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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Turbulence in Core-collapse Supernovae

It is understood in a general sense that turbulent fluid motion below the shock front in a core-collapse supernova stiffens the effective equation of state of the fluid and aids in the revival of the explosion. However, when one wishes to be precise and quantify the amount of turbulence in a supernova simulation, one immediately encounters the problem that turbulence is difficult to define and measure. Using the 3D magnetohydrodynamic code ELEPHANT, we study how different definitions of turbulence change one’s conclusions about the amount of turbulence in a supernova and the extent to which it helps the explosion. We find that, while all the definitions of turbulence we use lead to a qualitatively similar growth pattern over time of the turbulent kinetic energy in the gain region, the total amount of turbulent kinetic energy, and especially the ratios of turbulent to total kinetic energy, distinguish them. Some of the definitions appear to indicate turbulence is a necessary contributor to the explosion, and others indicate it is not. The different definitions also produce turbulence maps with different correlations with maps of the enstrophy, a quantity widely regarded as also indicating the presence of turbulence. We also compute the turbulent adiabatic index and observe that, in regions of low enstrophy, this quantity is sensitive to the definition used. As a consequence, the effective adiabatic index depends upon the method used to measure the turbulence, and thus it alters one’s conclusions regarding the impact of turbulence within the supernova.

computational astronomy↗
DOE OSTI2024

On discriminating tokamak sawtooth crash models via localized density and temperature measurements

The core electron temperature drops rapidly during the sawtooth crash in tokamak plasmas, which causes heat loss and may lead to fast particle losses or even a disruption. Several models have been proposed for the periodic crash, including the Kadomtsev model with magnetic reconnection and the quasi-interchange model with the growth of higher-mode-number pressure-driven instabilities. 3D MHD simulations were performed for these two models with a goal to develop intuition and to predict qualitatively how different types of sawtooth will appear in various diagnostics. The structures of electron density ne and electron temperature Te show a dominant (1, 1) mode for the Kadomtsev case and a dominant (4, 4) mode for the quasi-interchange case. The oscillations of ne and Te have a positive correlation near the inversion layer for both cases, while their frequencies and amplitudes are different depending on the dominant modes. Particularly, for the Kadomtsev case, we find a relation between the amount of flux reconnected during a sawtooth event and ne or Te oscillations. Therefore, we connect recently developed measurement capabilities for ne and Te to the internal sawtooth behavior. We propose that this method of analysis can help in identifying the type of sawtooth in future experiments augmented by simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Electronic structure of α - RuCl 3 by fixed-node and fixed-phase diffusion Monte Carlo methods

Layered material α-RuCl 3 has caught wide attention due to its possible realization of Kitaev's spin liquid and its electronic structure that involves the interplay of electron-electron correlations and spin-orbit effects. Several DFT+U studies have suggested that both electron-electron correlations and spin-orbit effects are crucial for accurately describing the band gap. This work studies the importance of these two effects using fixed-node and fixed-phase diffusion Monte Carlo calculations both in spin-averaged and explicit spin-orbit formalisms. In the latter, the Slater-Jastrow trial function is constructed from two-component spin orbitals using our recent quantum Monte Carlo (QMC) developments and thoroughly tested effective core potentials. Our results show that the gap in the ideal crystal is already accurately described by the spin-averaged case, with the dominant role being played by the magnetic ground state with significant exchange and electron correlation effects. We find qualitative agreement between hybrid DFT, DFT+U, and QMC. In addition, QMC results agree very well with available experiments, and we identify the values of exact Fock exchange mixing that provide comparable gaps. Explicit spin-orbit QMC calculations reveal that the effect of spin-orbit coupling on the gap is minor, of the order of 0.2 eV, which corresponds to the strength of the spin orbit of the Ru atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

The Role of Ligand–Ligand Interactions in Multimodal Ligand Conformational Equilibria and Surface Pattern Formation

