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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,657 records · Page 92
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

The Role of Titania Surface Coating by Atomic Layer Deposition in Improving Osteogenic Differentiation and Hard Tissue Formation of Dental Pulp Stem Cells

Recent studies have focused on modifying implant surface properties to improve bone regeneration and osseointegration. Herein, the role of titania surface coating in enabling dental pulp stem cells (DPSCs) differentiation and hard tissue formation is studied. Atomic layer deposition is applied at lower temperature to coat a nanolayer of titania onto hard and soft polybutadiene substrates without altering their moduli, to probe the effects of surface chemistry and substrate modulus. In the absence of titania, DPSCs prefer to attach and proliferate on the hard substrate, where particle-like biomineralization is present after 28 days in culture, whereas no biomineralization is observed on the soft substrate. Applying titania surface coating results in the improvement of adhesion and proliferation, regardless of substrate modulus, whereas cell and substrate moduli remain the same as control without titania coating. Furthermore, templated biomineralization is observed given the bone-like tissue composition by Raman analysis, in consistent with real time-polymerase chain reaction (RT-PCR) results showing upregulation of osteopontin (OPN) and bone sialoprotein (BSP), representing osteogenic differentiation. Furthermore, the results indicate that titania surface coating improved the ability to nucleate banded collagen fibers which in turn templated mineral deposits, and further induced the osteogenesis of DPSCs, regardless of its substrate modulus.

36 MATERIALS SCIENCE↗
DOE OSTI2026

VIC-Global Parameter Dataset Sensitivity with the Variable Infiltration Capacity Model: Evaluating the importance of dynamic land surface parameters when using the VIC-Global parameter dataset

Accurate prediction of runoff is essential to water resources management, flood risk assessment, and ecosystem protection. However, many hydrological models still have relatively substantial limitations when representing the influence of land use and land cover (LULC) on runoff generation and routing. Changes in LULC, such as deforestation, urban expansion, agricultural intensification, and wetland loss, have been shown to alter the water balance at the land surface through fundamental hydrologic processes (e.g., interception, infiltration, evapotranspiration, and soil storage). However, it remains an open question what the exact magnitude and timing of these impacts are for the spatial and temporal scales commonly used in engineering applications. In this analysis we focus on one aspect of recent LULC change for assessing human impacts, which is urbanization. Specifically we seek to determine the impacts of urbanization on the magnitude and timing of surface runoff and baseflow in HUC-12 basins in Clark County, Nevada which has experienced rapid urbanization. We use the Variable Infiltration Capacity (VIC) hydrology model with a widely used off-the-shelf dataset of land surface parameters, VIC-Global, both of which have been commonly used in the past for water and energy balance modeling for large scale hydrologic studies. We examine two scenarios where the first scenario removes all urbanized land cover and parameterizes those areas of the basins as barren or open shrubland. The second scenario tests the opposite case where all areas of the basins are classified as urban regardless of their present classification. The results from the VIC model show there is a low sensitivity for daily surface runoff between scenarios. The daily baseflow values indicate similar low sensitivity to the classification change during specific periods, but then have substantial differences during other period when large precipitation events are occurring. This is likely due to the assumed parameter values for the urban land cover classification made by the VIC-Global dataset. Using a static land cover parameterization is reasonable for large domain hydrology models that are being used for near-term planning horizons (<30 years). However, longer planning horizons where feedbacks between the atmosphere and land surface are important, especially in transient climate situations, considerations for how to update land surface parameters should be incorporated.

42 ENGINEERING↗
DOE OSTI2021

Uranium (VI) Adsorbate Structures on Portlandite [Ca(OH)2] Type Surfaces Determined by Computational Modelling and X-ray Absorption Spectroscopy

