion power comparable to PT H-mode reactor concepts. Heating and seeded impurities are leveraged to accomplish the same fusion performance and scrape-off layer exhaust power for various pressure edge boundary conditions. Scans over these pressure edge conditions accommodate any current uncertainty of the properties of the NT edge and show that the performance of an NT reactor will be extremely dependent on the edge pressure. The high-field case is found to enable lower scrape-off layer power because it is capable of reaching high fusion powers at a relatively compact size, which allows increased separatrix density without exceeding the Greenwald density limit. Adjustments in NT shaping exhibit small changes in fusion power, with an increase in fusion power density seen at weaker NT. Infinite-n ballooning instability models indicate that an NT reactor core can reach fusion powers comparable to leading PT H-mode reactor concepts while remaining ballooning-stable. Seeded krypton is leveraged to further lower scrape-off layer power since NT does not have a requirement to remain in H-mode while still maintaining high confinement. We contextualize the NT reactor operating space by comparing to popular PT H-mode reactor concepts, and find that NT exhibits competitive ELM-free performance with these concepts for a variety of edge conditions while maintaining relatively low scrape-off layer power.

The commonly adopted scaling for the maximum achievable plasma density in tokamak fusion devices, the so-called ‘Greenwald limit’, refers to the line-averaged density along a central chord and depends only on the average plasma current density. However, the Greenwald limit has been exceeded in tokamak experiments in the case of peaked density profiles, indicating that the edge density is the real parameter responsible for the density limit. Furthermore, the Greenwald limit has been obtained for fixed density profiles, so that the scaling can be very different when introducing density profile dependencies on plasma parameters. Dedicated density limit experiments were performed in recent years on the Frascati Tokamak Upgrade, exploring the high density domain in a wide range of values of plasma current, toroidal magnetic field and edge safety factor. New data were collected in the latest experimental campaigns, extending the study of the density limit towards lower values of toroidal magnetic field and plasma current. These experiments confirmed the edge nature of the density limit, as a Greenwald-like scaling was obtained for the maximum achievable line-averaged density along a peripheral chord, while a clear scaling of the maximum achievable line-averaged density along a central chord with the toroidal magnetic field only was found and successfully interpreted as due to interplay between the peripheral Greenwald limit and the specific density profile behavior when approaching the density limit. In particular, an analytical relation between the peripheral and the central density limit was derived for the first time, with the introduction of a generalized parabolic density profile with the peaking factor dependent on the plasma parameters.

One of the main problems in tokamak fusion devices concerns the capability to operate at a high plasma density, which is observed to be limited by the appearance of catastrophic events causing loss of plasma confinement. The commonly used empirical scaling law for the density limit is the Greenwald limit, predicting that the maximum achievable line-averaged density along a central chord depends only on the average plasma current density. However, the Greenwald density limit has been exceeded in tokamak experiments in the case of peaked density profiles, indicating that the edge density is the real parameter responsible for the density limit. Recently, it has been shown on the Frascati Tokamak Upgrade (FTU) that the Greenwald density limit is exceeded in gas-fuelled discharges with a high value of the edge safety factor. In order to understand this behaviour, dedicated density limit experiments were performed on FTU, in which the high density domain was explored in a wide range of values of plasma current (Ip = 500–900 kA) and toroidal magnetic field (BT = 4–8 T). These experiments confirm the edge nature of the density limit, as a Greenwald-like scaling holds for the maximum achievable line-averaged density along a peripheral chord passing at r/a ≃ 4/5. On the other hand, the maximum achievable line-averaged density along a central chord does not depend on the average plasma current density and essentially depends on the toroidal magnetic field only. This behaviour is explained in terms of density profile peaking in the high density domain, with a peaking factor at the disruption depending on the edge safety factor. The possibility that the MARFE (multifaced asymmetric radiation from the edge) phenomenon is the cause of the peaking has been considered, with the MARFE believed to form a channel for the penetration of the neutral particles into deeper layers of the plasma. Finally, the magnetohydrodynamic (MHD) analysis has shown that also the central line-averaged density at the onset of the MHD activity depends only on the toroidal magnetic field.

