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DOE OSTI2021

Aerosol Direct Radiative Effects at the ARM SGP and TWP Sites: Clear Skies

The clear-sky aerosol direct radiative effect (DRE) was estimated at the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) and Tropical Western Pacific (TWP) sites. The NASA Langley Fu-Liou radiation model was used with observed inputs including aerosol vertical extinction profile from the Raman lidar; spectral aerosol optical depth (AOD), single-scattering albedo and asymmetry factor from Aerosol Robotic Network; temperature and water vapor profiles from radiosondes; and surface shortwave (SW) spectral albedo from radiometers. A radiative closure experiment was conducted for clear-sky conditions. The mean differences of modeled and observed surface downwelling SW total fluxes were 1 W m-2 at SGP and 2 W m -2 at TWP, which are within observational uncertainty. At SGP, the estimated annual mean clear-sky aerosol DRE is -3.00 W m -2 at the top of atmosphere (TOA) and -6.85 W m -2 at the surface. The strongest aerosol DRE of -4.81 (-10.77) W m -2 at the TOA (surface) are in the summer when AODs are largest. The weakest aerosol DRE of -.28 (-2.77) W m -2 at the TOA (surface) are in November–January when AODs and single-scattering albedos are lowest. At TWP, the annual mean clear-sky DRE is -2.82 W m-2 at the TOA and -10.34 W m -2 at the surface. The strongest aerosol DRE of -5.95 (-22.20) W m -2 at the TOA (surface) are in November (October) due to the biomass burning season’s peak. The weakest aerosol DRE of -0.96 (-4.16) W m -2 at the TOA (surface) are in March (April) when AODs are smallest.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

All-sky aerosol direct radiative effects at the ARM SGP site

All-sky aerosol direct radiative effect (DRE) was estimated for the first time at the Atmospheric Radiation Measurement Southern Great Plains site using multi-year ground-based observations. The NASA Langley Fu-Liou radiation model was employed. Observed inputs for the radiation model include aerosol and cloud vertical extinction profile from Raman lidar; spectral aerosol optical depth, single-scattering albedo, and asymmetry factor from Aerosol Robotic Network; cloud water content profiles from radars; temperature and water vapor profiles from radiosondes; and surface shortwave spectral albedo from radiometers. A cloudy-sky radiative closure experiment was performed. The relative mean differences between modeled and observed surface downwelling shortwave total fluxes were 6% (7%) for transparent (opaque) cloudy-skies. The estimated annual mean all-sky aerosol DRE is -2.13±0.54W m -2 at the top of atmosphere (TOA) and -5.95±0.87 W m -2 at the surface, compared to -3.00±0.58 W m -2 AND -6.85±1.00 W m -2 , respectively, under clear-sky conditions. The seasonal cycle of all-sky aerosol DRE is similar to that of the clear-sky, except with secondary influences of the clouds: The cloud radiative effect is strongest (most negative) in the spring, which reduces the all-sky aerosol DRE. The relative uncertainties in all-sky aerosol DRE due to measurement errors are generally comparable to those in clear-sky conditions except for the aerosol single-scattering albedo. Finally, the TOA all-sky aerosol DRE relative uncertainty due to aerosol single-scattering albedo uncertainty is larger than that in clear-sky, leading to a larger total relative uncertainty. The measurement errors in cloud properties have small effects on the all-sky aerosol DRE.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Time-resolved 3D imaging of two-phase fluid flow inside a steel fuel injector using synchrotron X-ray tomography