Portlandite [Ca(OH) 2 ] is a potentially dominant solid phase in the high pH fluids expected within the cementitious engineered barriers of Geological Disposal Facilities (GDF). This study combined X-ray Absorption Spectroscopy with computational modelling in order to provide atomic-scale data which improves our understanding of how a critically important radionuclide (U) will be adsorbed onto this phase under conditions relevant to a GDF environment. Such data are fundamental for predicting radionuclide mass transfer. Surface coordination chemistry and speciation of uranium with portlandite [Ca(OH) 2 ] under alkaline groundwater conditions (ca. pH 12) were determined by both in situ and ex situ grazing incidence extended X-ray absorption fine structure analysis (EXAFS) and by computational modelling at the atomic level. Free energies of sorption of aqueous uranyl hydroxides, [UO 2 (OH) n ] 2–n (n = 0–5) with the (001), (100) and (203) or (101) surfaces of portlandite are predicted from the potential of mean force using classical molecular umbrella sampling simulation methods and the structural interactions are further explored using fully periodic density functional theory computations. Although uranyl is predicted to only weakly adsorb to the (001) and (100) clean surfaces, there should be significantly stronger interactions with the (203/101) surface or at hydroxyl vacancies, both prevalent under groundwater conditions. The uranyl surface complex is typically found to include four equatorially coordinated hydroxyl ligands, forming an inner-sphere sorbate by direct interaction of a uranyl oxygen with surface calcium ions in both the (001) and (203/101) cases. In contrast, on the (100) surface, uranyl is sorbed with its axis more parallel to the surface plane. The EXAFS data are largely consistent with a surface structural layer or film similar to calcium uranate, but also show distinct uranyl characteristics, with the uranyl ion exhibiting the classic dioxygenyl oxygens at 1.8 Å and between four and five equatorial oxygen atoms at distances between 2.28 and 2.35 Å from the central U absorber. These experimental data are wholly consistent with the adsorbate configuration predicted by the computational models. These findings suggest that, under the strongly alkaline conditions of a cementitious backfill engineered barrier, there would be significant uptake of uranyl by portlandite to inhibit the mobility of U(VI) from the near field of a geological disposal facility.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Persistent Structure and Frustrated Magnetism in High Entropy Rare-Earth Zirconates

The configurational complexity and distinct local atomic environments of high entropy oxides remain largely unexplored, leaving structure-property relationships and the hypothesis that the family offers rich tunability for applications ambiguous. This work investigates the influence of cation size and materials synthesis in determining the resulting structure and magnetic properties of a family of high entropy rare-earth zirconates (HEREZs, nominal composition RE 2 Zr 2 O 7 with RE = rare-earth element combinations including Eu, Gd, Tb, Dy, Ho, La, or Sc). Here, the structural characterization of the series is examined through synchrotron X-ray diffraction and pair distribution function analysis, and electron microscopy, demonstrating average defect-fluorite structures with considerable local disorder, in all samples. The surface morphology and particle sizes are found to vary significantly with preparation method, with irregular micron-sized particles formed by high temperature sintering routes, spherical nanoparticles resulting from chemical co-precipitation methods, and porous nanoparticle agglomerates resulting from polymer steric entrapment synthesis. In agreement with the disordered cation distribution found across all samples, magnetic measurements indicate that all synthesized HEREZs show frustrated magnetic behavior, as seen in a number of single-component RE 2 Zr 2 O 7 pyrochlore oxides. These findings advance the understanding of the local structure of high entropy oxides and demonstrate strategies for designing nanostructured morphologies in the class.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Effect of Topology on Transient Dynamic and Shock Response of Polymeric Lattice Structures

Architected cellular materials, such as lattice structures, offer potential for tunable mechanical properties for dynamic applications of energy absorption and impact mitigation. In this work, the static and dynamic behavior of polymeric lattice structures was investigated through experiments on octet-truss, Kelvin, and cubic topologies with relative densities around 8%. Here, dynamic testing was conducted via direct impact experiments (25–70 m/s) with high-speed imaging coupled with digital image correlation and a polycarbonate Hopkinson pressure bar. Mechanical properties such as elastic wave speed, deformation modes, failure properties, particle velocities, and stress histories were extracted from experimental results. At low impact velocities, a transient dynamic response was observed which was composed of a compaction front initiating at the impact surface and additional deformation bands whose characteristics matched low strain-rate behavior. For higher impact velocities, shock analysis was carried out using compaction wave velocity and Eulerian Rankine–Hugoniot jump conditions with parameters determined from full-field measurements.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Influence of graphite geography on the yield of mechanically exfoliated few-layer graphene