Multimodal chromatography uses multiple modes of interaction such as charge, hydrophobic, or hydrogen bonding to separate proteins. Recently, we used molecular dynamics (MD) simulations to show that ligands immobilized on surfaces can interact and associate with neighboring ligands to form hydrophobic and charge patches, which may have important implications for the nature of protein–surface interactions. Here, we study interfacial systems of increasing complexity—from a single immobilized multimodal ligand to high density surfaces—to better understand how ligand behavior is affected by the presence of a surface and the presence of other ligands in the vicinity, and how this behavior scales to larger systems. Furthermore, we find that tethering a ligand to a surface restricts its conformations to a subset of those observed in free solution, yet the ligand maintains flexibility in the plane of the surface and can form contacts with neighboring ligands. We find that although the formation of a contact between two neighboring ligands is slightly unfavorable, three neighboring ligands exhibit a preference for the formation of a fully connected cluster. To explore how these trends in ligand association extend to a larger surface with high density of ligands, we performed coarse-grained Monte Carlo (MC) simulations of a 132-ligand surface using ligand interactions parametrized based on free energies obtained from the three-ligand MD simulations. Despite their simplicity, the coarse-grained simulations qualitatively capture the cluster size distribution of ligands observed in detailed MD simulations. Quantitative differences between the two suggest opportunities for improvements in the coarse-grained energy function for efficient predictions of cluster and pattern formations. Our approach presents a promising route to the engineering of multimodal patterns for future chromatographic resin design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Benchmarking the multiconfigurational Hartree method by the exact wavefunction of two harmonically trapped bosons with contact interaction

Highlights: • Comparison of exact and numerical single-particle density matrices. • Benchmark for multiconfigurational Hartree. • Convergence for large number of orbitals. We consider two bosons in a one-dimensional harmonic trap, interacting by a contact potential, and compare the exact solution of this problem to a self-consistent numerical solution by using the multiconfigurational time-dependent Hartree (MCTDH) method. We thereby benchmark the predictions of the MCTDH method with a few-body problem that has an analytical solution for the most commonly experimentally realized interaction potential in ultracold quantum gases. It is found that exact ground state energy and first order correlations are accurately reproduced by MCTDH up to the intermediate dimensionless coupling strengths corresponding to typical background scattering lengths of magnetically trapped ultracold dilute Bose gases. For larger couplings, established for example by (a combination of) Feshbach resonances and optical trapping, the MCTDH approach overestimates the depth of the trap-induced correlation dip of first order correlations in position space, as well as overestimates the fragmentation, defined as the average relative occupation of orbitals other than the energetically lowest one. We anticipate that qualitatively similar features in the correlation function may arise for larger particle numbers, paving the way for a quantitative assessment of the accuracy of MCTDH by experiments with ultracold atoms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Quality Ranking System for Molten Salt Thermal Property Data

A simple ranking system for use with data and property values compiled in the Molten Salt Thermal Database-Thermophysical Properties (MSTDB-TP) is presented. The approach includes assessments of five features of data collection: the method used to measure the property value, calibration of devices used to make the measurements, the quantified uncertainty of the results, control of the environmental conditions, and determination of the salt composition. The verifiability of how the property value was determined is also assessed based on information provided or cited within the data set. The quality of each facet is ranked as High, Moderate, or Incomplete based on objective metrics. The overall quality of the dataset is ranked based on rankings of the five data features and the reported property value, with rankings of A and B indicating the data and property value are deemed suitable for quantitative use and U indicating uncertainties that restrict the recommended use to qualitative purposes. The system is suitable for assessing data already in the MSTDB-TP and screening new entries.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

High-Energy X-ray Diffraction Microscopy for Nuclear Forensics FY2022 Project Report

