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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 55 records · Page 3

Porting CMS Heterogeneous Pixel Reconstruction to Kokkos

Programming for a diverse set of compute accelerators in addition to the CPU is a challenge. Maintaining separate source code for each architecture would require lots of effort, and development of new algorithms would be daunting if it had to be repeated many times. Fortunately there are several portability technologies on the market such as Alpaka, Kokkos, and SYCL. These technologies aim to improve the developer productivity by making it possible to use the same source code for many different architectures. In this paper we use heterogeneous pixel reconstruction code from the CMS experiment at the CERNL LHC as a realistic use case of a GPU-targeting HEP reconstruction software, and report experience from prototyping a portable version of it using Kokkos. The development was done in a standalone program that attempts to model many of the complexities of a HEP data processing framework such as CMSSW. We also compare the achieved event processing throughput to the original CUDA code and a CPU version of it.

Childers, Taylor↗

Magnetic field effects on laser energy deposition and filamentation in magneto-inertial fusion relevant plasmas

We report on experimental measurements of how an externally imposed magnetic field affects plasma heating by kJ-class, nanosecond laser pulses. The experiments reported here took place in gas cells analogous to magnetized liner inertial fusion targets. We observed significant changes in laser propagation and energy deposition scale lengths when a 12T external magnetic field was imposed in the gas cell. We find evidence that the axial magnetic field reduces radial electron thermal transport, narrows the width of the heated plasma, and increases the axial plasma length. Reduced thermal conductivity increases radial thermal gradients. This enhances radial hydrodynamic expansion and subsequent thermal self-focusing. Our experiments and supporting 3D simulations in helium demonstrate that magnetization leads to higher thermal gradients, higher peak temperatures, more rapid blast wave development, and beam focusing with an applied field of 12T.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

An investigation of the very rare ${K}^{+}\to {\pi}^{+}\nu \overline{\nu}$ decay

The NA62 experiment reports an investigation of the ${K}^{+}\to {\pi}^{+}\nu \overline{\nu}$ mode from a sample of ${K}^{+}$ decays collected in 2017 at the CERN SPS. The experiment has achieved a single event sensitivity of (0.389 ± 0.024) × 10 -10 , corresponding to 2.2 events assuming the Standard Model branching ratio of (8.4 ± 1.0) × 10 -11 . Two signal candidates are observed with an expected background of 1.5 events. Combined with the result of a similar analysis conducted by NA62 on a smaller data set recorded in 2016, the collaboration now reports an upper limit of 1.78 × 10 -10 for the ${K}^{+}\to {\pi}^{+}\nu \overline{\nu}$ branching ratio at 90% CL. This, together with the corresponding 68% CL measurement of (${0.48}_{-0.48}^{+0.72}$) × 10 -10 , are currently the most precise results worldwide, and are able to constrain some New Physics models that predict large enhancements still allowed by previous measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Ionization by XFEL radiation produces distinct structure in liquid water

In the warm dense matter (WDM) regime, where condensed, gas, and plasma phases coexist, matter frequently exhibits unusual properties that cannot be described by contemporary theory. Experiments reporting phenomena in WDM are therefore of interest to advance our physical understanding of this regime, which is found in dwarf stars, giant planets, and fusion ignition experiments. Using 7.1 keV X-ray free electron laser radiation (nominally 5×10 5 J/cm 2 ), we produced and probed transient WDM in liquid water. Wide-angle X-ray scattering (WAXS) from the probe reveals a new ~9 Å structure that forms within 75 fs. By 100 fs, the WAXS peak corresponding to this new structure is of comparable magnitude to the ambient water peak, which is attenuated. Simulations suggest that the experiment probes a superposition of two regimes. In the first, fluences expected at the focus severely ionize the water, which becomes effectively transparent to the probe. In the second, out-of-focus pump radiation produces O 1+ and O 2+ ions, which rearrange due to Coulombic repulsion over 10 s of fs. Our simulations account for a decrease in ambient water signal and an increase in low-angle X-ray scattering but not the experimentally observed 9 Å feature, presenting a new challenge for theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Comparing photosynthetic light harvesting of single photons and pseudothermal light under ultraweak illumination

