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Modeling of the heat transfer in bypass transitional boundary-layer flows

A low Reynolds number k-epsilon turbulence model and conditioned momentum, energy and turbulence equations were used to predict bypass transition heat transfer on a flat plate in a high-disturbance environment with zero pressure gradient. The use of conditioned equations was demonstrated to be an improvement over the use of the global-time-averaged equations for the calculation of velocity profiles and turbulence intensity profiles in the transition region of a boundary layer. The approach of conditioned equations is extended to include heat transfer and a modeling of transition events is used to predict transition onset and the extent of transition on a flat plate. The events, which describe the boundary layer at the leading edge, result in boundary-layer regions consisting of: (1) the laminar, (2) pseudolaminar, (3) transitional, and (4) turbulent boundary layers. The modeled transition events were incorporated into the TEXSTAN 2-D boundary-layer code which is used to numerically predict the heat transfer. The numerical predictions in general compared well with the experimental data and revealed areas where additional experimental information is needed.

Simon, Frederick F.↗

Thermally driven diffusion of SO2 within the surface of Io

The presence of sulfur dioxide (SO2) on Io, together with the fact that the surface layer of Io has extremely high porosity, suggests the possibility of diffusion of this volatile within the surface, as well as exchange between the surface and an atmosphere. The former possibility is investigated through the development of a surface layer thermal model and subsequent calculations of the thermally driven diffusion flux of SO2 within the layer. The major factors affecting the diffusion process are the temperature and temperature gradient in the surface layer throughout the day, and the porosity and grain size in the surface layer. The results indicate that the net transport of SO2 in the near-surface region is downward into the subsurface, causing near-surface depletion of SO2. Near-surface depletion would result in a layer of reduced thermal inertia overlying the bulk of the surface, consistent with thermal eclipse observations of Io. For the present nominal model with 10-micron grains and a porosity of 85 percent, the peak net diurnal downward flux reaches nearly 0.008 g/sq cm per period.

Meade, Paul E.↗

The linear stability of a flat plate boundary-layer approaching a cylindrical obstacle

The linear stability of the low-speed three-dimensional flow over a flat plate with an attached cylinder is studied. The region of interest is upstream of the initial separation point and includes the effects of both adverse and favorable pressure gradients, as well as crossflow. The resulting boundary-layer is subject to both the Tollmien-Schlichting (TS) and crossflow instabilities. Linear stability calculations, using N-factor correlations, indicate that the transition process would be dominated by TS instabilities, although for low frequencies crossflow-type disturbances are important.

Spall, R. E.↗

A New Analytical Approach to Predict Spacing Selection in Lamellar and Rod Eutectic Systems

The Jackson and Hunt (JH) theory has been modified to relax the assumption of isothermal solid/liquid interface(SLI) used in their treatment. Based on the predictions of this modified theory the traditional definitions of regular and irregular eutectics are revised. For regular eutectics the new model identifies a range of spacing within the limits defined by the minimum undercooling of the alpha and beta phase. For the irregular Al-Si eutectic system two different spacing selection mechanisms were identified: a) for a particular growth rate, a nearly isothermal interface can be achieved at a unique minimum spacing lambda(sub I); b) the average spacing (lambda(sub av) greater than lambda(sub I)) is essentially dictated by the undercooling of the faceted phase. Based on the modified theoretical model a semiempirical expression has been developed to account for the influence of the temperature gradient, which is dominant in the irregular Al-Si system. The behavior of the Fe-Fe3C eutectic is also discussed The theoretical calculations have been found to be in good agreement with the published experimental measurements.

Catalina, Adrian V.↗

A New Analytical Approach to Predict Spacing Selection in Lamellar and Rod Eutectic Systems

The Jackson and Hunt (JH) theory has been modified to relax the assumption of isothermal solid liquid interface used in their treatment. Based on the predictions of this modified theory, the traditional definitions of regular and irregular eutectics are revised. For regular eutectics, the new model identifies a range of spacing within the limits defined by the minimum undercooling of the a and beta phases. For the irregular Al-Si eutectic system, two different spacing selection mechanisms were identified: (1) for a particular growth rate, a nearly isothermal interface can be achieved at a unique minimum spacing lambda (sub t); (2) the average spacing (lambda (sub av) greater than lambda (sub t) is essentially dictated by the undercooling of the faceted phase. Based on the modified theoretical model, a semiempirical expression has been developed to account for the influence of the temperature gradient, which is dominant in the irregular Al-Si system. The behavior of the Fe-Fe3C eutectic is also discussed. The theoretical calculations have been found to be in good agreement with the published experimental measurements.

