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Single crystal neutron and magnetic measurements of Rb 2 Mn 3 (VO 4 ) 2 CO 3 and K 2 Co 3 (VO 4 ) 2 CO 3 with mixed honeycomb and triangular magnetic lattices

Two new alkali vanadate carbonates with divalent transition metals have been synthesized as large single crystals via a high-temperature (600 °C) hydrothermal technique. Compound I, Rb 2 Mn 3 (VO 4 ) 2 CO 3 , crystallizes in the trigonal crystal system in the space group P[3 with combining macron]1c, and compound II, K 2 Co 3 (VO 4 ) 2 CO 3 , crystallizes in the hexagonal space group P6 3 /m. Both structures contain honeycomb layers and triangular lattices made from edge-sharing MO 6 octahedra and MO 5 trigonal bipyramids, respectively. The honeycomb and triangular layers are connected along the c-axis through tetrahedral [VO 4 ] groups. The MO 5 units are connected with each other by carbonate groups in the ab-plane by forming a triangular magnetic lattice. The difference in space groups between I and II was also investigated with Density Functional Theory (DFT) calculations. Single crystal magnetic characterization of I indicates three magnetic transitions at 77 K, 2.3 K, and 1.5 K. The corresponding magnetic structures for each magnetic transition of I were determined using single crystal neutron diffraction. At 77 K the compound orders in the MnO 6 -honeycomb layer in a Néel-type antiferromagnetic orientation while the MnO 5 triangular lattice ordered below 2.3 K in a colinear ‘up–up–down’ fashion, followed by a planar ‘Y’ type magnetic structure. K 2 Co 3 (VO 4 ) 2 CO 3 (II) exhibits a canted antiferromagnetic ordering below T N = 8 K. Here, the Curie–Weiss fit (200–350 K) gives a Curie–Weiss temperature of –42 K suggesting a dominant antiferromagnetic coupling in the Co 2+ magnetic sublattices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On the effect of negative triangularity on ion temperature gradient turbulence in tokamaks

Considering the same magnetic equilibrium and plasma conditions as in Duff et al., we perform linear and nonlinear simulations of electrostatic ion temperature gradient turbulence investigating the role of triangularity δ. Differently from what was previously reported, we find that triangularity increases the transport level regardless of its sign, but more strongly when δ is positive. Here, for the case analyzed, we identify the shear of triangularity as the critical parameter determining the transport level, indicating that even in the local limit negative triangularity can reduce the transport efficiently, suggesting that confinement improvement can also be expected for larger devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Verification of the kinetic electron role in the microinstabilities in a negative triangularity model equilibrium

Effect of kinetic electrons on negative triangularity plasmas has been investigated and compared against the corresponding positive triangularity plasmas, using the global gyrokinetic code X-point Gyrokinetic Code with scale-separated delta-f option without Coulomb collisions. Our model magnetic equilibria have strong positive and negative triangularities and weak magnetic shear. However, unusually large ρ i > a and low density plasmas are chosen to maximize the nonlocal effect to investigate the finite ρ i effect and to be clearly away from kinetic ballooning modes. Similar conclusions to previous flux tube and global simulations have been obtained in this highly nonlocal model plasma: it is essential to include kinetic electrons in the micro-instability study of negative triangularity plasmas. Most physics findings agree with existing reports, with some disagreement. We offer a new “effective trapping fraction” concept that can add to the explanation of the growth rate difference between NT and PT plasmas, pointing to the significant variation in trapped particle fractions that have turning points in the mode growth regions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Alfvén mode spectrum in the advanced steady-state tokamak scenario with negative triangularity

In the earlier studies [Zheng et al. Fundam. Plasma Phys. 10, 100051 (2024)], the negative triangularity tokamak was shown to have a unique and outstanding feature for the steady-state confinement. In addition to relieving the divertor heat load concern, it can reach a much higher beta limit in the nearly steady-state confinement, about twice the Troyon limit in the positive triangularity case. In this work, we extend the investigation to the Alfvén spectrum and toroidal Alfvén eigenmodes (TAEs). This helps to evaluate the property of energetic particle confinement in this advanced scenario of a negative triangularity tokamak. We found that, because of the large safety factor and reversed magnetic shear in the core plasma region near the magnetic axis, the TAE gap tends to be closed or have only a short radial extension between the continua. in the on-axis core region and open primarily in the off-axis region, where TAEs are shown to be present. This indicates that energetic particle confinement in the core region near the magnetic axis, where nuclear fusion reactions prevail, is not seriously affected by the excitation of TAEs in this scenario. The configuration with off-axis TAEs helps the confinement of energetic particles as compared to the configuration with near-axis TAEs. The results show that the advanced steady-state tokamak scenario with negative triangularity, because of the rapid variation of the safety factor, also has a favorable feature for energetic particle confinement.