Photosynthesis in vivo is driven by sunlight, an ultraweak incoherent thermal source. However, most experiments and theories have studied photosynthetic light harvesting driven by strong coherent laser sources. The quantum states of light are characterized by their photon statistics, in addition to classical properties such as intensity and frequency spectrum. Here, we report experiments that investigate how photon statistics affect a natural photosynthetic system and vice versa. We directly compare how single photons and pseudothermal light from spontaneous parametric down-conversion drive light harvesting in the light-harvesting 2 complex from a purple bacterium. We find that the fluorescence lifetime and quantum efficiency are unchanged while the fluorescence photon statistics are markedly different, resembling that of the incident light, implying that the dynamics do not fundamentally modify the photon statistics. This represents a step toward clarification of the similarities and differences between photosynthetic light harvesting in laboratory and in natural sunlight conditions.

Li, Quanwei [University of California, Berkeley, C↗

AIF for Vis (Active Inference for simulating human interpretation of data visualization) [SWR-26-084]

AIF for Vis contains the Active Inference models and analysis scripts used to study a simple visualization-interpretation task: estimating the average value of two bars in a bar chart. The work is a proof of concept for translating hypothesized cognitive strategies into executable, inspectable process models. We implement two idealized strategies inspired by dual-process accounts of visualization-aided decision making: *Fast model: a compressed, heuristic strategy that estimates the visual midpoint of the two bars and maintains a single belief over their average. *Slow model: a sequential, analytic strategy that estimates the two bar heights separately and maintains them in working memory before computing an average. Both models use a common Active-Inference-inspired framework for sequential perception, belief updating, action selection, and reporting. Their different internal representations produce distinct predicted vulnerabilities: *the Fast model is more susceptible to tick-salience bias; *the Slow model is more susceptible to working-memory decay. The repository includes the model implementations, scripts used for the experiments reported in the paper, precomputed trial-level results, and plotting scripts.

Goldwyn, Harrison [National Laboratory of the Rock↗

First principles modeling of polymer encapsulant degradation in Si photovoltaic modules

An outstanding issue in the longevity of photovoltaic (PV) modules is the accelerated degradation caused by the presence of moisture. Moisture leads to interfacial instability, de-adhesion, encapsulant decomposition, and contact corrosion. However, experimental characterization of moisture in PV modules is not trivial and its impacts can take years or decades to establish in the field, presenting a major obstacle to designing high-reliability modules. First principles calculations provide an alternative way to study the ingress of water and its detrimental effect on the structure and decomposition of the polymer encapsulant and interfaces between the encapsulant and the semiconductor, the metal contacts, or the dielectric layer. Here, we use density functional theory (DFT) computations to model single chain, crystalline and cross-linked structures, infrared (IR) signatures, and degradation mechanisms of ethylene vinyl acetate (EVA), the most common polymer encapsulant used in Si PV modules. IR-active modes computed for low energy EVA structures and possible decomposition products match well with reported experiments. The EVA decomposition energy barriers computed using the Nudged Elastic Band (NEB) method show a preference for acetic acid formation as compared to acetaldehyde, are lowered in the presence of a water solvent or hydroxyl ion catalyst, and match well with reported experimental activation energies. This systematic study leads to a clear picture of the hydrolysis-driven decomposition of EVA in terms of energetically favorable mechanisms, possible intermediate structures, and IR signatures of reactants and products.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mineral Scale Formation during Crossflow Reverse Osmosis at Constant Flux and Constant Transmembrane Pressure Conditions