Catalina, Adrian V.↗

Geochemical Insights Into Volcanic and Lithospheric Evolution of Mars

Introduction: The Martian lithosphere plays a pivotal role in volcanic processes, altering surface features, climate shifts, and the planet's early habitability. Crucially, the rigid lithosphere significantly influences Mars' long-term thermal conditions. Studying various geological eons’ volcanic compositions unveils how the lithosphere has evolved, even though understanding the early Noachian volcanic chemistry remains challenging due to weathering and resurfacing. In this study, newly discovered Noachian volcanic terranes[1-2] along with Hesperian and Amazonian volcanic terranes[3] are considered(Figure 1), to infer the evolution of the Martian lithosphere. Figure 1:Mars topographic map derived from MOLA-HRSC data [4] highlights the study regions including the Noachian volcanic terranes, Arabia Terra (AT), Thaumasia Minor (TM), and the Southwest Margin of Icaria Planum (SWIP)[5].Additionally, the Hesperian volcanic terranes such as Syrtis Major (SM), Hesperia Planum (HP), and, the Amazonian volcanic terranes encompass Elysium Mons (EM), Alba Patera (AP), and Olympus Mons (OM) are marked. Methods and Datasets: We use the most recent elemental mass fraction maps derived from gamma spectroscopy data from the Mars Odyssey 2001mission [6]to ascertain the bulk composition of the Martian landscape. Utilizing the updated geochemical provinces dataset of Mars[7], we consider bulk chemistry variations within our study regions. The maps, at a resolution of 50×50, encompass elements like Al, Ca, Fe, Si, K, Th, H2O, Cl, and S, detected through Gamma-Ray Spectroscopy (GRS) with decimeter scale depth sensitivity[6].Additional major and minor elements like Mg, Na, Ti, P, and Mn, using mass balance methods [8]serve as inputs for melting and crystallization simulations. We employ the pMELTS model with FMQ-3to FMQ oxygen fugacity to estimate the Pressure(P)and melting degree(F)in various eons of volcanic terranes. We have also used conventional thermobarometric calculations to determine their formation P-T conditions, using silica activity and olivine-melt Mg-exchange thermometry[9-10]. Results: Chemical Composition of Studied Volcanic Terranes: To assess formation conditions, we have investigated if GRS-measured compositions signify primary igneous processes by evaluating weathering through the Chemical Index of Alteration (CIA), K/Th ratios, and ternary plots for aqueous alteration. Consistent K/Th ratios and low CIA (<50) across volcanic regions suggest minimal large-scale weathering, affirming well-preserved igneous material extending at decimeter depths. In addition, the calculated bulk compositions align with Martian mantle equilibrium, confirming studied volcanic terranes-Arabia Terra, Thaumasia Minor, and SWIP -as primary or less altered compositions, reinforcing their representativeness at a regional GRS scale on Mars. We have also estimated the bulk compositions of Hesperian and Amazonian volcanic terranes shown in Figure 1. All volcanic terranes represent the primary or minimally altered composition. Temporal Evolution of Martian Volcanic Terranes: Our results show P-T conditions ranging from 1.3-1.6 GPa and 1350-1390°C for Noachian terranes, while Hesperian volcanic terranes vary from 1.6-1.7 GPa and 1370-1395°C, and Amazonian volcanic terranes range between 1.9-2.8 GPa and 1380-1415°C. Our analyses correspond to lithospheric thicknesses/ depth of melting for Noachian which ranges from110-135 km, 120-235 km for Hesperian terranes, and 160-235 km for Amazonian terranes. Partial melting percentages (F) range from 8-12% for Noachian, 10-11% for Hesperian, and 10-12% for Amazonian. We have also calculated mantle potential temperatures (Tp) to show variations across epochs(Figure 2). Heat flux estimation shows variations from 51-65 mW/m2 for Noachian, 38-45 mW/m2for Hesperian, and 27-39 mW/m2for Amazonian terranes, implying temporal changes in lithospheric thickness and heat flow. Comparison of Noachian volcanic terranes with Hesperian and Amazonian reveals variations in lithospheric thickness and heat flux, indicating potential implications for Martian surface conditions, including volcanic activity, climate evolution, and early habitability. Figure 2: P-T diagram displays formation conditions of studied Martian volcanic regions using GRS data, alongside Noachian-age surface basalt samples from Gusev, Gale, and Jezero. Dashed lines represent Martian mantle potential temperatures, calculated by adding the latent heat of fusion to the equilibrium temperature at which melt and solid mantle coexist and subtracting the Martian adiabatic gradient corresponding to the depth of melt. The solid line shows the Martian mantle solidus [11].Discussion& Implication: The study explores Martian volcanic activity across eons. Uniform lithospheric thickness from the Noachian to Hesperian eons suggests persistent weak plumes until Hesperian, influencing heat flow variations. Noachian's high heat flux, likely due to concentrated radioactive elements, shows spatial heterogeneity, indicating early Mars' differentiated mantle. Volcanic outgassing plays avital role in the formation of the Martian climate, likely sustained water on the surface, influencing warm-wet or cold-dry conditions. Hesperian's favorable lithospheric heat flow (45 mW/m2) supports extended water existence, resembling Earth's conditions. Whereas, Amazonian's diminished heat flux (25 mW/m2) corresponds to water loss and arid climate. Hesperian's similar lithospheric thickness to mid-Noachian implies prolonged water retention, influencing climate and potential for astrobiological research, expanding perspectives for future Martian missions. Future work: As volcanism was active throughout its history. The emergence of Mars' extensive volcanic regions, known as large igneous provinces, which are linked to intermittent volcanic activity driven by mantle plumes, poses challenges to understanding the scale and persistence of these phenomena in Martian convection models. Therefore, understanding the regional-scale changes in eruptive processes within Martian volcanic provinces over time remains unclear and crucial for deciphering the evolution of the Martian interior without Earth-like plate tectonics. We will continue this work with petrological and thermoelastic analyses to study the compositional and spatiotemporal evolution of the Elysium Volcanic Province.