The multiphase flow inside a diesel injection nozzle is imaged using synchrotron X-rays from the Advanced Photon Source at Argonne National Laboratory. Through acquisitions performed at several viewing angles and subsequent tomographic reconstruction, in-situ 3D visualization is achieved for the first time inside a steel injector at engine-like operating conditions. The morphology of the internal flow reveals strong flow separation and vapor-filled cavities (cavitation), the degree of which correlates with the nozzle's asymmetric inlet corner profile. Micron-scale surface features, which are artifacts of manufacturing, are shown to influence the morphology of the resulting liquid-gas interface. The data obtained at 0.1 ms time resolution exposes transient flow features and the flow development timescales are shown to be correlated with in-situ imaging of the fuel injector's hydraulically-actuated valve (needle). As more than 98.5% of the X-ray photon flux is attenuated within the steel injector body itself, we are posed with a unique challenge for imaging the flow within. Time-resolved imaging under these low-light conditions is achieved by exploiting both the refractive and absorptive properties of X-ray photons. The data-processing strategy converted these images with a signal-to-noise ratio of similar to 10 into a meaningful dataset for understanding internal flow and cavitation in a nozzle of diameter 200 mu m enclosed within 1-2 millimeters of steel.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Charge Transport and Space-Charge Formation in Cd 1 - x Zn x Te 1 - y Se y Radiation Detectors

The electron- and hole-transport properties in cadmium zinc telluride selenide (CZTS) crystals are studied using a laser-induced transient-current technique with pulsed and dc bias. The internal electric field profile and velocity of surface recombination are determined by Monte Carlo simulations of electron and hole transient currents combined with a numerical solution of the drift-diffusion equation coupled with Poisson’s equation. Electron and hole drift mobilities of μe = 830 cm 2 /Vs and μh = 40 cm 2 /Vs, respectively, are determined. We also develop a simple technique for evaluating surface recombination directly from measured current waveforms without the need for numerical simulation. The good quality of the prepared detector at pulsed bias, with electron- and hole-mobility-lifetime products of (μτ)e = 1.9 × 10 -3 cm 2 /V and (μτ)h = 1.4 × 10 -4 cm 2 /V, respectively, are observed. The formation of a positive space charge, originating from hole injection combined with a recombination level, is found. We observe a significant position dependence of the lifetime of electrons and holes in dc bias due to hole injection. The experiment is successfully fitted by a simple model dominated by a single deep recombination level with an energy of E t =E C -0.73eV; concentration of 7.3 × 10 11 cm -3 ; and electron- and hole-capture cross sections of 3.5 × 10 -14 cm 2 and 6.5 × 10 -14 cm 2 , respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Interfacial Characterization of Positive Bias Voltage Degradation in PV Modules

Degradation from high system voltage is a prevailing failure mode in fielded photovoltaic modules, and the degradation mechanism is inherently dependent on the bias polarity. Here we report the effects of positive bias. Modules under positive bias demonstrated a significant photocurrent loss caused by two routes. First, delamination and discoloration of the silicon nitride layer, leading to optical loss determined by reflectance measurements. Second, chemical discoloration of the cell gridlines and encapsulant (EVA), which is linked to an electrochemical reaction at the silver electrodes. Chemical compositional analysis using X-ray photoemission spectroscopy demonstrated that the discoloration is attributed to Ag 2 S and/or Ag 2 O. Evidence of Ag ion migration from the cell grid into the encapsulant is observed after shallow depth profiling on the EVA surface. However, Ag was not detected at the EVA/glass interface, inferring limited Ag ion transport through the EVA. The source of sulfur is believed to be ambient air, which diffused into the module through the breathable backsheet.

characterization↗

DOE OSTI2021

No ordinary proteins: Adsorption and molecular orientation of monoclonal antibodies

The interaction of monoclonal antibodies (mAbs) with air/water interfaces plays a crucial role in their overall stability in solution. We aim to understand this behavior using pendant bubble measurements to track the dynamic tension reduction and x-ray reflectivity to obtain the electron density profiles (EDPs) at the surface. Native immunoglobulin G mAb is a rigid molecule with a flat, “Y” shape, and simulated EDPs are obtained by rotating a homology construct at the surface. Comparing simulations with experimental EDPs, we obtain surface orientation probability maps showing mAbs transition from flat-on Y-shape configurations to side-on or end-on configurations with increasing concentration. The modeling also shows the presence of β sheets at the surface. Overall, the experiments and the homology modeling elucidate the orientational phase space during different stages of adsorption of mAbs at the air/water interface. These finding will help define new strategies for the manufacture and storage of antibody-based therapeutics.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Bayesian Inference for the Seismic Moment Tensor Using Regional Waveforms and Teleseismic- P Polarities with a Data-Derived Distribution of Velocity Models and Source Locations