Some of graphene's exciting properties that inspired countless studies over the last two decades are exclusive to defect-free, few-layer graphene (FLG, ≤4 layers) produced by mechanical exfoliation. Despite graphite exfoliation having been thoroughly studied, the influence of the graphite source on the successful exfoliation of FLG remains unexplored. Here, in this work, we examine the physicochemical properties and exfoliation performance of various graphite types (e.g., natural crystalline flake, natural vein, and synthetic) from around the globe (e.g., Alaska, Tanzania, China, etc.). We first established a normalization method for the facile comparison of FLG (Φ) yields between separately exfoliated graphites. Using this approach, we find that the relative yield of FLG ranges from 0% to 22% across graphite types, with regular natural crystalline flakes (NCF-R) performing the best overall (Φ NCF-R = 16% ± 5%). FLG yield was also found to depend on source geography, evidenced by Φ NCF-R ranging from 8% to 22% for NCF-R sourced from Alabama and Canada, respectively. We employed machine learning and Pearson correlation analysis to determine the graphite characteristics that govern FLG yield. Graphite source-dependent properties such as graphite surface area and mineral impurities, including aluminum and calcium, were found to be critically important. Our findings highlight the importance of the graphite source when trying to maximize the yield of mechanically exfoliated FLG and represent an important step toward producing higher quantities of defect-free FLG for graphene-based research.

42 ENGINEERING↗
DOE OSTI2026

Coupling geophysical, geological, geochemical and mineralogical assessments to examine preferential contaminant transport pathways in interbedded fractured bedrock

This study shows that a multi-faceted approach, combining borehole geophysical logging and surface seismic P-wave first-arrival tomography with confirmatory coring, well installation, and chemical and mineralogical analysis, is effective for identifying difficult-to-locate preferential contaminant transport pathways in deeper fractured bedrock. Seismic tomography detected porous 10–20 m wide elongated fractured conduits that allow acidic groundwater contaminated with uranium (U) and nitrate (NO 3 - ) to migrate within interbedded shale-limestone bedrock over 1000 m from a former disposal facility (S-3 Ponds site) located at the DOE Y-12 National Security Complex in Tennessee (USA). Conventional drilling techniques would easily miss these conduits because they are oriented parallel with fractured bedding planes. Synchrotron analysis of aquifer solids revealed that > 95 % of the U is hexavalent (U VI ). This uranyl (UO 2 2+ ) species is coordinated with carbonate, iron oxide, silicate and phosphate minerals within cemented white to yellow precipitates, which contain U concentrations as high as ∼21.6 % by weight fraction. Identifying the presence of these mineral phases, enables a further understanding of the potential effectiveness of remediation actions. The combination of methodologies presented here can also be applied to other explorations, such as the detection of water supply.

Fate and transport↗
DOE OSTI2025

Characterizing Ultrafast Intersystem Crossing Pathways in Molecular Pt Dimers Using Time-Resolved Wide-Angle X-ray Scattering

Vibronic coupling between transition metal charge transfer states is a potential mechanism for enhancing the intersystem crossing (ISC) rate. Vibronic coupling-driven ISC has been observed in Pt­(II) dimer complexes, where the trajectory across excited-state pathways is tuned by atomic displacements via Pt–Pt stretching vibrations. Time-resolved wide-angle X-ray scattering (TR-WAXS) was utilized to quantify the Pt–Pt contraction following metal–metal-to-ligand charge transfer (MMLCT) excitation in Pt dimers with different bridging ligands. Both complexes exhibit Pt–Pt bond formation with a decrease in Pt–Pt distance of ∼ 0.25 Å and coherent vibrational wavepackets (CVWPs) encoded in the Pt–Pt contraction of both dimers. However, the complexes exhibit different time-dependent evolution of their CVWPs. Analysis of interference patterns between different CVWPs is used to track the trajectory across the excited-state surfaces. Furthermore, this work demonstrates that the interference between CVWPs in ultrafast TR-WAXS encodes indirect information regarding electronic excited-states to reveal the Pt dimer bridge-dependent ISC mechanism.