Fourier analysis↗

Plasma edge and scrape-off layer turbulence in gyrokinetic simulations of negative triangularity plasmas

Gyrokinetic simulations in the long-wavelength or drift-kinetic limit are carried out of DIII-D inner-wall-limited (IWL) plasmas to investigate the effect of triangularity on edge and scrape-off layer (SOL) turbulence. The effect of neutral interactions and triangularity on plasma blobs is explored due to the impact blobs can have in setting the SOL width or introducing impurities through interactions with plasma-facing components. Seeded blob simulations with neutrals in shaped SOL scenarios demonstrate that increasing elongation, triangularity, or Shafranov shift decreases radial blob velocities, but neutral interactions have a minor effect. Fully turbulent simulations of DIII-D IWL plasmas include both open- and closed-field-line regions. The negative triangularity (NT) simulation has lower average core T e , lower normalized T e fluctuations, and lower fluxes, but a greater number of coherent structures (blobs) identified with increased size and velocity, on average. Density and electron temperature profiles are within a factor of 2 of experimental values. In conclusion, the increased trapped electron particle fraction in NT simulations is consistent with previous studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effects of negative triangularity shaping on energetic particle driven Alfvén eigenmodes in DIII-D

Shape variations from positive to negative triangularity may lead to improved performance regimes in a tokamak with a reduction in microturbulence as well as improved thermal confinement. The motivation of this investigation is to model and compare the neutral beam driven Alfvén eigenmode (AE) activity in two DIII-D discharges with positive and negative triangularity shaping of plasma. The simulations are performed using the linear version of the FAR3d code, which solves the reduced MHD equations for thermal plasma with addition of moment equations for the energetic ion density and parallel velocity with appropriate Landau closure relations. Overall, our numerical results indicate that for similar physical parameters, the unstable AEs observed in the negative triangularity case have lower growth rates as compared to the positive triangularity regime. Our findings may be useful to analyze the influence of the reverse-D like geometry on the AE instabilities in DIII-D and may lead to better configurations for minimizing fast ion losses in a tokamak device.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Manipulating Cu vacancy in Yb triangular lattice Materials: Investigating the quantum disordered compound CuYbSe 2 and spin glass Cu 2.73 ⁢YbP 2

Yb-based triangular lattice materials have attracted significant attention due to their potential for hosting exotic magnetic quantum states. In this paper, we report the structural, magnetic, and thermodynamic properties of two Yb triangular lattice compounds with vacancy disorder at nonmagnetic Cu sites: CuYbSe 2 and Cu 2.73 ⁢YbP 2 . Single-crystal x-ray diffraction determines notable Cu-site vacancies in both materials. Unlike a single Cu site with 0.5 occupancy in CuYbSe 2 , Cu 2.73 ⁢YbP 2 only presents 27% vacancies on one of three Cu sites. Magnetic susceptibility measurements indicate dominant antiferromagnetic interactions between Yb 3+ ions. The effective magnetic moment is consistent with an effective spin-1/2 state of Yb 3+ . CuYbSe 2 exhibits strong magnetic anisotropy between in-plane and out-of-plane directions with the estimated exchange interactions 𝐽 𝑎 /𝑘 B = 6.48 K and 𝐽 𝑐 /𝑘 B = 2.55 K. No magnetic ordering is observed down to 0.4 K, supporting its quantum disordered ground state and candidacy as a quantum spin liquid. In contrast, Cu 2.73 ⁢YbP 2 shows clear evidence of spin freezing at 4.5 K in both magnetization and heat capacity data, indicating a spin glass state. The field-induced magnetic orders are found in CuYbSe 2 . These results highlight the critical role of structural vacancies in perturbing Yb-based triangular lattices. In conclusion, we demonstrate that while the intrinsic Yb triangular lattices are comparable, the presence of Cu vacancies can fundamentally alter the magnetic ground state—tuning the system between quantum disordered and spin glass behavior.