The largest source of uncertainty in any source inversion is the velocity model used in the transfer function that relates observed ground motion to the seismic moment tensor. However, standard inverse procedure often does not quantify uncertainty in the seismic moment tensor due to error in the Green’s functions from uncertain event location and Earth structure. Here, we incorporate this uncertainty into an estimation of the seismic moment tensor using a data-derived distribution of velocity models based on complementary geophysical data sets, including thickness constraints, velocity profiles, gravity data, surface-wave group velocities, and regional body-wave travel times. The data-derived distribution of velocity models is then used as a prior distribution of Green’s functions for use in Bayesian inference of an unknown seismic moment tensor using regional and teleseismic-P waveforms. The use of multiple data sets is important for gaining resolution to different components of the moment tensor. The combined likelihood is estimated using data-specific error models and the posterior of the seismic moment tensor is estimated and interpreted in terms of the most probable source type.

58 GEOSCIENCES↗

DOE OSTI2020

A Bezier Curve Informed Melt Pool Geometry to Model Additive Manufacturing Microstructures Using SPPARKS

Additive manufacturing is a transformative technology with the potential to manufacture designs which traditional subtractive machining methods cannot. Additive manufacturing offers fast builds at near final desired geometry; however, material properties and variability from part to part remain a challenge for certification and qualification of metallic components. AM induced metallic microstructures are spatially heterogeneous and highly process dependent. Engineering properties such as strength and toughness are significantly affected by microstructure morphologies resulting from the manufacturing process Linking process parameters to microstructures and ultimately to the dynamic response of AM materials is critical to certifying and qualifying AM built parts and components and improving the performance of AM materials. The AM fabrication process is characterized by building parts layer by layer using a selective laser melt process guided by a computer. A laser selectively scans and melts metal according to a designated geometry. As the laser scans, metal melts, fuses, and solidifies forming the final geometry in a layerwise fashion. As the laser heat source moves away, the metal cools and solidifies forming metallic microstructures. This work describes a microstructure modeling application implemented in the SPPARKS kinetic Monte Carlo computational framework for simulating the resulting microstructures. The application uses Bzier curves and surfaces to model the melt pool surface and spatial temperature profile induced by moving the laser heat source; it simulates the melting and fusing of metal at the laser hot spot and microstructure formation and evolution when the laser moves away. The geometry of the melt pool is quite flexible and we explore effects of variances in model parameters on simulated microstructures.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Transmitted wave measurements in cold sprayed materials under dynamic compression

Spray-formed materials have complex microstructures which pose challenges for microscale and mesoscale modeling. To constrain these models, experimental measurements of wave profiles when subjecting the material to dynamic compression are necessary. The use of a gas gun to launch a shock into a material is a traditional method to understand wave propagation and provide information of time-dependent stress variations due to complex microstructures. This data contains information on wave reverberations within a material and provides a boundary condition for simulation. Here we present measurements of the wavespeed and wave profile at the rear surface of tantalum, niobium, and a tantalum/niobium blend subjected to plate impact. Measurements of the Hugoniot elastic limit are compared to previous work and wavespeeds are compared to longitudinal sound velocity measurements to examine wave damping due to the porous microstructure.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Impact of Seasonal Snow-Cover Change on the Observed and Simulated State of the Atmospheric Boundary Layer in a High-Altitude Mountain Valley

The structure and evolution of the atmospheric boundary layer (ABL) under clear-sky fair weather conditions over mountainous terrain is dominated by the diurnal cycle of the surface energy balance and thus strongly depends on surface snow cover. We use data from three passive ground-based infrared spectrometers deployed in the East River Valley in Colorado's Rocky Mountains to investigate the response of the thermal ABL structure to changes in surface energy balance during the seasonal transition from low to high snow cover. Temperature profiles were retrieved from the infrared radiances using the optimal estimation physical retrieval Tropospheric Remotely Observed Profiling via Optimal Estimation. A nocturnal surface inversion formed in the valley during clear-sky days, which was subsequently mixed out during daytime with the development of a convective boundary layer when snow cover was low. Over high snow cover, a very shallow convective boundary layer formed, above which the inversion persisted through the daytime hours. We compare these observations to NOAA's operational High-Resolution-Rapid-Refresh model and find large warm biases on clear-sky days resulting from the model's inability to form strong nocturnal inversions and to maintain the stable stratification in the valley during daytime when there was snow on the ground. We suggest several factors contributing to the large model errors. These are (a) the inability of the model to represent well-developed thermally driven flows likely due to the too coarse horizontal grid spacing (3 km), (b) too much convective mixing during daytime, and (c) too strong vertical coupling between the valley atmosphere and the free troposphere.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Directly resolving surface vs. lattice self-diffusion in iron at the nanoscale using in situ atom probe capabilities

