Negative Triangularity in Tokamak Plasmas

• Negative triangularity is a plasma shaping regime characterized by a reversed-D (δ < 0) configuration that differs fundamentally from positive-triangularity (PT) setups.
• NT enhances performance by deepening edge electric field wells, reducing turbulent heat flux, and enabling robust ELM-free high-confinement operation across varied parameters.
• NT’s unique geometry impacts divertor design, vertical stability, and core-edge integration, challenging conventional reactor concepts while offering novel operational advantages.

Negative triangularity (NT) is a tokamak shaping regime in which the plasma cross-section has negative triangularity, $\delta<0$, giving a reversed-D rather than the conventional positive-triangularity (PT) D-shape. In the recent literature, NT has become a distinct confinement and reactor-integration scenario rather than a mere geometric variant of PT, because experiments and simulations associate it with H-mode-level confinement, intrinsically ELM-free operation over broad parameter ranges, modified edge and scrape-off-layer transport, and a different balance among performance, exhaust, and robustness than in PT H-mode (Thome et al., 25 Jun 2026).

1. Geometric definition and shaping conventions

A standard definition writes the average triangularity as

$\delta=\frac{\delta_u+\delta_l}{2},$

with upper and lower triangularities defined by

$$\delta_{u,l}=\frac{R_{\rm geo}-R_{u,l}}{a_{\rm minor}},$$

so that NT corresponds to $\delta<0$ and PT to $\delta>0$ (Nelson et al., 2023). In this convention, NT reverses the usual outboard-pointing D-shape; the outboard midplane is indented, and the x-points are displaced to larger major radius than in PT (Collaboration et al., 2024).

For equilibrium parameterization, the SPARC feasibility study used the Miller form

$$R_s = R_0 + r \cos\!\left[\theta + (\sin^{-1}\delta)\sin\theta\right], \qquad z_s = \kappa r \sin\theta,$$

where $R_0$ is the geometric major radius, $r$ the minor radius, $\kappa$ the elongation, and $\delta$ the triangularity (Yüksek et al., 1 Mar 2026). This description is useful because much of the NT literature studies not only the sign of $\delta=\frac{\delta_u+\delta_l}{2},$0, but also its coupling to elongation, aspect ratio, divertor placement, and vertical stability.

Geometrically, NT has two recurring consequences in the cited literature. First, it moves the x-points and divertor to larger major radius, which increases the effective divertor circumference and target area and is therefore relevant to exhaust design (Collaboration et al., 2024). Second, it places more plasma volume on the outboard side, in a region of unfavorable curvature; this would naively seem unfavorable, yet the empirical and simulation literature repeatedly reports improved confinement and edge stability relative to PT under matched conditions (Thome et al., 25 Jun 2026). This tension between geometric intuition and observed transport behavior is central to the subject.

2. Confinement and turbulence characteristics

The confinement literature identifies NT as a high-performance, non-ELMy regime rather than a degraded L-mode. In strongly shaped diverted NT plasmas on DIII-D, simultaneous access was reported to

$\delta=\frac{\delta_u+\delta_l}{2},$1

with a robustly stable edge free from deleterious edge-localized mode instabilities (Paz-Soldan et al., 2023). The same work found that confinement time scales at least linearly with plasma current, albeit with significant power degradation, both stronger than expected from standard H-mode scalings (Paz-Soldan et al., 2023).

On TCV, direct edge radial electric field measurements strengthened the transport interpretation of NT. Doppler backscattering measured the perpendicular turbulence velocity through

$\delta=\frac{\delta_u+\delta_l}{2},$2

used as a proxy for the radial electric field via

$\delta=\frac{\delta_u+\delta_l}{2},$3

In matched Ohmic, NBI, and ECRH comparisons, NT consistently exhibited a deeper edge $\delta=\frac{\delta_u+\delta_l}{2},$4 well and stronger associated $\delta=\frac{\delta_u+\delta_l}{2},$5 shear than PT. In a matched Ohmic L-mode pair, the NT discharge had $\delta=\frac{\delta_u+\delta_l}{2},$6 compared with $\delta=\frac{\delta_u+\delta_l}{2},$7 in PT, together with about 30% higher energy confinement time, where

$\delta=\frac{\delta_u+\delta_l}{2},$8

This was interpreted as a plausible connection between NT shaping, stronger edge shear, and improved confinement (Rienäcker et al., 11 Jul 2025).