A Rani↗

Gyrokinetic modelling of stationary electron and impurity profiles in tokamaks

Particle transport due to Ion Temperature Gradient (ITG)/Trapped Electron Mode (TEM) turbulence is investigated using the gyrokinetic code GENE. Both a reduced quasilinear treatment and nonlinear simulations are performed for typical tokamak parameters corresponding to ITG dominated turbulence. The gyrokinetic results are compared and contrasted with results from a computationally efficient fluid model. A selfconsistent treatment is used, where the stationary local profiles are calculated corresponding to zero particle flux simultaneously for electrons and trace impurities. The scaling of the stationary profiles with magnetic shear, safety factor, electron-to-ion temperature ratio, collisionality, toroidal sheared rotation, plasma β, triangularity, and elongation is investigated. In addition, the effect of different main ion mass on the zero flux condition is discussed. The electron density gradient can significantly affect the stationary impurity profile scaling. It is therefore expected that a selfconsistent treatment will yield results more comparable to experimental results for parameter scans where the stationary background density profile is sensitive. This is shown to be the case in scans over magnetic shear, collisionality, elongation, and temperature ratio, for which the simultaneous zero flux electron and impurity profiles are calculated. A slight asymmetry between hydrogen, deuterium, and tritium with respect to profile peaking is obtained, in particular, for scans in collisionality and temperature ratio.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Numerical Study of Solidification Crack Susceptibility in Novel Refractory Alloy Systems

Calculation of Phase Diagrams (CALPHAD) -based solidification computa­tions, such as Scheil or equilibrium computations, have been utilized to propose crack solidification susceptibility indices (CSSIs) of cracking. These CSSIs have been proposed in order to predict the cracking susceptibility of an alloy in the solidification range, as a function of its solidification frac­tion and as dependent upon its wt.% elemental composition through the CALPHAD computation & via comparative methods between one composition & the next. Recently Kou at al. have proposed a novel CSSI where the gradient of the e.x. Scheil solidification curve is obtained in the critical solidification cracking region of greater than 0.95 fraction of solid. Therefore, a direct Temperature dependent metric is now available for the prediction, and presumably the control, of solidification cracking. In this TM, the researchers apply this Kou gradient method to refractory alloys for the first time & discuss justification for the approach via Spearman rank correlation with Varestraint cracking test data as well as by comparisons with Thermocalc based vulnerability time CSSI calculations. A Python Pycalphad module example of the approach is provided & can be utilized as an open-source resource that utilizes also open-source available thermodynamical databases, making the CSSI quantitative aspect of ICME more available and freely available to practitioners.