Surface self-diffusion studies on metals under elevated reaction conditions are limited, as it is inherently challenging to unambiguously follow atomic transport across highly-reactive surfaces. Here, quantitative and mechanistic insight into thermally induced atomic transport processes in bcc α-iron at the sub-nanometer level was achieved using isotopic tracer techniques coupled with in situ atom probe tomography (APT) capabilities. Specifically, using a reactor directly connected to the APT, needle-shaped specimens fabricated from epitaxial thin films with an embedded 57 Fe tracer layer were annealed in Ar at 500 °C and 350 °C for 1 hour. Furthermore, the tracer was positioned at various depths in the APT specimen by field evaporation, enabling targeted and simultaneous analysis of lattice and surface diffusion. 57 Fe concentration profiles reveal lattice self-diffusion occurs at 500 °C on the order of ~7 – 9 monolayers, while lattice diffusion is not resolvable at 350 °C. Considerable surface transport was, however, observed at both conditions, where atomic transport over the specimen surface led to the formation of a thin (≤1 nm), isotopically-intermixed layer at the surface. Further, the observed isotopic redistributions at 500 °C were convoluted by additional processes occurring in the subsurface, such as atomic intermixing in correlation with lattice diffusion. However, surface diffusion was determined to be the primary transport process at 350 °C and was thereby quantified. Ultimately, these results demonstrate the significance of surface self-diffusion as a short circuit pathway. More broadly, this approach has the potential to provide detailed insight into (self-)diffusion mechanisms across various materials while targeting site-specific reactions under elevated reaction conditions.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Distance-dependent dielectric constant at the calcite/electrolyte interface: Implication for surface complexation modeling

Hypothesis: The electrical double layer formed at the mineral/electrolyte interface is often modeled using mean-field approaches based on a continuum description of the solvent whose dielectric constant is assumed to decrease monotonically with decreasing distance to the surface. In contrast, molecular simulations show that the solvent polarizability oscillates near the surface similar to the water density profile - as shown previously, for example, by Bonthuis et al. (D.J. Bonthuis, S. Gekle, R.R. Netz, Dielectric Profile of Interfacial Water and its Effect on Double-Layer Capacitance, Phys Rev Lett 107(16) (2011) 166102). Here, we showed that molecular and mesoscale pictures agree by spatially averaging the dielectric constant obtained from molecular dynamics simulations over the distances relevant to the mean-field representation. In addition, the values of capacitances used to describe the electrical double layer in Surface Complexation Models (SCMs) of the mineral/electrolyte interface can be estimated using molecularly informed spatially averaged dielectric constants and positions of hydration layers. Experiments: First, we used molecular dynamics simulations to model the calcite 101¯4/electrolyte interface. Next, by using atomistic trajectories, we calculated the distance-dependent static dielectric constant and water density in the direction normal to the. Finally, we applied spatial compartmentalization consistent with the model of parallel-plate capacitors connected in series to estimate SCM capacitances. Findings: Computationally expensive simulations are required to determine the dielectric constant profile of interfacial water near the mineral surface. On the other hand, water density profiles are readily assessable from much shorter simulation trajectories. Our simulations confirmed that dielectric and water density oscillations at the interface are correlated. Here, we parametrized linear regression models to estimate the dielectric constant directly from the local water density. This is a significant computational shortcut compared to slowly converging calculations relying on total dipole moment fluctuations. The amplitude of the interfacial dielectric constant oscillation can exceed the dielectric constant of the bulk water, suggesting an ice-like frozen state, but only if there are no electrolyte ions. The interfacial accumulation of electrolyte ions causes a decrease in the dielectric constant due to the reduction of water density and re-orientation of water dipoles in ion hydration shells. Finally, we show how to use the computed dielectric properties to estimate SCM's capacitances.