Edge/SOL gyrokinetic simulations in diverted geometry reinforce the experimental picture. In GENE-X, comparable NT and PT cases evolved toward similar density and temperature profiles, but the total turbulent heat flux was

$\delta=\frac{\delta_u+\delta_l}{2},$9

so PT had about 57% more heat flux than NT. The inferred confinement times were

$$\delta_{u,l}=\frac{R_{\rm geo}-R_{u,l}}{a_{\rm minor}},$$0

corresponding to about 67% better confinement in NT (Ulbl et al., 1 Apr 2025). That study attributed the difference primarily to reduced trapped-electron-mode (TEM) turbulence in NT, rather than to a radical change in equilibrium profiles.

The aspect-ratio dependence is not uniform across turbulence classes. Flux-tube GENE calculations found that NT improves confinement at any aspect ratio for ITG turbulence, whereas for TEM-dominated turbulence it is beneficial only at large and conventional aspect ratios. In the SMART spherical-tokamak regime, both PT and NT were found to be dominated by micro-tearing modes (MTMs), and NT was more susceptible to MTMs at tight aspect ratio unless operation could be shifted into an ITG-dominated regime (Balestri et al., 2024). This implies that NT’s confinement benefit is robust but not universal; it depends on the dominant microinstability spectrum.

3. Edge organization, pedestals, and ELM suppression

A defining property of strong NT is robust avoidance of ELMs. In DIII-D, sufficiently negative triangularity suppressed all observed ELM activity across

$$\delta_{u,l}=\frac{R_{\rm geo}-R_{u,l}}{a_{\rm minor}},$$1

corresponding to

$$\delta_{u,l}=\frac{R_{\rm geo}-R_{u,l}}{a_{\rm minor}},$$2

The dataset was consistent with the interpretation that local magnetic shear in the NT edge inhibits access to ELMing H-mode regimes, and all experimental pressure profiles were found to be at or below the infinite-$$\delta_{u,l}=\frac{R_{\rm geo}-R_{u,l}}{a_{\rm minor}},$$3 ballooning stability limit (Nelson et al., 2023).

DIII-D database studies further identified a critical triangularity

$$\delta_{u,l}=\frac{R_{\rm geo}-R_{u,l}}{a_{\rm minor}},$$4

beyond which operation is inherently ELM-free. Near this threshold, average triangularity is not the only relevant quantity: it was also found possible to close access to the second stability region for infinite-$$\delta_{u,l}=\frac{R_{\rm geo}-R_{u,l}}{a_{\rm minor}},$$5 ballooning modes when at least one of the two x-points is sufficiently negative, even if the average $$\delta_{u,l}=\frac{R_{\rm geo}-R_{u,l}}{a_{\rm minor}},$$6 is weaker (Nelson et al., 2024). In this regime the NT edge can support small pedestals and edge pressure gradients steeper than those in traditional ELM-free L-mode plasmas, so the NT state is not well described as ordinary L-mode (Nelson et al., 2023).

The edge-physics interpretation is not identical across all machines. On MAST-U, the first access to ELM-free NT at low aspect ratio occurred only when the triangularity was reduced below about

$$\delta_{u,l}=\frac{R_{\rm geo}-R_{u,l}}{a_{\rm minor}},$$7

However, the second stability region for ideal ballooning modes closed earlier in the scan, while Type-III ELMy H-mode persisted to less negative $$\delta_{u,l}=\frac{R_{\rm geo}-R_{u,l}}{a_{\rm minor}},$$8. This showed a qualitative difference from conventional-aspect-ratio machines and suggested that ELM suppression in the MAST-U case is not simply the same second-stability-closure mechanism documented on DIII-D or TCV; the paper instead pointed to a likely role for a KBM-limited pedestal below the ideal ballooning limit (Nelson et al., 2024). This is one of the clearest indications that NT edge phenomenology is machine-dependent even when the broad ELM-free outcome is shared.

Neoclassical calculations isolate only part of the edge-flow picture. In XGC, a strongly NT DIII-D-like equilibrium and a corresponding PT equilibrium showed substantial differences in Pfirsch-Schlüter flow and, more importantly, in X-point orbit-loss physics. PT tended to produce a positive co-current toroidal flow, whereas NT tended toward a negative or counter-current tendency. Yet the study also found that agreement between neoclassical simulation and experiment was validated only within the middle of the pedestal slope, roughly $$\delta_{u,l}=\frac{R_{\rm geo}-R_{u,l}}{a_{\rm minor}},$$9, indicating that the far edge requires turbulence-inclusive modeling (Ku et al., 6 Oct 2025).