Mineral scale formation on membrane surfaces is a significant challenge in reverse osmosis water purification. Laboratory fouling experiments are typically run such that the transmembrane pressure (TMP) is fixed, and the permeate flux decreases over time as scales accumulate on the membrane surface. However, this change in flux means that the hydrodynamic conditions at the membrane surface are continuously changing, which could affect crystallization and foulant deposition processes. Operating under constant permeate flux conditions, in contrast, is advantageous because it keeps the hydrodynamic conditions relatively consistent, making it possible to compare how membrane properties (e.g., surface chemistry) affect fouling propensity. Industrial reverse osmosis operations are not run strictly in either constant TMP or constant flux mode; while they may start at a constant TMP, feed pressure may be periodically adjusted to maintain permeate water production within a specified range. Here, the scarcity of constant permeate flux reverse osmosis scaling experiments reported in the literature frustrates efforts to compare membrane fouling processes under constant TMP and constant flux conditions. For the first time, the evolution of the fouling layer resistance was compared as a function of cumulative permeate volume per membrane area during constant TMP and constant flux reverse osmosis filtrations. Scaling experiments were conducted by challenging commercial reverse osmosis membranes with a model feed solution nearly saturated with calcium sulfate dihydrate (gypsum). At low fluxes, the increase in fouling layer resistance was quantitatively similar for the two operational modes. In contrast, at high fluxes, the fouling layer resistance increased more rapidly in constant flux filtration than in constant TMP filtration. The mechanism of scale formation in constant TMP and constant flux operation was self-limiting and self-reinforcing, respectively.

36 MATERIALS SCIENCE↗

Exploring the Neutron Substructure with Advanced Polarized Helium-3 Targets (Or: How I Learned to Stop Worrying and Love Spectroscopy)

As we seek to understand the smallest, physical aspects of our universe, we cannot simply rely on our senses to probe the world around us as we did in the past. The smallest physical elements of our universe behave in strange, probabilistic ways and are completely invisible to the naked eye/ear/etc. So, we design clever experiments (such as scattering experiments) to probe these minute realms. Then, just as with the larger, observable world, we devise models and equations to describe what we think is happening. Due to the nature of the physical universe at the quantum scale and with the aid of symmetries such as Lorentz invariance, we can write down equations that describe the scattering, but the expressions contain functions, which we call ?form factors? and ?structure functions?, that we cannot compute from first principles. We can, however, formulate models that make predictions for these functions. By comparing our predictions with the observed data, we can gain insight into the validity of our models and thus a better physical understanding of what is happening at these minuscule scales. Studying the constituents inside of the nucleus of an atom adds another layer of difficulty if we can?t remove those components from the nucleus. This is the case with the neutron. When not bound in the nucleus with protons and other neutrons, the neutron will decay into a proton after about 15 minutes. So, we?re forced to study the neutron while it is still bound in the nucleus of an atom such as helium-3 (3He). For the last 1,000 years (rounding up), our group has developed high quality, polarized 3He targets made of an aluminosilicate glass. These targets are made in order to perform experiments at Jefferson Lab (JLab), experiments which let us determine the form factors and structure functions of the neutron by scattering polarized electrons from polarized neutrons (or rather polarized 3He). The specific experiments reported on in this thesis push the bounds of our understanding of the internal structure of the neutron. Good science is often about pushing experimental techniques to a new level. Toward that goal we study our polarized 3He targets both to advance the technology and to choose the best ones for our experiments. We do this using a process called nuclear magnetic resonance (NMR) to gauge the maximum polarization of a target and how fast the polarization decays with time. While these tests primarily provide us information that make analysis of our experimental scattering data possible, they also let us determine whether or not a target-cell is useful or even, dare I say, of spectacular quality. Our latest targets utilize a novel convection design allowing 3He to be polarized and quickly moved in front of the electron-beam, making it possible to use larger targets with higher electron-beam currents than ever before. This means more electrons scatter and we get more data. And by studying our targets in detail prior to using them in our experiments, we have found techniques to take effects which could have been detrimental to target quality and turn them to our advantage! It?s a real case of making lemonade out of lemons. We also use laser spectroscopy to study the absorption lines of alkali-metals in the target (potassium and rubidium, specifically). We add these alkali-metals to our target to facilitate polarizing the 3He. We can use the measurement of these pressure broadened absorption lines to determine the 3He density inside of the target with great precision. Historically, we understood the width of these lines would be dependent on the temperature of the target. Specifically, if I raise the temperature, the width should get bigger. I found that was not the case, which was very confusing at first, though very exciting now that I realize the data are self-consistent and suggestive of unexpected behavior. This thesis details the development of high quality, glass, polarized 3He targets for the 2020 An 1 /dn 2 and 2023 Gn E experiments, which utilized the first 3He convection targets and broke records in target quality. This thesis also covers the initial development of metal windows for the next-generation of 3He target-cells. Finally, this thesis documents the temperature dependence of the width of potassium (K) and rubidium (Rb) absorption lines as measured with laser spectroscopy.