Morphological information on nuclear material has been identified using visible light and scanning electron microscopy. These identify qualitative differences in particle morphology. Three-dimensional imaging of materials through alternating scanning electron microscopy imaging and focused ion beam milling has also been used. Unfortunately, these techniques are time- and labor-intensive, with significant sample preparation required and lengthy analysis times. Further, the resulting 3D images are qualitative, require manual identification, and do not capture statistically-representative populations. High energy X-ray 3D imaging using a direct-beam or diffracted-beam (High-Energy Diffraction Microscopy) have been developed at the Advanced Photon Source and can produce quantitative information on grains (phase, location, etc.) and pores (size distribution, sphericity) in a material. These techniques require only minutes to characterize a sample volume and are non-destructive, thus suitable for a wide range of existing samples and for confirmatory analyses to be carried out using conventional microscopy techniques. In this first year of the project, all uranium oxide samples were synthesized and characterized using conventional analyses by the analytical chemistry laboratory. Conventional analysis methods included powder x-ray diffraction, scanning electron microscopy, impurity analysis via inductively coupled plasma mass spectrometry, and infrared spectroscopy. Impurity analysis shows a drop in boron content from UO 3 to the lowest U 3 O 8 calcination temperature, but otherwise no appreciable difference in any sample. Analysis of diffraction data shows a flip of peaks from UO 3 dominated for the 600 °C calcined sample to U 3 O 8 dominated at 700 °C and 800 °C. Analysis of scanning electron microscopy images shows that with increased calcination temperature the size distribution of particles seems to increase and broaden. Both of these last findings are in line with previously published data, though this work used significantly fewer particles to simply show similar trends instead of getting truly quantitative particle analysis. Infrared analysis similarly shows ingrowth of U 3 O 8 as calcination temperature is increased, along with depression of peaks associated with UO 3 and water. Samples were prepared for analysis at the Advanced Photon Source at beamline 1-ID. It is anticipated that analysis will occur in November of 2022. AI/ML techniques to de-noise data coming out of 1-ID during the analyses was also developed during this time using previously gathered data. Preliminary results using a self-supervision technique called Noise2Selfshow good de-noising of data. Once the uranium oxide samples are analyzed, real data will be used to test the de-noising and other AI/ML techniques that may be developed in the second year of the project.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Full circle mechanical dynamic characterization including experimental modal analysis and finite element analysis

During operation, it was observed that a specific mechanical system experienced undesirable vibration and it became necessary to understand and mitigate this phenomenon. This document investigates the tools, methodology, and results of the dynamic characterization of the system. The characterization makes use of the experimental modal analysis (EMA) methods of single input multiple output (SIMO) and single input single output (SISO). The validity of the theory of reciprocity is confirmed to minimize measurement error, cost, and time of repeat testing. Finite element analysis (FEA) is used in choosing transducer and modal impact locations to adequately characterize the system. Single degree of freedom (SDOF) and multiple degree of freedom (MDOF) curve fitting is used to fully characterize the system’s mode shapes and natural frequencies. The EMA characterization results are used to modify and validate the FEA model so that FEA can be used to model potential structural modifications to the system to mitigate the undesirable vibration. Structural modifications are chosen, implemented, and their effectiveness is quantified using EMA. Finally, a qualitative evaluation of the methodology of FEA validation by EMA and tuning of the model to match the experimental results is discussed.

42 ENGINEERING↗
DOE OSTI2023

Characterization of Fe-6Si Soft Magnetic Alloy Produced by Laser-Directed Energy Deposition Additive Manufacturing

Abstract Commercial electrical steels, Fe-Si alloys with < 4 wt.% Si, are inexpensive and efficient materials for electrical power conversion. Further efficiency improvements require increasing the silicon concentration to 6 wt.%, at which point the material becomes brittle and difficult to form by conventional rolling and sheet fabrication methods. Additive manufacturing stands to overcome challenges with commercial manufacturing techniques by leveraging near-net-shape fabrication. The wide array of process conditions provides additive manufacturing with increased flexibility, enabling control over the microstructure and mechanical properties. This work explores the microstructures and magnetic properties of ring-shaped Fe-Si alloys produced using concentric and cross-hatch tool paths on a laser-directed energy deposition additive manufacturing system. Concentric-built samples exhibit elongated grain structures while cross-hatch-built samples comprise lower aspect ratio grain structures. Thermal finite element analysis simulations model the stress conditions produced by the different scan path geometries. Microhardness measurements probe the mechanical properties as a function of anneal temperature, providing a qualitative understanding of the intergranular defect density. Soft magnetic properties measured under quasistatic and AC conditions show frequency- and microstructure-dependent coercivity and permeability. Finally, analysis of the core loss quantifies how the build strategies and thermal treatments influence efficiency in electrical power conversion applications. Understanding the influences of scan path geometry and thermal treatment provides a pathway towards application of additively manufactured soft magnetic materials.