4. SOL transport, detachment, and radiative operation

The exhaust literature presents NT as beneficial but nontrivial. TCV experiments found that detachment is universally more difficult to access in NT than in PT during core density ramps in lower single-null Ohmic L-mode plasmas. For NT with $\delta<0$0, the outer divertor leg could not be cooled below $\delta<0$1 through density ramps alone, whereas PT did reach the practical detachment threshold $\delta<0$2. In the same experiments, $\delta<0$3 was constant to within 30% across an upper triangularity scan, while the spreading factor $\delta<0$4 was lower by up to 50% for NT, implying a generally smaller integral SOL width,

$\delta<0$5

At fixed fuelling rate, NT also showed higher line-averaged core density but lower divertor neutral pressure and lower integrated particle fluxes to the targets (Février et al., 2023).

SOLPS-ITER modeling has not reduced this issue to a single explanation. One TCV study of opposite-triangularity lower single-null Ohmic discharges, using identical anomalous transport coefficients in PT and NT, still recovered dissimilar neutral accumulation, ionization sources, and poloidal and cross-field fluxes, with the outer target remaining hotter in NT, $\delta<0$6 (Tonello et al., 2024). A later matched-divertor comparison, deliberately constructed with the same divertor geometry and nearly identical connection lengths, found instead that magnetic geometry alone produced no significant NT/PT differences, even when drifts were included, and that reproducing the experimental profiles required lower particle diffusivity in NT (Mombelli et al., 4 Jun 2025). This suggests that the divertor problem is sensitive to whether one compares full configurations or near-identical divertor geometries; a plausible implication is that both geometry-dependent neutral dynamics and transport suppression can matter, but they need not dominate in the same way in every comparison.

For double-null L-mode plasmas, global nonlinear GBS simulations found that NT suppresses resistive-ballooning/interchange turbulence by weakening curvature effects in the unfavorable region at the outer midplane. In these simulations, the poloidal length of the separatrix in the bad-curvature region was about $\delta<0$7 in NT versus $\delta<0$8 in PT. NT reduced fluctuation levels, produced a steeper near-SOL pressure gradient, reduced in-out and up-down target power asymmetries, and generated smaller, slower blobs; for example, at $\delta<0$9, blob radius and velocity changed from $\delta>0$0, $\delta>0$1 in PT to $\delta>0$2, $\delta>0$3 in NT (Lim et al., 2024).

At the same time, NT is compatible with strongly radiating operation. In DIII-D, the first highly radiating NT plasmas were obtained using reactor-relevant seeded impurities, including Ne, Ar, Kr, and mixtures with N, reaching total radiated fractions up to 0.85, $\delta>0$4, high Greenwald fraction, and no ELMs. Moderate Kr or Ar seeding increased stored energy and $\delta>0$5 without degrading neutron rate, while BES measured reduced density fluctuations in the $\delta>0$6 band over $\delta>0$7 during impurity injection (Casali et al., 2024). Thus, NT can be simultaneously harder to detach in some present divertor configurations and attractive for radiative mantle operation. The literature treats this as a core-edge integration problem rather than a simple contradiction.

5. Vertical stability and engineering implications

NT’s principal macroscopic engineering penalty is vertical stability. In pilot-plant stability scans, NT equilibria coupled to a conformal wall were confirmed to be less vertically stable than equivalent PT configurations, and unlike PT their stability degraded at higher poloidal beta. The principal metric was

$\delta>0$8

where $\delta>0$9 is the vertical instability growth rate and $$R_s = R_0 + r \cos\!\left[\theta + (\sin^{-1}\delta)\sin\theta\right], \qquad z_s = \kappa r \sin\theta,$$0 the wall diffusion time; smaller values correspond to easier control. The study noted $$R_s = R_0 + r \cos\!\left[\theta + (\sin^{-1}\delta)\sin\theta\right], \qquad z_s = \kappa r \sin\theta,$$1 as a reasonable future-machine target and showed that optimized passive conductors could compensate for the intrinsic NT disadvantage (Guizzo et al., 2024).

The strongest mitigation result in that study was an optimized highly elongated NT configuration with outboard passive plates, for which

$$R_s = R_0 + r \cos\!\left[\theta + (\sin^{-1}\delta)\sin\theta\right], \qquad z_s = \kappa r \sin\theta,$$2

reducing the absolute growth rate to about $$R_s = R_0 + r \cos\!\left[\theta + (\sin^{-1}\delta)\sin\theta\right], \qquad z_s = \kappa r \sin\theta,$$3, lower than the PT baseline growth rate of $$R_s = R_0 + r \cos\!\left[\theta + (\sin^{-1}\delta)\sin\theta\right], \qquad z_s = \kappa r \sin\theta,$$4, and improving the estimated catching time by roughly a factor of six (Guizzo et al., 2024). Outboard plates were most effective overall, while inboard plates were uniquely useful in NT because they can help spatially separate passive stabilizers from active control coils.