Computational chemistry↗
DOE OSTI2026

Tea ( Camellia sinensis ) Extract-Mediated Green Synthesis of Co 3 O 4 and Co 3 O 4 @Graphene Nanocomposites for Multifunctional Applications in Pollutant Degradation, Sensing, and Energy Storage

A novel solution-mixing method was proposed to synthesize Co 3 O 4 /graphene nanocomposites (Co 3 O 4 @Gr) using a green tea leaf (Camellia sinensis) extract as the reducing agent. XRD analysis shows that the as-prepared Co 3 O 4 @Gr exhibits a cubic spinel crystal structure. From morphological analysis, the obtained Co 3 O 4 NS forms spherical clusters that are uniformly distributed on the graphene surface. FT-IR and Raman analyses confirmed the strong molecular and vibrational interactions between the Co 3 O 4 NS and Gr. The suppressed PL intensity peak of the Co 3 O 4 @Gr NCs indicated significant inhibition in the recombination of charge carriers between the hybrid orbitals within the composites. As a result, the catalytic efficiency of Co 3 O 4 @Gr NCs increased to 80% compared to pristine Co 3 O 4 , which exhibited only 45% efficiency against methylene blue (MB) dye. Moreover, the as-prepared NCs exhibited a detection limit of 0.01−224 μM, demonstrating a superior low-DPA detection with high sensitivity. The Co 3 O 4 @Gr/GCE exhibits admirable selectivity for various pesticides, fungicides, and metal ions, with outstanding reproducibility and stability. From electrochemical investigations, the highest specific capacitance values of the as-synthesized Co 3 O 4 @Gr were 349 F/g at a scan rate of 5 mV/s and 158 F/g at a current density of 1 A/g.

Capacitors↗
DOE OSTI2021

A Theory-Guided X-ray Absorption Spectroscopy Approach for Identifying Active Sites in Atomically Dispersed Transition-Metal Catalysts

Atomically dispersed supported metal catalysts offer new properties and the benefits of maximized metal accessibility and utilization. The characterization of these materials, however, remains challenging. Using atomically dispersed platinum supported on crystalline MgO (chosen for its well-defined bonding sites) as a prototypical example, we demonstrate in this work how systematic density functional theory calculations for assessing all the potentially stable platinum sites, combined with automated analysis of extended X-ray absorption fine structure (EXAFS) spectra, leads to unbiased identification of isolated, surface-enveloped platinum cations as the catalytic species for CO oxidation. The catalyst has been characterized by atomic-resolution imaging and EXAFS and high-energy resolution fluorescence detection X-ray absorption near edge spectroscopy. The proposed platinum sites are in agreement with experiment. This theory-guided workflow leads to rigorously determined structural models and provides a more detailed picture of the structure of the catalytically active site than what is currently possible with conventional EXAFS analyses. As this approach is efficient and agnostic to the metal, support, and catalytic reaction, we posit that it will be of broad interest to the materials characterization and catalysis communities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Emergent Trends Complicate the Interpretation of the United States Drought Monitor (USDM)

Abstract Effective drought management must be informed by an understanding of whether and how current drought monitoring and assessment practices represent underlying nonstationary climate conditions, either naturally occurring or forced by climate change. Here we investigate the emerging climatology and associated trends in drought classes defined by the United States Drought Monitor (USDM), a weekly product that, since 2000, has been used to inform drought management in the United States. The USDM classifies drought intensity based in part on threshold percentiles in key hydroclimate quantities. Here we assess how those USDM‐defined drought threshold percentiles have changed over the last 23 years, examining precipitation, runoff, soil moisture (SM), terrestrial water storage (TWS), vapor pressure deficit (VPD), and near‐surface air temperature. We also assess underlying trends in the frequency of drought classifications across the U.S. Our analysis suggests that the frequency of drought class occurrence is exceeding the threshold percentiles defined by the USDM in a number of regions in the United States, particularly in the American West, where the last 23 years have emerged as a prolonged dry period. These trends are also reflected in percentile‐based thresholds in precipitation, runoff, SM, TWS, VPD, and temperature. Our results emphasize that while the USDM appears to be accurately reflecting observed nonstationarity in the physical climate, such trends raise critical questions about whether and how drought diagnosis, classification, and monitoring should address long‐term intervals of wet and dry periods or trends.