Adamczyk, Jesse M.↗
DOE OSTI2023

Development of fracture diagnostic methods for fluid distribution based on quantitative interpretation of distributed acoustic sensing and distributed temperature sensing

Multistage hydraulic fracturing design on horizontal wells has significantly evolved with larger fluid volume, more fracturing stages, and tighter perforation cluster spacing to efficiently stimulate unconventional reservoirs. From the published field observations, the recent fracturing design results in complex fracture networks or swarm of fractures. Fracture treatment evaluation is extremely challenging in such a case because of the large amount of variables in well completion and stimulation design. Combined measurements from different technologies can help in fracture diagnosis. Fluid distribution, either during fracture injection or during production, directly relates to the stimulation efficiency at the cluster level and at the stage level. Because it is unlikely in the real world to distribute the injected fluid uniformly among all the clusters, we need diagnostic techniques to generate the flow profile along a lateral. Fiber-optic measurements, such as distributed acoustic sensing (DAS) and distributed temperature sensing (DTS), are currently used to diagnose downhole flow conditions. This technology allows us to qualitatively confirm the fluid flow profile and other issues occurring downhole during fracturing such as leakage through plugs. For optimizing a fracturing design, we also need to understand how the design parameters are correlated with the stimulation efficiency. In this study, we combine two sets of models of DAS and DTS data interpretation for injected fluid volume distribution. The DAS is interpreted based on an empirical correlation between fluid flow rates and frequency band energy from the acoustic signals. The DTS is interpreted by performing temperature history match-based thermal energy conservation. Because of the completely different physics behind the interpretations, the confirmation of two interpretations provides confidence in fluid distribution.

Geochemistry & Geophysics↗
DOE OSTI2021

Application of molecular convergent close-coupling cross sections in a collisional radiative model for the triplet system of molecular hydrogen

Collisional radiative (CR) models for molecular hydrogen are of high relevance for performing qualitative and quantitative analysis of excited-state population densities measured in plasmas or predicting the dependence of plasma emission on parameter variations. Although the development of such models for H 2 started decades ago, major uncertainties still exist regarding the most important set of input parameters, namely the cross sections for electron-impact excitation. The deviations between cross sections from different datasets are particularly pronounced in the energy region close to the threshold energy, strongly increasing the uncertainty of CR models applied to low-temperature plasmas. This paper presents experimental validation of a set of newly calculated non ro-vibrationally resolved electron-impact cross sections calculated for the triplet system of H 2 using the molecular convergent close-coupling method in the adiabatic-nuclei formulation. These cross sections are implemented into a CR model based on the flexible solver Yacora. A first comparison of CR calculations with the different datasets to experimentally-determined population densities is performed at a planar ICP discharge for varying pressure (between 1 and 10 Pa) and RF power (between 700 and 1100 W). For the experimentally-accessible electron temperature and density range (2.5–10 eV and 1.8–3.3 × 10 16 m –3 , respectively), very good agreement between the model and experiment is obtained using the new data set, in contrast to previously used cross sections.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Examination of synthetic gas puff imaging diagnostic data from a gyrokinetic turbulence code

A synthetic gas puff imaging (GPI) diagnostic has been developed for the purpose of validating the three-dimensional gyrokinetic turbulence code XGC. The synthetic diagnostic is described and applied to XGC simulations of two Alcator C-Mod discharges. The turbulence characteristics deduced from the resulting simulated GPI frames, using analysis techniques similar to those applied to experimental data, are compared with locally derived characteristics extracted directly from the XGC output. The comparison of the two is shown to be potentially impacted by misalignment between the GPI view and the magnetic field, the dependence of the light emission on the electron density and temperature, and spatial and temporal variations in the neutral gas cloud induced by the turbulent plasma fluctuations. We conclude that quantitative and, in some cases even qualitative, validation of turbulence simulations need to account for these effects. While we cannot directly compare our results with experimental data due to the absence of high quality GPI data from the shots and times simulated by XGC, we do relate the overall characteristics obtained from the synthetic GPI analysis to published Alcator C-Mod GPI data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Orbital dependent complications for close vs well-separated electrons in diradicals