Jantzi, Christopher↗

Uranium–Molybdenum Alloy Critical Experiments for the Design of the Health Physics Research Reactor

Clean critical experiments with a uranium-molybdenum alloy (average of 10.1616 wt. % Mo with a density of 17.08 g/cm 3 ) were performed at the Oak Ridge Critical Experiments Facility in 1961 to support the design of the Health Physics Research Reactor (HPRR). The HPRR was similar to the Godiva burst reactor at Los Alamos National Laboratory and was designed to produce 50 microseconds burst of 10 17 fission pulses of radiation for dosimetry measurements, initially in support of the determination of the doses from the nuclear detonations in Japan during World War II. These experiments reported here were used to verify the calculational methods used to design the HPRR. These delayed critical measurements were:1) a solid unreflected and unmoderated 8-in.-dimeter U-Mo cylinder, 2) an unmoderated and unreflected annulus with 8-in.-outside diameter, 2-in.-inside diameter cylinder with a central void, 3) an unmoderated and unreflected annulus with 8-in.-outside diameter, 2-in.-inside diameter cylinder with a central void filled with stainless steel, 4) Same as 3) but with 3-in-thick Plexiglas reflector on top with and without cadmium between the reflector and the U-Mo alloy assembly with steel in the center, and 5) an unmoderated and unreflected annulus which was a modification of the second but with the lower 5 inches of the central hole enlarged to 3.5 in. with various reflector conditions. The reflector conditions were: 1-in.-thick Plexiglas on all outer surfaces-void in the center; 1-in.-thick Plexiglas on all outer surfaces-Plexiglas in the center; 2-in.- thick Plexiglas on radial surface-void in the center; 6-in.-thick Plexiglas on the bottom only-Plexiglas in the center; and 6-in.-thick Plexiglas on bottom, 1-in.-thick on top and on the lower 8.25-cm.-section of the radial surface-void in the center. For some of these reflector conditions 0.025-cm.thick cadmium was located between the reflector and the U-Mo alloy. The uranium contained 93.17 wt. % 235 U. Reflection was a safety concern for this unmoderated and unreflected reactor and reduction of reflection effects was also investigated by insertion of neutron absorber around the U-Mo alloy. The stainless steel 304 contained 18% nickel and 8% chromium and the rest iron. The reflector material was a methacrylate plastic (Plexiglas) containing 5.8 x 10 22 atoms/cm 3 of hydrogen and 3.6 x 10 22 atoms/cm 3 of carbon with a density of 1.20 g/cm 3 . The purpose of this report is to document the experimental information for the measurements performed so that at a later date researchers could perform the required uncertainty and calculational analyses and documentation to use these data for an International Nuclear Criticality Safety Benchmark Program (ICSBEP) or a EURATON Nuclear Energy Agency (NEA) benchmark. The data from the experiments described should be acceptable for use as criticality safety benchmark experiments for the ICSBEP and the NEA nuclear criticality safety benchmark program, once the uncertainty analysis is completed. Based on previous ICSBEP benchmarks with this enriched uranium metal at ORCEF, the uncertainties in k eff could be as low as ±0.0002 for some configurations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

On the competitive antagonism effect in combined chloride-sulfate attack: A numerical exploration

Highlights: • A chemo-physical-mechanical method based on thermodynamic modelling is implemented. • The contradicting findings from reported experiments are numerically explored. • The competitive antagonism effect is time-dependent rather than a conclusive term. • The competitive antagonism effect is quantifiable with a novel assessment criterion. It is of tremendous difficulty to draw a conclusive verdict on the complex process of mutual interference regarding the combined chloride-sulfate attack on concrete, where many have explored the topic, but contradicting results have been reported. In this paper, by taking advantages of the chemo-physical-mechanical method, based on the robust technique of thermodynamic modelling, the competitive antagonism effect in combined chloride-sulfate attack is investigated. Firstly, a range of reported tests are numerically modelled to demonstrate the effectiveness of the employed method in interpreting those opposing and diverse experimental outcomes. More importantly, a fresh conjecture incorporating a novel assessment criterion for the competitive antagonism effect is proposed and supported through a carefully designed illustrative example. Based on the numerical exploration, unique findings and implications for future engineering practices are revealed.