Geology↗
DOE OSTI2025

Contemporary income inequality outweighs historic redlining in shaping intra-urban heat disparities in Los Angeles

The roots of intra-urban heat disparity in the U.S. often trace back to historical discriminatory practices, such as redlining, which categorized neighborhoods by race or ethnicity. In this study, we compare the relative impacts of historic redlining and current income inequality on thermal disparities in Los Angeles. A key innovation of our work is the use of land surface temperature data from the ECOSTRESS instrument aboard the International Space Station, enabling us to capture diurnal trends in urban thermal disparities. Our findings reveal that present-day income inequality is a stronger predictor of heat burden than the legacy of redlining. Additionally, land surface temperature disparities exhibit a seasonal hysteresis effect, intensifying during extreme heat events by 5−7 °C. Sociodemographic analysis highlights that African-American and Hispanic populations in historically and economically disadvantaged areas are often the most vulnerable. Our findings suggest that while the legacy of redlining may persist, the present-day heat disparities are not necessarily an immutable inheritance, where targeted investments and interventions can pave the way for a more thermally just future for these communities.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Direct analysis of cotton swipes for plutonium isotope determination by microextraction-ICP-MS

This study demonstrates a method for determining the isotopic composition of low-level (sub-pg) plutonium (Pu) directly from a cotton swipe. Environmental sample (ES) swipes are routinely employed as a tool for monitoring activities in nuclear facilities. Traditional ES swipe analysis, as employed in nuclear safeguards, utilizes laborious ashing, digestion, and chemical separation procedures prior to mass spectrometric (MS) analysis. Here, an innovative sample introduction technique employing a microextraction probe to extract Pu directly from the swipe surface is described. The microextraction probe lowers onto the swipe surface, seals on a small area (8 mm 2 ), and delivers solvent (2% HNO 3 ) to extract actinide material that may be present. The extracted analyte is subsequently directed into a sector field inductively coupled plasma (ICP)-MS for isotope ratio determination. This microextraction-ICP-MS method successfully determined the isotopic composition ( 240 Pu/ 239 Pu and 242 Pu/ 239 Pu) of three Pu certified reference materials (CRM 136, 137, and 138) that were deposited (1 pg) onto ES swipes. The percent relative difference from the certified value, uncorrected for instrumental fractionation, was <2% for the 240 Pu/ 239 Pu ratio on all three CRMs and <10% for the 242 Pu/ 239 Pu ratio on CRM 136 and 138. Here, the percent relative standard deviation, an estimate of the sample-to-sample isotopic precision, was <4% for the 240 Pu/ 239 Pu and <15% for the 242 Pu/ 239 Pu. Method limits of detection were determined, based on measurements of an enriched 244 Pu material, to be ~7 fg. Additionally, a mixed uranium (U) and Pu deposition was made to determine the method's ability to simultaneously extract U and Pu and determine the isotopic composition of both analytes.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Synergistic effects of Pd single atoms and nanoclusters boosting SnO 2 gas sensing performance

Tin(IV) oxide-supported Pd is a promising heterogenous catalyst for CO oxidation relevant for environmental cleanup reactions. In this study, an atomically dispersed Pd catalyst on SnO 2 (ADC Pd/SnO 2 ) hybrid material is successfully synthesized via a straightforward wet chemistry method and is found to exhibit superior performance toward CO sensing. Ex situ EXAFS analysis confirms the formation of single Pd atoms and small Pd nanoclusters stabilized on the SnO 2 (110) surface. Further, the material exhibits high efficiency in generating adsorbed O 2 - as well as high activity in catalyzing CO oxidation at low temperatures, resulting in exceptional sensitivity and selectivity toward CO in comparison to pure SnO 2 and Pd nanoparticles loaded on SnO 2 respectively. In situ FTIR measurements unravel CO adsorption kinetics on ADC Pd/SnO 2 under reaction conditions, and a possible sensing mechanism is put forth in which CO is transformed into CO 2 by reaction with active oxygen species; and concurrently, carbon-related species (bicarbonates and carbonates) are formed and decomposed into CO 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

A variational method for the sheath potential of hypersonic leading edges with space-charge limitations