These control ideas have been incorporated into dedicated device concepts. The pre-conceptual Negative Triangularity Tokamak (NTT) used TokaMaker to design a compact machine with

$$R_s = R_0 + r \cos\!\left[\theta + (\sin^{-1}\delta)\sin\theta\right], \qquad z_s = \kappa r \sin\theta,$$5

capable of accessing

$$R_s = R_0 + r \cos\!\left[\theta + (\sin^{-1}\delta)\sin\theta\right], \qquad z_s = \kappa r \sin\theta,$$6

In that design, high-field-side and/or low-field-side passive stabilizing plates reduced vertical instability growth rates by approximately 75%, making the NT parameter space operable with existing copper magnet technology (Guizzo et al., 24 Jan 2025).

Retrofitting PT-optimized machines to NT is feasible but costly in geometric margin. In SPARC, more than 600 FreeGS equilibria showed that a moderate NT double-null plasma with $$R_s = R_0 + r \cos\!\left[\theta + (\sin^{-1}\delta)\sin\theta\right], \qquad z_s = \kappa r \sin\theta,$$7, $$R_s = R_0 + r \cos\!\left[\theta + (\sin^{-1}\delta)\sin\theta\right], \qquad z_s = \kappa r \sin\theta,$$8, $$R_s = R_0 + r \cos\!\left[\theta + (\sin^{-1}\delta)\sin\theta\right], \qquad z_s = \kappa r \sin\theta,$$9, and $R_0$0 is achievable within coil-current and wall constraints. However, NT required a plasma-volume reduction from $R_0$1 to $R_0$2, a connection-length reduction from $R_0$3 to $R_0$4, and roughly a factor of $R_0$5 higher PF$R_0$6 current magnitude, even though central-solenoid demand fell by 54% relative to the PT 8 T case (Yüksek et al., 1 Mar 2026). This supports the design conclusion that purpose-built NT devices are preferable to PT retrofits.

6. Reactor concepts, integrated modeling, and unresolved questions

NT has motivated full pilot-plant concepts. MANTA adopted $R_0$7 specifically to keep the edge in the first ballooning stability region and make the second stability region inaccessible, thereby preventing H-mode access. Its integrated design point combined

$R_0$8

with a radiated power fraction of about 0.82, a peak divertor heat flux of $R_0$9, pulse length of about 15 min, and $r$0 net electricity, while retaining a conventional divertor (Collaboration et al., 2024). In that design logic, NT is not merely a transport optimization but the basis of a “power-handling first” reactor strategy.

Integrated reactor-core scans using STEP reached a similar conclusion, but with a strong caveat. By coupling CHEASE, TGYRO/TGLF, BALOO, and heating models, the study found NT operating points with fusion power comparable to PT H-mode reactor concepts and less than $r$1 scrape-off-layer power. Seeded krypton lowered $r$2 almost linearly with impurity fraction, and the high-field compact case was favored because it could maintain higher separatrix density without exceeding the Greenwald limit. However, performance depended extremely strongly on the edge pressure boundary condition at $r$3; the study explicitly concluded that edge pressure matters more than geometry across its scans (Wilson et al., 2024).

A broader review of experimental progress frames NT around three reactor criteria: performance, exhaust, and robustness. It emphasizes that NT studies have accelerated across TCV, DIII-D, AUG, JET, and MAST-U; that NT routinely accesses very high Greenwald fractions and low $r$4 while remaining ELM-free; and that it exhibits high reproducibility across discharge-to-discharge comparisons (Thome et al., 25 Jun 2026). The same review also identifies the major open problems: confinement extrapolation to reactor conditions, determination of the optimal triangularity rather than simply the strongest achievable NT, and fully integrated core-edge solutions with closed pumped divertors rather than the predominantly open divertors of present experiments (Thome et al., 25 Jun 2026).

Two misconceptions are therefore rejected by the current literature. NT is not simply conventional L-mode with inverted shaping; it supports distinct pedestals, edge shear structure, and high-performance states (Nelson et al., 2024). Nor is NT a complete reactor solution by geometry alone; the present evidence instead indicates a configuration with unusually favorable confinement and edge robustness, but with nontrivial detachment, turbulence, and vertical-control requirements that remain central to extrapolation (Thome et al., 25 Jun 2026).