Frustrated magnetism↗

Achievement of Reactor-Relevant Performance in Negative Triangularity Shape in the DIII-D Tokamak

Plasma discharges with a negative triangularity (δ=−0.4) shape have been created in the DIII-D tokamak with a significant normalized beta (βN=2.7) and confinement characteristic of the high confinement mode (H98y2=1.2) despite the absence of an edge pressure pedestal and no edge localized modes (ELMs). These inner-wall-limited plasmas have a similar global performance as a positive triangularity (δ=+0.4) ELMing H-mode discharge with the same plasma current, elongation and cross sectional area. For cases both of dominant electron cyclotron heating with Te/Ti>1 and dominant neutral beam injection heating with Te/Ti=1, turbulent fluctuations over radii 0.5<ρ<0.9 were reduced by 10–50% in the negative triangularity shape compared to the matching positive triangularity shape, depending on the radius and conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Structure and magnetism of the triangular lattice material YbBO 3

Abstract YbBO 3 is a member of the orthoborate family of materials which contains a triangular arrangement of Yb 3+ ions. Here we study the physical properties of YbBO 3 with neutron diffraction, inelastic neutron scattering, specific heat, and ac susceptibility measurements. The neutron diffraction measurements confirm that our samples of YbBO 3 crystallize in the monoclinic space group C 2 / c (#15) which contains two crystallographically distinct Yb 3+ sites decorating a slightly distorted triangular lattice. Heat capacity and ac susceptibility measurements indicate a potential transition to magnetic order at 0.4 K. In agreement with these observations, neutron diffraction measurements at 0.044 K observe magnetic Bragg peaks which can be indexed by a propagation vector of (0 0 1). Although determining a unique spin configuration corresponding to the observed magnetic Bragg peaks is not possible, model refinements indicate that the ordered moments are likely in the range of 0.4–0.9 μ B and, notably, require moments on both Yb sites. In addition to the magnetic Bragg peaks, diffuse scattering at low Q is observed indicating that the transition does not correspond to complete long range magnetic order. The two-site picture for YbBO 3 is further evidenced by the number of crystal field excitations observed by inelastic neutron scattering measurements. Together these results show that YbBO 3 is a two-site triangular lattice material with signatures of long-range order as well as shorter ranged spin correlations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Investigation of core impurity transport in DIII-D diverted negative triangularity plasmas

Abstract Tokamak operation at negative triangularity has been shown to offer high energy confinement without the typical disadvantages of edge pedestals (Marinoni et al 2021 Nucl. Fusion 61 116010). In this paper, we examine impurity transport in DIII-D diverted negative triangularity experiments. Analysis of charge exchange recombination spectroscopy reveals flat or hollow carbon density profiles in the core, and impurity confinement times consistently shorter than energy confinement times. Bayesian inferences of impurity transport coefficients based on laser blow-off injections and forward modeling via the Aurora package (Sciortino et al 2021 Plasma Phys. Control. Fusion 63 112001) show core cross-field diffusion to be higher in L-mode than in H-mode. Impurity profile shapes remain flat or hollow in all cases. Inferred radial profiles of diffusion and convection are compared to neoclassical, quasilinear gyrofluid, and nonlinear gyrokinetic simulations. Heat transport is observed to be better captured by reduced turbulence models with respect to particle transport. State-of-the-art gyrokinetic modeling compares favorably with measurements across multiple transport channels. Overall, these results suggest that diverted negative triangularity discharges may offer a path to a highly-radiative L-mode scenario with high core performance.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Characterization of the ELM-free negative triangularity edge on DIII-D

Tokamak plasmas with strong negative triangularity (NT) shaping typically exhibit fundamentally different edge behavior than conventional L-mode or H-mode plasmas. On DIII-D, every plasma with sufficiently negative triangularity (δ < δ crit ≃ -0.12) is found to be inherently free of edge localized modes (ELMs), even at injected powers well above the predicted L-H power threshold. It is also possible to access an ELM free state at weaker average triangularities provided that at least one of the two x-points is still sufficiently negative. Access to the ELM-free NT scenario is found to coincide with the closure of the second stability region for infinite-n ballooning modes, suggesting that ballooning stability may play a role in limiting the accessible pressure gradient in NT plasmas. Despite this, NT plasmas are able to support small pedestals and are typically characterized by an enhancement of edge pressure gradients beyond those found in traditional L mode plasmas. Further, the pressure gradient inside of this small pedestal is unusually steep, allowing access to high core performance that is competitive with other ELM-free regimes previously achieved on DIII-D. Since ELM-free operation in NT is linked directly to the magnetic geometry, NT fusion pilot plants are predicted to maintain advantageous edge conditions even in burning plasma regimes, potentially eliminating reactor core-integration issues caused by ELMs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Gyrokinetic electromagnetic particle simulations in triangular meshes with C1 finite elements