Electron transpiration cooling for the leading edges (LE) of hypersonic aircraft utilizes thermionic emission; however, space-charge effects limit the electron emission rate, potentially diminishing the efficiency of this cooling mechanism. We develop a variational weak form of the Poisson equation that describes the sheath potential and then numerically solve it using the finite element method. This formulation has two main benefits: (1) the space-charge limit condition can be incorporated as a constraint and (2) it allows for the analysis of three-dimensional geometries with complex boundary conditions. We demonstrate that the current emitted from the surface of an LE is generally a small fraction of the Child–Langmuir limit due to space charge. We then propose several methods to enhance the emitted current from the surface and to boost the cooling effect of thermionic emission. These include increasing the plasma density, applying a negative surface potential, and using fringe fields under suitable geometric conditions. For a LaB6 emitting LE, the total emitted current is shown to be minimal and independent of the temperature of a surface with floating potential. However, when a negative potential is applied and the surface is heated, the emitted current follows the Richardson–Dushman relationship up to a critical temperature, beyond which it remains constant. At an applied surface potential of −5 V, the critical temperature is around 1700 K.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

X-ray diffraction strains in laser-ablated aluminum, nickel, sodium, and invar: Pressures to 475 GPa

Dynamically compressed materials in longitudinal waves are described by two physical models: hydrostatic pressure, with equal, normal, principal stresses or material uniaxially strained in the wave propagation direction. These models are disparate, so experimental comparisons and evaluations are important. Polycrystalline material in a state of hydrostatic pressure will have no eccentricity of x-ray-diffracted Debye–Scherrer rings. A general three-dimensional solution of Bragg diffracted x rays based on principal crystallographic strains in the compression wave was found. The distortion of x-ray diffraction beams has been used for strain measurements; the analysis developed incorporates a strained reciprocal lattice and the incident x-ray beam. Strain-distorted Polanyi surfaces form an annulus of compression with an ellipsoid of revolution in reciprocal space, which is intersected by Ewald's sphere for Bragg diffraction. The in situ measurements for strain describe nanosecond diffraction evaluated using two planes, (hkl) and (h′k′l′), both in the same crystallographic phase. Diffraction from Al, Ni, Na, and Invar quantifies the compression axial strains in these materials: The compression axial ratios are 0.65, 1.05, 0.88, and 1.58 at pressures of 291, 402, 409, and 367 GPa for the respective materials. Crystal structure transformations with homogeneous pressurized stresses, mandating equal normal strains, should not be anticipated to agree with heterogeneous, uniaxially strained, and sheared crystalline phases. Measurements support in-plane strains increasing with pressure, p , in fcc and hcp aluminum as ε 22 = −0.21 p /TPa.

Alloys↗
DOE OSTI2024

A computational analysis of effective R-values of buried ducts – the dynamic performance of buried ducts

Here, this paper evaluates the thermal performance of ducts partially or fully buried in loose-fill attic insulation. The overall thermal resistance between the ducts and the attic is referred to as an effective R-value. This paper shows a strong dependency of assumed attic temperature on the effective R-value. Based on the results, the effective R-value can be about twice as much with an attic temperature of 130 °F [54.4 °C], compared to when the attic temperature is 80 °F [26.7 °C]. Thus, this paper provides a polynomial regression equation based on a large set of simulations to determine the effective R-value of buried ducts depending on attic temperature and whether the HVAC system runs in cooling or heating mode. Further, the work presented in this paper investigated the potential impact of convective airflow within the attic insulation, particularly around the ducts. The analysis was based on computational fluid dynamics (CFD) and indicated that convectional forces are presented around the exterior surface of the ducts, but with negligible impact on the overall heat balance between the duct and the attic space.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Computation of linear MHD instabilities with the multi-region relaxed MHD energy principle

Over the last decade, a variational principle based on a generalisation of Taylor's relaxation, referred to as multi-region relaxed magnetohydrodynamics (MRxMHDs) has been developed. The numerical solutions of the MRxMHD equilibria have been constructed using the Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502). In principle, SPEC could also be established to describe the MRxMHD stability of an equilibrium. In this work, a theoretical framework is developed to relate the second variation of the energy functional to the so-called Hessian matrix, enabling the prediction of MHD linear instabilities of cylindrical plasmas, and is implemented in SPEC. The negative and positive eigenvalues of the Hessian matrix predict the stability of an equilibrium. Verification studies of SPEC stability results with the M3D-C 1 code and the tearing mode $\Delta^{^{\prime}}$ criterion have been conducted for ideal and resistive MHD instabilities, respectively, in a pressureless cylindrical tokamak, and have shown good agreement. Overall, our stability analysis is a critical step towards understanding the MHD stability of three-dimensional MHDs where nested flux surfaces, magnetic islands and stochastic regions co-exist.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