Easy access to the high-density regime without fatal disruptive phenomena is one of the important characteristics of the Large Helical Device (LHD). The operational density is considerably higher than the Greenwald density limit for tokamak plasmas. The density limit in LHD is reached when the edge density at the last closed flux surface exceeds a value approximately equivalent to the Sudo density limit that increases with the square root of the heating power. Extremely high central density of >1 × 1021 m−3 is achievable with a peaked density profile, as long as the edge density is kept lower than the Sudo limit. Furthermore, the central heating power must be larger than the radiation loss in the core region to avoid the “cold-core” phenomenon. As for the plasma edge, complete detachment takes place when the edge density exceeds the limit. Then, reattachment/Serpens mode/radiative collapse will follow, depending on the recycling condition.

In this work, we study the impact of aspect ratio A=R0/r (the ratio of major radius R 0 to minor radius r) on the confinement benefits of negative triangularity (NT) plasma shaping. We use high-fidelity flux tube gyrokinetic GENE simulations and consider several different scenarios: four of them inspired by TCV experimental data, a scenario inspired by DIII-D experimental data and a scenario expected in the new SMART spherical tokamak. The present study reveals a distinct and non-trivial dependence. NT improves confinement at any value of A for ITG turbulence, while for TEM turbulence confinement is improved only in the case of large and conventional aspect ratios. Additionally, through a detailed study of a large aspect ratio case with pure ITG drive, we develop an intuitive physical picture that explains the beneficial effect of NT at large and conventional aspect ratios. This picture does not hold in TEM-dominated regimes, where a complex synergistic effect of many factors is found. Finally, we performed the first linear gyrokinetic simulations of SMART, finding that both NT and PT scenarios are dominated by micro-tearing-mode (MTM) turbulence and that NT is more susceptible to MTMs at tight aspect ratio. However, a regime where ITG dominates can be found in SMART, and in this regime NT is more linearly stable.

Strongly-shaped diverted negative triangularity (NT) plasmas in the DIII-D tokamak demonstrate simultaneous access to high normalized density, current, pressure, and confinement. NT plasmas are shown to exist across an expansive parameter space compatible with high fusion power production, revealing surprisingly good core stability properties that compare favorably to conventional positive triangularity plasmas in DIII-D. Non-dimensionalizing the key parameters, expanded operating spaces featuring edge safety factors below 3, normalized betas above 3, Greenwald density fractions above 1, and high-confinement mode (H-mode) confinement qualities above 1 are observed, even simultaneously, and all with a robustly stable edge free from deleterious edge-localized mode instabilities. Scaling of the confinement time with engineering parameters reveals at least a linear dependence on plasma current although with significant power degradation, both in excess of expected H-mode scalings. These results increase confidence that NT plasmas are a viable approach to realize fusion power and open directions for future detailed study.

This paper investigates the predictive capabilities of TGYRO and TGLF models in assessing the
performance of negative triangularity (NT) plasmas compared to positive triangularity (PT) plasmas in fusion devices. TGYRO predicts kinetic profiles, while TGLF analyzes turbulent transport. The study reveals that TGYRO reasonably predicts NT profiles similar to PT, although it overpredicts the high-power scenarios where there is increased experimental MHD activity. TGLF analysis finds reduced linear growth rates in NT and altered flux spectra relative to PT. Additionally, the TGLF SAT0 saturation model is observed to predict high-k transport and a reduction of particle transport with the electron temperature gradient. These findings are further corroborated by core-pedestal modeling using the STEP (Stability Transport Equilibrium Pedestal) workflow, showing stronger confinement improvements in NT, particularly at higher power densities for the SAT0 saturation model. The study underscores the importance of accurately capturing turbulence saturation mechanisms for NT in order to project its performance accurately in fusion reactors.

Experiments have achieved high confinement discharges in tokamaks with a negative triangularity (NT) plasma shape accompanied by a lower pedestal and smaller and more frequent edge localized modes (ELMs) compared with positive triangularity (PT). Some existing theories emphasize the linear instability variations result from the change of pedestal. However, NT can directly bring significant changes on magnetic field structures which may also influence the instability of ELMs. Based on a series of equilibria constructed with different triangularities and pressure profiles, the influence of NT on peeling-ballooning mode (P–B mode) is investigated. It is found that NT can increase the growth rates of low to intermediate n (toroidal mode number) modes in the linear stage and lead to a larger pedestal collapse in the nonlinear stage if its pressure profile is the same with the PT shape. Further analyses demonstrate that NT enlarges the unfavorable curvature area, which provides stronger driving source and larger unstable region for the instability. Meanwhile, the diamagnetic effect and local magnetic shear helps to stabilize high n modes in the linear phase, and the E × B shearing rate at the top of the pedestal contributes to suppress the transport of turbulence into the plasma core in the nonlinear phase for the NT shape. What’s more, further simulations with different pedestal heights demonstrate that there exists a threshold value of pressure ratio, below which the ELM energy loss in NT shapes can be smaller than that in PT shapes, suggesting that the smaller energy loss with NT in experiment mainly results from the lower pedestal heigh. The results reveal behaviors of P–B modes and provide possible mechanisms for the phenomenon of lower pedestal height with negative triangularities in experiments.