58 GEOSCIENCES↗

DOE OSTI2022

Trivalent ion overcharging on electrified graphene

We report the structure of the electrical double layer (EDL) formed near graphene in aqueous environments strongly impacts its performance for a plethora of applications, including capacitive deionization. In particular, adsorption and organization of multivalent counterions near the graphene interface can promote nonclassical behaviors of EDL including overcharging followed by co-ion adsorption. In this paper, we characterize the EDL formed near an electrified graphene interface in dilute aqueous YCl 3 solution using in situ high resolution x-ray reflectivity (also known as crystal truncation rod) and resonant anomalous x-ray reflectivity (RAXR). These interface-specific techniques reveal the electron density profiles with molecular-scale resolution. We find that yttrium ions (Y 3+ ) readily adsorb to the negatively charged graphene surface to form an extended ion profile. This ion distribution resembles a classical diffuse layer but with a significantly high ion coverage, i.e., 1 Y 3+ per 11.4 ± 1.6 Å 2 , compared to the value calculated from the capacitance measured by cyclic voltammetry (1 Y 3+ per ~240 Å 2 ). Such overcharging can be explained by co-adsorption of chloride that effectively screens the excess positive charge. The adsorbed Y 3+ profile also shows a molecular-scale gap (≥ 5 Å) from the top graphene surfaces, which is attributed to the presence of intervening water molecules between the adsorbents and adsorbates as well as the lack of inner-sphere surface complexation on chemically inert graphene. We also demonstrate controlled adsorption by varying the applied potential and reveal consistent Y 3+ ion position with respect to the surface and increasing cation coverage with increasing the magnitude of the negative potential. This is the first experimental description of a model graphene-aqueous system with controlled potential and provides important insights into the application of graphene-based systems for enhanced and selective ion separations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Relative Contributions of Surface Parcel and Atmospheric Environment to Convective Potential during Interstorm Periods

Convective instability is affected by both surface heat fluxes into near-surface air parcels and the atmospheric profile encountered as these air parcels are lifted aloft. In this study, we investigate the evolution of buoyancy experienced by surface-based parcels, taking interstorm soil moisture drydowns as fundamental time periods. We use profile observations of atmospheric temperature and humidity from ground-based passive remote sensing and in situ observations available at the U.S. Department of Energy Atmospheric Radiation Measurement Southern Great Plains site in Oklahoma, United States, and examine drydown events during the warm seasons from 2017 to 2022. Results reveal new insights on the emergence and growth of convective available potential energy (CAPE) during drydowns. We observe that the peak convective potential appears in the afternoon and grows in the midtroposphere (68% of 66 drydown events), with the largest CAPE values toward the end of the drydown event. We also find that the near-surface parcel contributes more to the evolution of CAPE than the atmospheric environment (86% of drydown events). These findings highlight the importance of surface heat fluxes and moisture availability from surface-based parcels in modulating the evolution of atmospheric conditions favorable for convection, underscoring the interplay between surface processes and atmospheric dynamics in driving convective instability.

Atmosphere-land interaction↗

DOE OSTI2023

SURFACE ROUGHNESS REDUCTION AND PERFORMANCE OF Nb3Sn FILM FOR SRF APPLICATIONS

Nb3Sn offers better RF performance (Q and Eacc) than Nb at any given temperature because of its superior superconducting properties. The potential deployment of Nb3Sn-coated SRF cavities at 4 K, delivering similar performance to that of Nb cavities at 2 K, will be a transformational technology to enable new classes of SRF accelerator applications. A clean and smooth surface can enhance the performance of the Nb3Sn-coated cavity, typically, the attainable acceleration gradient. The reduction of surface roughness is often linked with a correlative reduction in average coating thickness and grain size. A new approach to enhance the nucleation centers using the pre-deposition of Sn on Nb is introduced for surface roughness reduction. Besides Sn supply's careful tuning, the temperature profiles were varied to engineer the coating surface with reduced roughness as low as ~40 nm in 20 µm × 20 µm AFM scans, one-third that of the typical coating. Electropolishing of coated sample shows surface a clear surface smoothening. A few sets of coating parameters were used to coat 1.3 GHz sin-gle-cell cavities to understand the effects of roughness variation on the RF performance. This presentation discusses ways to reduce surface roughness with results from a systematic analysis of the samples and Nb3Sn-coated single-cell cavities.