ICME integrated computational materials engineerin↗

Modeling of turbulent supersonic H2-air combustion with a multivariate beta PDF

Recent calculations of turbulent supersonic reacting shear flows using an assumed multivariate beta PDF (probability density function) resulted in reduced production rates and a delay in the onset of combustion. This result is not consistent with available measurements. The present research explores two possible reasons for this behavior: use of PDF's that do not yield Favre averaged quantities, and the gradient diffusion assumption. A new multivariate beta PDF involving species densities is introduced which makes it possible to compute Favre averaged mass fractions. However, using this PDF did not improve comparisons with experiment. A countergradient diffusion model is then introduced. Preliminary calculations suggest this to be the cause of the discrepancy.

Baurle, R. A.↗

Stable diagonal stripes in the t-J model at $\bar{n}$ h = 1/8 doping from fPEPS calculations

We investigate the two-dimensional t–J model at a hole doping of $\bar{n}$ h= 1 / 8 using recently developed high accuracy fermionic projected entangled pair states method. By applying the stochastic gradient descent method combined with the Monte Carlo sampling technique, we obtain the ground state hole energy Ehole = -1.621 for J/t = 0.4. We show that the ground state has stable diagonal stripes instead of vertical stripes with a width of 4 unit cells, and stripe filling ρ l = 0.5. We further show that the long-range superconductivity order is suppressed at this point.

36 MATERIALS SCIENCE↗

Convection and magnetic fields in an atmosphere with constant temperature gradient. II - The supergranules and magnetic fields

The hydrodynamic properties of convective motions in a stratified atmosphere suggest that the supergranules in the solar photosphere extend to depths in excess of their horizontal diameters. The calculations presented here show that the weak fields which appear at the photosphere are as strong as, or stronger than, the horizontal fields anywhere in the supergranules below the surface. Hence the general 10 to 100 gauss azimuthal field of the sun, whose presence is indicated by the emerging bipolar magnetic regions, must lie below the base of the supergranules, i.e., below a depth probably of the order of 20,000 to 50,000 km. Presumably then the azimuthal field is generated by nonuniform rotation below the supergranule convection and does not appear in the supergranule layer because of the high rate of turbulent diffusion loss from that layer.

Parker, E. N.↗

Local synthesis of 3D magnetic surfaces

Local synthesis of nested 3D toroidal magnetic surfaces is carried out on the basis of the general theory of surfaces by using magnetic coordinates (generally unknown a priori). An equilibrium magnetic surface is calculated by specifying two functions on the surface (the absolute value of the magnetic field and the distance to the nearest magnetic surface) and three parameters (the rotational transform, pressure gradient, and poloidal current). The choice of the parameters is restricted by the requirement that the surface should be closed toroidally. A method of synthesis of a closed magnetic surface is proposed when two functions—the absolute value of the magnetic field and the major radius—are specified. A set of harmonics of a new type of poloidally preudosymmetric configuration (a toroidal mirror with a large mirror ratio and small rotational transform) is obtained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The use of superconductivity in magnetic balance design

The magnetic field and field gradient requirements for magnetic suspension in a Mach 3, 6-in. diameter wind tunnel are stated, along with the power requirements for gradient coil pairs wound of copper operating at room temperature and aluminum cooled to 20 K. The power dissipated is large enough that the use of superconductivity in the coil design becomes an attractive alternative. The problems of stability and ac losses are outlined along with the properties of stabilized superconductors. A brief review of a simplified version of the critical state model of C. P. Bean is presented, and the problems involved in calculations of the ac losses in superconducting coils are outlined. A summary of ac loss data taken on pancake coils wound of commercially available Nb3Sn partially stabilized tape is presented and shown as leading to the U.Va. gradient coil design. The actual coil performance is compared with predictions based on the BNL results. Finally, some remarks are presented concerning scaling of the ac losses to larger magnetic suspension systems as well as prospects for improved performance using newer multifilament superconductors.