The combined effects of anisotropic thermal transport and the plasma shaping, including negative triangularity, on the n = 1 (n is the toroidal mode number) tearing mode (TM) stability are numerically investigated utilizing the MARS-F code [Liu et al., Phys. Plasmas 7, 3681–3690 (2000)]. While varying the plasma boundary triangularity, the TM stability is found to be dictated by the competing effects of the Shafranov shift induced stabilization and the bad-curvature induced destabilization. The negative triangularity shape increases the Shafranov shift (stabilizing) in the plasma core but also enlarges bad-curvature regions (destabilizing) near the plasma edge, with the net effect being largely destabilizing for the TM as compared to the positive triangularity counter-part. Large negative triangularity however can also lead to more stabilization for the plasma core-localized TM. Anisotropic thermal transport reduces the stabilizing effect on the TM associated with the favorable averaged curvature, resulting in more unstable core-localized TMs in both negative and positive triangularity plasmas. But the opposite effect can also take place for the edge-localized TM in finite-pressure plasmas with negative triangularity.

The Negative Triangularity (NT) plasma edge is studied with full orbit simulations and compared with similar simulations using a Positive Triangularity (PT) edge geometry. It is found that the thermal edge ions in NT are less well confined than in PT. The edge ion losses in NT set-up an electric field inside the plasma in the loss region. This electric field leads to counter-current edge plasma flows and are consistent with observations in NT plasmas. It could also explain the good edge confinement in NT discharges via the E × B flow shear turbulence suppression mechanism.

Densities achievable in ASDEX Upgrade discharges are restricted by a disruptive limit in the L-mode caused by an edge-power imbalance which is linking divertor detachment, Marfe formation and the separatrix density. The attainable average densities depend then on the internal particle sources and the core transport and can exceed the empirical Greenwald density. In H-mode an upper density limit is found which represents a non-disruptive H - L back transition, which is preceded by the occurrence of type-III ELMs. Close to the Greenwald limit this H - L transition cannot be avoided at any power flux across the separatrix and - at high external neutral gas fluxes - confinement compared with ITER H-92P scaling degrades even before the back transition. The H-mode operational window is determined by local edge-barrier parameters and their gradients, respectively. The boundaries are represented by the L - H transition-temperature threshold, the ideal ballooning edge-pressure gradient limit, the upper temperature limit for type-III ELMs and an upper H-mode barrier density limitation. The cause for the last limitation is not yet identified; it may be due to resistive ballooning modes or the separatrix density limit. Despite the limited edge densities the Greenwald density could be surpassed by a factor of three with pellet refuelling from the low magnetic-field side. Pellet injection from the high-field side gains from the strong increase of fuelling efficiency due to the assisting toroidal outward drift of the formed high- ablatant. Higher densities are achievable in H-mode compared with low-field side injection and diminished convective losses avoid confinement degradation up to the Greenwald density. In gas-puffed type-I ELMy H-modes the plasma thermal energy and the edge-pressure gradients, which are limited by ballooning stability, are linked via a robust temperature-profile stiffness and the flat density profiles resulting from dominant edge refuelling at high densities. Their confinement does not improve with increasing density (and neutral gas fluxes) and may even slightly degrade. Therefore, the superior confinement of type-I ELMy H-modes compared with type-III ELMy ones at medium densities is actually offset at densities close to the Greenwald density. In contrast to the temperature-profile resilience density profiles can be changed both by deep refuelling (with pellets) and intrinsic transport improvements connected with density peaking (observed in CDH-modes), which offers the combination of high confinement and high density operation. The possible alliance with radiation cooling, divertor detachment and divertor compatible type-III ELMs could solve the power exhaust problem.