Pudasaini, Uttar↗

DOE OSTI2023

SURFACE ROUGHNESS REDUCTION AND PERFORMANCE OF Nb3Sn FILM FOR SRF APPLICATIONS

Pudasaini, Uttar↗

DOE OSTI2020

Enhanced Menshutkin S N 2 Reactivity in Mesoporous Silica: The Influence of Surface Catalysis and Confinement

A significant enhancement in the Menshutkin S N 2 reaction between 1-methylimidazole (MeIm) and methyl thiocyanate (MeSCN) is observed when the reaction is confined in the nanoscale silica pores of MCM41 and SBA15. The experiments in the silica pores are conducted without surrounding bulk reaction mixture. The influences of temperature, pore radius, and surface chemistry on the kinetics of the confined reaction are analyzed with time-dependent infrared spectroscopy, molecular dynamics simulations, and ab initio calculations. The rate constant of the pseudo-first order reaction increases with decreasing pore size, and the activation energy is found to decrease by 5.6 kJ/mol in the smallest pore studied (2.8 nm) relative to the bulk reaction. The rate constant dependence on pore size is accurately described by a two-state model in which molecules within the 4.6 Å interfacial layer experience a 2.4-fold rate constant increase relative to those reacting at the bulk rate further away from the interface. The removal of polar silanol groups from the silica surface via passivation with trimethylsilyl chloride results in bulk-like kinetics despite a reduction in the pore diameter, demonstrating the role of silanols as catalytic sites. Here, electronic structure calculations of the energy profile on a model silica surface confirm that silanol groups, particularly those of the vicinal type, can reduce the activation energy and reaction endothermicity through the donation of hydrogen bonds to the reactant, transition state, and product complexes.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Structure of pressure-gradient-driven current singularity in ideal magnetohydrodynamic equilibrium

Abstract Singular currents typically appear on rational surfaces in non-axisymmetric ideal magnetohydrodynamic (MHD) equilibria with a continuum of nested flux surfaces and a continuous rotational transition. These currents have two components: a surface current (Dirac δ -function in flux surface labeling) that prevents the formation of magnetic islands, and an algebraically divergent Pfirsch–Schlüter current density when a pressure gradient is present across the rational surface. On flux surfaces adjacent to the rational surface, the traditional treatment gives the Pfirsch–Schlüter current density scaling as J ∼ 1 / Δ ι , where Δ ι is the difference of the rotational transform relative to the rational surface. If the distance s between flux surfaces is proportional to Δ ι , the scaling relation J ∼ 1 / Δ ι ∼ 1 / s will lead to a paradox that the Pfirsch–Schlüter current is not integrable. In this work, we investigate this issue by considering the pressure-gradient-driven singular current in the Hahm–Kulsrud–Taylor problem, which is a prototype for singular currents arising from resonant magnetic perturbations. We show that not only the Pfirsch–Schlüter current density but also the diamagnetic current density are divergent as ∼ 1 / Δ ι . However, due to the formation of a Dirac δ -function current sheet at the rational surface, the neighboring flux surfaces are strongly packed with s ∼ ( Δ ι ) 2 . Consequently, the singular current density J ∼ 1 / s , making the total current finite, thus resolving the paradox. Furthermore, the strong packing of flux surfaces causes a steepening of the pressure gradient near the rational surface, with ∇ p ∼ d p / d s ∼ 1 / s . In general non-axisymmetric MHD equilibrium, contrary to Grad’s conjecture that the pressure profile is flat around densely distributed rational surfaces, our result suggests a pressure profile that densely steepens around them.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