Moss, F. E.↗

Model Calculations of the Impact of NO(x) from Air Traffic, Lightning and Surface Emissions, Compared with Measurements

The impact of NO(x) from aircraft emissions, lightning and surface contributions on atmospheric nitrogen oxides and ozone has been investigated with the three-dimensional global chemistry transport model TM3 by partitioning the nitrogen oxides and ozone according to source category. The results have been compared with POLINAT II and SONEX airborne measurements in the North Atlantic flight corridor in 1997. Various cases have been investigated: measurements during a stagnant anti-cyclone and an almost cut-off low, both with expected high aircraft contributions, a southward bound flight with an expected strong flight corridor gradient and lightning contributions in the South, and a transatlantic flight with expected boundary layer pollution near the U.S. coast. The agreement between modeled results and measurements is reasonably good for NO and ozone. Also, the calculated impact of the three defined sources were consistent with the estimated exposure of the sampled air to these sources, obtained by specialized back-trajectory model products.

Meijer, E. W.↗

Fluid Dynamics Effects on Microstructure Prediction in Single Laser Tracks for Additive Manufacturing

The Laser Powder Bed Fusion Additive Manufacturing (LPBFAM) is one of the most important processes for the production of lightweight, cost-effective, complex, and high-performance enduse parts. At present, the cost and time associated with LPBFAM process development is very high due to a lack of fundamental process understanding. In this project, a multi-physics model was developed on a highly parallel open-source code, Truchas, with the ultimate goal of providing experimentally validated process maps for tailoring microstructure to achieve desired performance for LPBFAM. As a critical step towards fully LPBFAM modeling, modeling of single-track laser fusion (STLF) were conducted. Multi-physics simulations were conducted using Truchas for STLF by considering heat transfer, phase-change, fluid dynamics, surface tension phenomena, and evaporation. In order to assess the effect of the fluid dynamics on the solidification and ensuing microstructure, a heat transfer-and-solidification-only (HTS) model and a fully coupled heat-transfer-solidification and fluid-dynamics (HTS-FD) model were considered. In the HTS_FD model, the fluid flow was considered to be laminar while the molten alloy surface is assumed to be flat and non-deformable. This study is one the first attempt to understand the effect of the fluid flow on microstructure in STLF and LPBFAM. The results show that the fluid flow affects the solidification and ensuing microstructure in STLF. In order to validate Truchas for STLF and LPBFAM modeling, experimental data, which was obtained at GE Global Research (GEGR) for liquid pool shape and microstructure, were compared with those from numerical simulation results. For the keyhole regime case, numerical simulation results indicate that the melt-pool shape was typical to that of the conduction case with very large deviations from the measured melt-pool depths. Two sensitivity studies were conducted by varying the evaporation flux and the surface tension coefficient at fixed laser absorptivities of 0.5 and 0.3, respectively. The minimum value for the overall combined error, between the calculated values with the HTS_FD model and measured values for both the width and height of the melt-pool, was attained for a surface tension coefficient of -0.75e-4 N/m. An analytical solidification model for the columnar-to-equiaxed transition (CET) in rapid solidification was used to assess the microstructure variation within the melt-pool. From numerical simulation results, thermal gradient, G, and solidification velocity, V, were obtained in order to predict the microstructure type (e.g., dendritic, cellular). For the fluid-flow HTS_FD model, G was found to exhibit a maximum at the extremity of the solidified pool (i.e., at the free surface). By contrast, for HTS simulations, G was found to exhibit a maximum around the entire edge of the solidified pool. For the HTS_FD simulations, the minimum values of the cooling rate, GV, were found to be approximately half than their corresponding values for HTS simulations. By contrast with the min GV values, the maximum values for GV were found to occur for the HTS_FD simulations. Thus, HTS_FD simulations were found to exhibit a wider range of cooling rates than the HTS simulations. Concerning the solidification maps, the variation of the solidification velocity, V, as function of the thermal gradient, G, was obtained. It was found that the fluid flow model results (HTS_FD) exhibited an increased spread in the V(G) variation within the melt pool with respect to the HTS model results (without the fluid flow). A preliminary correlation model for the primary dendrite arm spacing (PDAS) based on a power law dependence on thermal gradient and solidification velocity was used to estimate PDAS from HTS and HTS_FD simulations. For low laser powers and low laser speeds, the PDAS obtained 6 with the fluid dynamics model (HTS_FD) was larger by more than 30% with respect to the PDAS calculated with the simple HTS model. In the second part of the project, fifty-seven simulations were conducted in order to obtain data on microstructure variables that can be used for process map development. In order to cover the entire processing space, thirty-three cases were selected STLF process simulations at six power levels and six laser scanning speeds. The 57 STLF process simulations were conducted as follows: 33 simulations with the heat-transfer-only (HTS) model and 24 simulations with the fluid flow model (HTS_FD). The solidification map data shows that for all simulations, a columnar dendritic microstructure would be expected. It was found that the minimum, average, and maximum thermal gradient exhibit exponential variations with respect to a process variable defined as the ratio between the power and square root of scan speed.