The triangular mesh-based gyrokinetic scheme enables comprehensive axis-to-edge studies across the entire plasma volume. Our approach employs triangular finite elements with first-derivative continuity (C1), building on previous work to facilitate gyrokinetic simulations. Additionally, we have adopted the mixed variable/pullback scheme for gyrokinetic electromagnetic particle simulations. The filter-free treatment in the poloidal cross-section with triangular meshes introduces unique features and challenges compared to previous treatments using structured meshes. Our implementation has been validated through benchmarks using ITPA-toroidicity-induced Alfvén eigenmode parameters, showing its capability in moderate to small electron skin depth regimes. Additional examinations using experimental parameters confirm its applicability to realistic plasma conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Experimental characterization of turbulence properties in negative triangularity DIII-D plasmas

Negative Triangularity (NT) plasmas have demonstrated robustly ELM-free high-performance operation and provide a unique testbed to study how plasma shaping affects turbulent transport. The Beam Emission Spectroscopy (BES) diagnostic provides localized 2D measurements of low-k ($k_{\theta} \rho_s < 1$) density fluctuations. In a sweep of upper triangularity at fixed power, H-mode access is suppressed and an NT-edge is observed. The turbulence amplitude ($\tilde{n}/n$) is shown to decrease by $\sim50\%$ for $\rho<0.9$ in the NT-edge phase as compared to the H-mode phase. Additionally, low-velocity edge modes below 70 kHz are suppressed by triangularity and the dominant mode propagating in the electron diamagnetic direction is seen to broaden in wavenumber space in the NT-edge phase. In a strong NT plasma ($\delta_{avg}\sim-0.5$), low amplitude modes ($\tilde{n}/n <0.5\%$) propagating in the ion-diamagnetic direction with radially-poloidally symmetric eddy structure are identified for $\rho \sim 0.65-0.83$ consistent with Ion Temperature Gradient (ITG) turbulence. Modes consistent with Trapped Electron Mode (TEM) turbulence are observed propagating in the electron-diamagnetic direction for $\rho\gtrsim0.83$ with poloidally extended eddy structure and reduced amplitudes observed at the separatrix. The turbulence properties presented in this paper help validate our understanding of NT turbulence and help explain the improved confinement and unique edge features of NT plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effect of anisotropic fast ions on internal kink stability in DIII-D negative and positive triangularity plasmas

Recent DIII-D experiments show that sawtooth stability is strongly affected by anisotropic fast ions from neutral beam injection (NBI) in both negative and positive triangularity plasmas. Fast ions from co-current NBI are stabilizing for the sawtooth stability, resulting in longer sawtooth periods. On the other hand, fast ions from counter-current NBI are destabilizing, leading to small and frequent sawteeth. The relative change of sawtooth period and amplitude is more than a factor of two. These observations appear to hold in both plasma shapes. Non-perturbative toroidal modeling, utilizing the magnetohydrodynamic-kinetic hybrid stability code MARS-K (Liu et al 2008 Phys. Plasmas 15 112503), reveals an asymmetric dependence of the stability of the n = 1 (n is the toroidal mode number) internal kink mode on the injection direction of NBI, being qualitatively consistent with the experimentally observed sawtooth behavior. The MARS-K modeling results suggest that anisotropic fast ions affect the mode growth rate and frequency through both adiabatic and non-adiabatic contributions. Here, the asymmetry of the internal kink mode instability relative to the NBI direction is mainly due to the non-adiabatic contribution of passing fast ions, which stabilize (destabilize) the internal kink with the co-(counter-) current NBI as compared to the fluid counterpart. However, finite orbit width (FOW) correction to passing particles partially cancels the asymmetry. Trapped particles are always stabilizing due to precessional drift resonance. Modeling also shows that fast ions affect the internal kink in a similar manner in both negative and positive triangularity plasmas, although being slightly more unstable in the negative triangularity configuration already in the fluid limit. The similarity is mainly attributed to the fact that the mode is localized in the plasma core region, with very similar eigenmode structures in both negative and positive configurations. Furthermore, MARS-K modeling indicates that other factors, such as the plasma rotation and the drift kinetic effects of thermal plasmas, weakly modify the mode stability as compared to the drift kinetic resonance effects and FOW correction of fast ions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