36 MATERIALS SCIENCE↗

Measurement of the very rare K+ → $ {\pi}^{+}\nu \overline{\nu} $ decay

The NA62 experiment reports the branching ratio measurement BR K + → π + ν ν ¯ = 10.6 - 3.4 + 4.0 stat ± 0.9 syst × 10 - 11 at 68% CL, based on the observation of 20 signal candidates with an expected background of 7.0 events from the total data sample collected at the CERN SPS during 2016–2018. This provides evidence for the very rare K + → π + ν ν ¯ decay, observed with a significance of 3.4 σ . The experiment achieves a single event sensitivity of (0 . 839 ± 0 . 054) × 10 - 11 , corresponding to 10.0 events assuming the Standard Model branching ratio of (8 . 4 ± 1 . 0) × 10 - 11 . This measurement is also used to set limits on BR( K + → π + X ), where X is a scalar or pseudo-scalar particle. Details are given of the analysis of the 2018 data sample, which corresponds to about 80% of the total data sample.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Photoelectrochemical Proton-Coupled Electron Transfer of TiO 2 Thin Films on Silicon

TiO 2 thin films are often used as protective layers on semiconductors for applications in photovoltaics, molecule–semiconductor hybrid photoelectrodes, and more. Experiments reported here show that TiO 2 thin films on silicon are electrochemically and photoelectrochemically reduced in buffered acetonitrile at potentials relevant to photoelectrocatalysis of CO 2 reduction, N 2 reduction, and H 2 evolution. On both n-type Si and irradiated p-type Si, TiO 2 reduction is proton-coupled with a 1e – :1H + stoichiometry, as demonstrated by the Nernstian dependence of the Ti 4+/3+ E 1/2 on the buffer pK a . Experiments were conducted with and without illumination, and a photovoltage of ∼0.6 V was observed across 20 orders of magnitude in proton activity. The 4 nm films are almost stoichiometrically reduced under mild conditions. The reduced films catalytically transfer protons and electrons to hydrogen atom acceptors, based on cyclic voltammogram, bulk electrolysis, and other mechanistic evidence. TiO 2 /Si thus has the potential to photoelectrochemically generate high-energy H atom carriers. Characterization of the TiO 2 films after reduction reveals restructuring with the formation of islands, rendering TiO 2 films as a potentially poor choice as protecting films or catalyst supports under reducing and protic conditions. Altogether, this work demonstrates that atomic layer deposition TiO 2 films on silicon photoelectrodes undergo both chemical and morphological changes upon application of potentials only modestly negative of RHE in these media. While the results should serve as a cautionary tale for researchers aiming to immobilize molecular monolayers on “protective” metal oxides, the robust proton-coupled electron transfer reactivity of the films introduces opportunities for the photoelectrochemical generation of reactive charge-carrying mediators.

Electrodes↗

Reactive Transport Modeling of Hydrogen Production from Serpentinization of Olivine

Hydrogen production from serpentinization of ultramafic rocks represents a promising natural pathway for generating carbon-free energy, yet its kinetics and controlling factors remain incompletely understood. A key challenge in advancing serpentinization research lies in the heterogeneity of porosity and permeability in rocks, which leads to nonuniform fluid velocity fields, as well as uncertainties in estimating reactive surface area and identifying appropriate mineral reaction equilibria. Additional complexities arise from the role of dissolved SiO 2 , Fe 2+ /Fe 3+ partitioning, and the limited effect of pH variations within the strongly alkaline regime on hydrogen yields. These challenges hinder straightforward extrapolation from laboratory tests to practical applications of hydrogen production from natural rocks. Here, in this work, we address these questions using a simulation-based reactive transport modeling framework calibrated against controlled laboratory experiments reported elsewhere. The model couples geochemical kinetics, multiphase flow, and mineralogical feedbacks, enabling systematic evaluation of how surface area, dissolved silica concentration, Fe redox state, temperature, and pressure govern serpentinization and H2 generation. We find that surface area exerts the strongest control on reaction rates and hydrogen yields, while Fe 2+ /Fe 3+ ratios act as secondary modulators. Elevated dissolved silica concentrations suppress hydrogen production but accelerate serpentine precipitation, whereas increasing pH beyond 12 within the strongly alkaline regime produces only marginal gains. Finally, we demonstrate that integrating targeted experiments with calibrated simulations offers a powerful and efficient approach for predicting hydrogen yields and assessing parameter trade-offs in industrial-scale applications. This integration can substantially reduce the experimental burden while improving predictive capability, thereby enhancing both the mechanistic understanding and the practical feasibility of hydrogen production from serpentinization.