We investigate two limits in open-shell diradical systems: O3, in which the interesting orbitals are in close proximity to one another, and (C21H13)2, where there is a significant spatial separation between the two orbitals. In accord with earlier calculations, we find that standard density-functional approximations do not predict the open-shell character for the former case but uniformly predict the open-shell character for the latter case. We trace the qualitatively incorrect behavior in O3 predicted by these standard density functional approximations to self-interaction error and use the Fermi–Löwdin-orbital-self-interaction-corrected formalism to determine accurate triplet, closed-shell singlet, and open-shell broken-spin-symmetry electronic configurations. Analysis of the resulting many-electron overlap matrices allows us to unambiguously show that the broken-spin-symmetry configurations do not participate in the representation of the Ms = 0 triplet states and allows us to reliably extract the singlet–triplet splitting in O3 by analyzing the energy as a function of Fermi-orbital-descriptor permutations. The results of these analyses predict the percentage of open-shell character in O3, which agrees well with conventional wavefunction-based methods. While these techniques are expected to be required in cases near the Coulson–Fischer point, we find that they will be less necessary in diradical systems with well-separated electrons, such as (C21H13)2. Results based on energies from self-interaction-corrected generalized gradient, local density, and Hartree–Fock approximations and experimental results are in generally good agreement for O3. These results help form the basis for deriving extended Heisenberg-like Hamiltonians that are needed for descriptions of molecular magnets when there are competing low-energy electronic configurations.

Chemistry↗
DOE OSTI2025

De Nive Quinquangula: Pentagonal Snowflake Metal Nanocrystals as an Example of Emergence Phenomenon in Nanotechnology Complex Systems

The formation of snowflakes (SFL) is one of the most captivating phenomena in nature. The fabrication of multimetallic gold (Au) nanoparticles containing copper (Cu) and iron (Fe) is reported, which adopt snowflake-like morphology after nanoparticle aggregation. The synthesis of these snowflake-like Au microcrystals occurs mainly by kinetic control. In this process, a surfactant-assisted salt reduction method is employed on a heated substrate. Here, the metal salts react within seconds to form nanoparticles. This process results in a hierarchical structure with pseudo-pentagonal symmetry and chiroptical activity. We discuss how large superstructures emerge from nanoparticle aggregation, resembling natural snowflakes. However, unlike ice snowflakes, which exhibit hexagonal symmetry, the Au snowflakes display pentagonal symmetry. It is proposed that the formation of these snowflake-like microcrystals is the result of the complexity involved in the crystal growth process and represents an example of the phenomenon of emergence, which has become very significant in several fields of modern science, including physics, biology, chemistry, economics, philosophy, and poetry. The term emergent is used to evoke the collective behavior of a large number of microscopic constituents that is qualitatively different than the behaviors of the individual constituents.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Andreev reflection at the altermagnet-superconductor interface

Altermagnets are a new class of magnetic materials, which exhibit large spin splitting, but due to the combined spin and real space group symmetry protection maintain zero net macroscopic magnetization. Such a characteristic may prove them to be superior in applications in superconducting heterostructures and thus here we investigate the Andreev reflection at the altermagnet/superconductor interface. We compare and contrast altermagnets to other magnetic materials, revealing qualitative differences in the behavior of altermagnetic junction depending on the Fermi surface orientation. We study the resonant states arising in setups with strong tunneling barriers and show that sensitivity to nonmagnetic disorder is also dependent on the orientation. In conclusion, our results provide a building block for altermagnetic superconducting heterostructures such as Josephson π junctions with superior properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Microscopic Mechanisms of Glasslike Lattice Thermal Transport in Cubic Cu 12 Sb 4 S 13 Tetrahedrites