MHD stability of negative triangularity DIII-D plasmas

Abstract Negative triangularity (NT) experiments in DIII-D point to an emergent reactor scenario free of sawteeth, endowed with benign, nondisruptive n = 2 tearing modes, which experience q min ⩾ 1 similar to the positive triangularity hybrid scenario. Plasmas exhibiting this behavior attain β N > 3 , high enough to reconsider long held views of NT stability. Ideal MHD and tearing stability analysis of well-diagnosed equilibrium reconstructions of experimental hybrid-like plasmas predict that among shape parameters, MHD stability limits are only sensitive to average triangularity. Operation is predicted to be possible at β N relevant to upcoming tokamaks and commercial NT reactors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

First access to ELM-free negative triangularity at low aspect ratio

A plasma scenario with negative triangularity (NT) shaping is achieved on MAST-U for the first time. While edge localized modes (ELMs) are eventually suppressed as the triangularity is decreased below δ ≲ –0.06, an extended period of H-mode operation with Type-III ELMs is sustained at less negative δ even through access to the second stability region for ideal ballooning modes is closed. This documents a qualitative difference from the ELM-free access conditions documented in NT scenarios on conventional aspect ratio machines. The electron temperature at the pedestal top drops across the transition to ELM-free operation, but a steady rise in core temperature as δ is decreased allows for similar normalized β in the ELM-free NT and H-mode positive triangularity shapes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Phase Diagram of the Easy-Axis Triangular-Lattice 𝐽 1 −𝐽 2 Model

Our work studies the largely unexplored phase diagram of the S = 1/2 easy-axis triangular-lattice J 1 -J 2 model, motivated by recent interest in rare-earth and transition-metal compounds that exhibit strong quantum fluctuations and broad spin excitation continua—hallmarks of spin-liquid behavior. Combining density-matrix renormalization group simulations with analytical insights, we present a comprehensive study of the model that describes these materials. Our results provide compelling evidence for a robust spin-liquid phase stabilized between the exotic supersolid Y phase and the collinear stripe phase, remarkably persistent even in the presence of symmetry-breaking anisotropy. Additionally, we analyze the supersolid Y phase, offering a quantitative characterization of its order parameters and clarifying the surprising absence of a ferromagnetic moment; both features relevant to recent experiments on Ising-like triangular-lattice magnets. Altogether, our work provides the necessary framework and important theoretical guidance to the ongoing searches of the spin liquid and other exotic states in the rare-earth and transition-metal triangular-lattice compounds, as well as for advancing the understanding of anisotropic-exchange magnets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Two Distinct Cu(II)-V(IV) Superexchange Interactions with Similar Bond Angles in a Triangular ?CuV2? Fragment

The strength and sign of superexchange interactions are often predicted on the basis of the bond angles between magnetic ions, but complications may arise in situations with a nontrivial arrangement of the magnetic orbitals. We report on a novel molecular tetramer compound [Cu(H2O)dmbpy]2[V2O2F8] (dmbpy = 4,4 '-dimethyl-2,2 ' bipyridyl) that is composed of triangular "CuV2" fragments and displays a spin gap behavior. By combining first-principles calculations and electronic models, we reveal that superexchange Cu-V interactions carry drastically diHerent coupling strengths along two Cu-F-V pathways with comparable bond angles in the triangular "CuV2" fragment. Counterintuitively, their strong disparity is found to originate from the restricted symmetry of the half-filled Cu dx2-y2 orbital stabilized by the crystal field, leading to one dominating antiferromagnetic Cu-V coupling in each fragment. We revisit the magnetic properties of the reported spin-gapped chain compound [enH2]Cu(H2O)2[V2O2F8] (enH2 = ethylene diammonium) containing similar triangular "CuV2" fragments, and the magnetic behavior of the molecular tetramer and the chain compounds is rationalized as that of weakly coupled spin dimers and spin trimers, respectively. This work demonstrates that fundamentally diHerent magnetic couplings can be observed between magnetic ions with similar bond angles in a single spin motif, thus providing a strategy to introduce various exchange interactions combined with low dimensionality in heterometallic Cu(II)-V(IV) compounds.

Complexes↗