08 HYDROGEN↗

Isospin dependence of Nucleon-Nucleon Short-range Correlations in Inclusive Scattering with Tritium and Helium-3

The nucleon-nucleon (NN) potential has a strong repulsive core. When a two-nucleon (sub)system falls into this range, they will interact strongly at short distance, and move away from each other with momenta above the Fermi level. This is called the NN Short range Correlations (SRCs). Previous experiments reported a neutron-proton pair (isos inglet) dominance in high-momentum nucleons. In inclusive electron scattering, this np dominance will cause a scaling behavior of cross sections at 1.4 < xbj = Q2/2m? < 2 where the high-momentum nucleons dominate. At Je?erson Lab Hall A we checked this hypothesis with electron Quasi-elastic (QE) scattering on A=3 nuclei systems. Our unique gas cell design made electron-tritium scattering possible for the ?rst time in a decade. The 2H, 3H, and 3He inclusive cross sections at 1 < xbj < 3 were measured in two experiments (E12-11-112 and E12-14-011) with a wide Q2 range (0.4 < Q2 < 3 GeV2). This thesis dis cusses the physics goals, experiment setup, and data analysis of the E12-11-112 experiment. Ratios of 3H/2H, 3He/2H and 3H/3He as well as absolute cross sections are presented at 0.4 < Q2 < 1.8 GeV2. NN SRC plateaus are observed in the cross section ratios at high Q2. The 3H/3He ratio of 0.84±0.01 at NN SRC dominant kinematics indicates a np to pp SRC pair ratio of 2.2±0.2 in A=3 nuclei. That implies a preference in T = 0 isospin singlet con?guration. No plateaus are observed at xbj > 2.

Li, Shujie↗

Enhancement of mid-/high-Z impurity transport by continuous Li-granule dropping in a stellarator plasma

An enhancement of core impurity transport is observed in high-density plasmas of the stellarator large helical device, heated by neutral beam injection, when continuous lithium (Li) granule dropping is performed. In the reported experiments, in which the tracer-encapsulated solid pellet is employed to inject trace amounts of titanium (Ti) and molybdenum (Mo) into the plasma core, confinement times for these impurities are seen to reduce significantly when Li dropping is applied, this reduction being more notable for Mo. To gain some initial insight into these observations, simulations are performed using the drift-kinetic transport code SFINCS for the Mo case. These simulations indicate that, while neoclassical transport prevails for the main plasma components (electrons, majority ions, and low-Z impurities), the classical contribution appears dominant for transporting Mo impurities. In summary, this work reports the first experimental observation of the degradation of mid-Z and high-Z impurity confinement induced by the continuous dropping of Li granules into a high-density stellarator plasma. In the case of the Mo impurity, simulations suggest that classical transport is the key mechanism underlying the enhanced impurity transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

On how avalanches penetrate the SOL and broaden heat loads

Recent experiments reported a correlation between power law core temperature spectra and Dα emission, suggesting that heat avalanches penetrate the SOL. This paper derives a threshold criterion for avalanche penetration using a reduced model. Avalanches with ($\bigtriangledown$$\tilde{T}$) rms > $\bigtriangledown$$\tilde{T}$ crit at the separatrix are predicted to penetrate, and so broaden the SOL and heat load distribution. $\bigtriangledown$$\tilde{T}$ crit is ~ 1/$τ$ ∥ , where $τ$ ∥ is the parallel heat flow time through the SOL. Penetration occurs when avalanches are strong enough to steepen sufficiently to shock at the separatrix. A positive correlation is found between the nonlinear drive for steepening and the penetration depth. In particular, penetration depth exceeds that of the heuristic drift limit when shocks form. Implications for numerical and physical experiments are also discussed.

SOL heat load↗