Materials based on cubic tetrahedrites (Cu 12 Sb 4 S 13 ) are useful thermoelectrics with unusual thermal and electrical transport properties, such as very low and nearly temperature-independent lattice thermal conductivity (κ L ). We explain the microscopic origin of the glasslike κ L in Cu 12 Sb 4 S 13 by explicitly treating anharmonicity up to quartic terms for both phonon energies and phonon scattering rates. We show that the strongly unstable phonon modes associated with trigonally coordinated Cu atoms are anharmonically stabilized above approximately 100 K and continue hardening with increasing temperature in accord with experimental data. This temperature-induced hardening effect reduces scattering of heat carrying acoustic modes by reducing the available phase space for three-phonon processes, thereby balancing the conventional ∝ T increase in scattering due to phonon population and yielding nearly temperature independent κ L . Furthermore, we find that very strong phonon broadening leads to a qualitative breakdown of the conventional phonon-gas model and modify the dominant heat transport mechanism from the particlelike phonon wave packet propagation to incoherent contributions described by the off-diagonal terms in the heat-flux operator, which are typically prevailing in glasses and disordered crystals. Furthermore, our work paves the way to a deeper understanding of glasslike thermal conductivity in complex crystals with strong anharmonicity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Accurate simulation of surfaces and interfaces of ten FCC metals and steel using Lennard–Jones potentials

Abstract The earlier integration of validated Lennard–Jones (LJ) potentials for 8 fcc metals into materials and biomolecular force fields has advanced multiple research fields, for example, metal–electrolyte interfaces, recognition of biomolecules, colloidal assembly of metal nanostructures, alloys, and catalysis. Here we introduce 12-6 and 9-6 LJ parameters for classical all-atom simulations of 10 further fcc metals (Ac, Ca (α), Ce (γ), Es (β), Fe (γ), Ir, Rh, Sr (α), Th (α), Yb (β)) and stainless steel. The parameters reproduce lattice constants, surface energies, water interfacial energies, and interactions with (bio)organic molecules in 0.1 to 5% agreement with experiment, as well as qualitative mechanical properties under standard conditions. Deviations are reduced up to a factor of one hundred in comparison to earlier Lennard–Jones parameters, embedded atom models, and density functional theory. We also explain a quantitative correlation between atomization energies from experiments and surface energies that supports parameter development. The models are computationally very efficient and applicable to an exponential space of alloys. Compatibility with a wide range of force fields such as the Interface force field (IFF), AMBER, CHARMM, COMPASS, CVFF, DREIDING, OPLS-AA, and PCFF enables reliable simulations of nanostructures up to millions of atoms and microsecond time scales. User-friendly model building and input generation are available in the CHARMM-GUI Nanomaterial Modeler. As a limitation, deviations in mechanical properties vary and are comparable to DFT methods. We discuss the incorporation of reactivity and features of the electronic structure to expand the range of applications and further increase the accuracy.

Kanhaiya, Krishan (ORCID:0000000236222655)↗
DOE OSTI2020

Enabling Efficient and Accurate Computational Studies of MOF Reactivity via QM/MM and QM/QM Methods

Electronic structure calculations can provide unique insight into metal–organic framework (MOF) reactivity and defect formation. Such calculations can be broadly categorized as utilizing either periodic or cluster models, each with their respective advantages and disadvantages. In the present study, we demonstrate how multiscale methods can leverage the advantages of both approaches to enable high levels of accuracy and computational efficiency in studies of MOF reactivity. Using defect formation in a zeolitic imidazolate framework (ZIF) as a prototypical example, we benchmark a quantum mechanics/molecular mechanics (QM/MM) scheme that enables highly efficient cluster-based calculations on MOFs. We demonstrate the importance of correctly accounting for the influence of both dative bond cleavage in the QM cluster and long-range mechanical coupling to the bulk to achieving accurate QM/MM studies of MOFs. We subsequently leverage these cluster models in a QM/QM scheme that goes beyond standard DFT to yield “gold-standard” correlated wave function results on MOFs at modest computational cost. Crucially, we find several cases in which the incorporation of these correlated corrections yields qualitatively important corrections over conventional DFT values.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