36 MATERIALS SCIENCE↗

Description of plasmon-like band in silver clusters: The importance of the long-range Hartree-Fock exchange in time-dependent density-functional theory simulations

Absorption spectra of Ag{sub 20} and Ag{sub 55}{sup q} (q = +1, −3) nanoclusters are investigated in the framework of the time-dependent density functional theory in order to analyse the role of the d electrons in plasmon-like band of silver clusters. The description of the plasmon-like band from calculations using density functionals containing an amount of Hartree-Fock exchange at long range, namely, hybrid and range-separated hybrid (RSH) density functionals, is in good agreement with the classical interpretation of the plasmon-like structure as a collective excitation of valence s-electrons. In contrast, using local or semi-local exchange functionals (generalized gradient approximations (GGAs) or meta-GGAs) leads to a strong overestimation of the role of d electrons in the plasmon-like band. The semi-local asymptotically corrected model potentials also describe the plasmon as mainly associated to d electrons, though calculated spectra are in fairly good agreement with those calculated using the RSH scheme. Our analysis shows that a portion of non-local exchange modifies the description of the plasmon-like band.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Pitting Corrosion of 10Ni8CrMoV High-Strength Steel Induced by a Potential Perturbation

Pitting corrosion of high-strength steel 10Ni8CrMoV under square wave polarization (SWP) in simulated deep-sea environment is investigated and the possible mechanism is proposed. The results show that potential perturbation generates periodic intensification effect on both anodic and cathodic processes by frequently breaking the electrode equilibrium state. The intensity of periodic intensification effect essentially depends on the concentration gradient of Fe{sup 2+} cations at the steel/solution interface which acts as the forced electrochemical oscillator. The concentration gradient and the resulting concentration polarization effect increase periodically with the increase in SWP potential range. The morphology observation of the pitting and electric charge calculation indicate that the periodic intensification effect can promote the initiation and growth of pits by enhancing the anodic dissolution even under cathodic protection, but it is ineffective below the hydrogen evolution potential. The decrease in either upper or lower potential can mitigate anodic dissolution. Through the statistical analysis of pitting size, it is found that the wide potential range tends to activate the metastable pitting formed under hydrostatic pressure, forming densely distributed pitting. Meanwhile, it is more favorable to the formation of fully grown pits with high size dispersion degree when the proportion of electric charge in the anodic process is higher.

36 MATERIALS SCIENCE↗

Lithium granule ablation and penetration during ELM pacing experiments at DIII-D

At DIII-D, lithium granules were radially injected into the plasma at the outer midplane to trigger and pace edge localized modes (ELMs). Granules ranging in size from 300 to 1000 microns were horizontally launched into H-mode discharges with velocities near 100 m/s, and granule to granule injection frequencies less than 500 Hz. While the smaller granules were only successful in triggering ELMs approximately 20% of the time, the larger granules regularly demonstrated ELM triggering efficiencies of greater than 80%. A fast visible camera looking along the axis of injection observed the ablation of the lithium granules. We used the duration of ablation as a benchmark for a neutral gas shielding calculation, and approximated the ablation rate and mass deposition location for the various size granules, using measured edge plasma profiles as inputs. In conclusion, this calculation suggests that the low triggering efficiency of the smaller granules is due to the inability of these granules to traverse the steep edge pressure gradient region and reach the top of the pedestal prior to full ablation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