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DOE OSTI2018

Asymptotic scaling laws and semi-similarity solutions for a finite-source spherical blast wave

A spherical blast wave generated by a sudden release of a sphere of compressed gas is an important model problem to understand blast phenomena such as volcanic eruptions and explosive detonations. The resulting explosion flow physics, such as the instability at the gas contact discontinuity and the interaction between the shock wave and the gas contact, are dictated by the initial pressure and sound-speed ratios between the compressed gas and the ambience. Since the initial pressure and sound-speed ratios vary over a wide range in practical applications, it is of interest to investigate the scaling laws and similarity solutions for the spherical symmetric explosion flow. In the present study, numerical simulation of a spherical blast wave is performed. A long-term length scale that incorporates the initial charge radius and the initial pressure ratio is introduced. The trajectories of the main shock normalized by the long-term length scale for a wide range of parameters collapse after a short transition time, indicating an asymptotic similarity solution exists for the far field in the long term. With the assistance of this similarity solution, the full evolution of the main shock can be obtained semi-analytically. For near-field features, i.e. the gas contact and the secondary shock wave, only semi-similarity solutions are observed, which depend on the initial sound-speed ratio but not the initial pressure ratio. The gas contact and the secondary shock share the same scaling relations. Asymptotic analysis is performed to obtain the short-term dynamics of the gas contact, including the gas contact acceleration and the Atwood number, which are the key parameters determining the Rayleigh–Taylor instability development at the gas contact. The asymptotic contact radius as $t\rightarrow \infty$ is also obtained, which is found to be well represented by the long-term length scale and thus only depends on the initial pressure ratio. A simple model of an oscillating bubble is employed to explain the scaling relation of the asymptotic gas contact radius.

Mechanics↗

DOE OSTI2018

Similarity of wake meandering for different wind turbine designs for different scales

The wake meandering characteristics of four different wind turbine designs with diameters ranging from a few centimetres (wind tunnel scale) to a hundred metres (utility scale) are investigated using large-eddy simulation with the turbine blades and nacelle parametrised using a new actuator surface model. Different velocity fields and meandering behaviours are observed at near-wake locations. At far-wake locations, on the other hand, the mean velocity deficit profiles begin to collapse when scaled by the centreline velocity deficit based on the incoming wind speed at turbine hub height, suggesting far-wake similarity across scales. The turbine-added turbulence kinetic energy profiles are shown to also nearly collapse with each other in the far wake when normalised using a velocity scale defined by the thrust on the turbine rotor. Moreover, we show that at far-wake locations, the simulated flow fields for all four turbine designs exhibit similar wake meandering characteristics in terms of (1) a Strouhal number independent of rotor designs of different sizes and (2) the distributions of wake meandering wavelengths and amplitudes when normalised by the rotor diameter and a length scale defined by the turbine thrust respectively.

Mechanics↗

DOE OSTI2022

A scale-wise analysis of intermittent momentum transport in dense canopy flows

We investigate the intermittent dynamics of momentum transport and its underlying time scales in the near-wall region of the neutrally stratified atmospheric boundary layer in the presence of a vegetation canopy. This is achieved through an empirical analysis of the persistence time scales (periods between successive zero-crossings) of momentum flux events, and their connection to the ejection–sweep cycle. Using high-frequency measurements from the GoAmazon campaign, spanning multiple heights within and above a dense canopy, the analysis suggests that, when the persistence time scales ( $t_p$ ) of momentum flux events from four different quadrants are separately normalized by $\varGamma _{w}$ (integral time scale of the vertical velocity), their distributions $P(t_p/\varGamma _{w})$ remain height-invariant. This result points to a persistent memory imposed by canopy-induced coherent structures, and to their role as an efficient momentum-transporting mechanism between the canopy airspace and the region immediately above. Moreover, $P(t_p/\varGamma _{w})$ exhibits a power-law scaling at times $t_{p}<\varGamma _{w}$ , with an exponential tail appearing for $t_{p} \geq \varGamma _{w}$ . By separating the flux events based on $t_p$ , we discover that around 80 % of the momentum is transported through the long-lived events ( $t_{p} \geq \varGamma _{w}$ ) at heights immediately above the canopy, while the short-lived ones ( $t_{p} < \varGamma _{w}$ ) only contribute marginally ( $\approx 20\,\%$ ). To explain the role of instantaneous flux amplitudes in momentum transport, we compare the measurements with newly developed surrogate data and establish that the range of time scales involved with amplitude variations in the fluxes tends to increase as one transitions from within to above the canopy.

Mechanics↗

DOE OSTI2015

Investigating the reversibility of structural modifications of Li x Ni y Mn z Co 1-y-z O₂ cathode materials during initial charge/discharge, at multiple length scales

In this work, we investigate the structural modifications occurring at the bulk, subsurface, and surface scales of Li x Ni y Mn z Co 1-y-z O₂ (NMC; y, z = 0.8, 0.1 and 0.4, 0.3, respectively) cathode materials during the initial charge/discharge. Various analytical tools, such as X-ray diffraction, selected-area electron diffraction, electron energy-loss spectroscopy, and high-resolution electron microscopy, are used to examine the structural properties of the NMC cathode materials at the three different scales. Cut-off voltages of 4.3 and 4.8 V are applied during the electrochemical tests as the normal and extreme conditions, respectively. The high-Ni-content NMC cathode materials exhibit unusual behaviors, which is deviate from the general redox reactions during the charge or discharge. The transition metal (TM) ions in the high-Ni-content NMC cathode materials, which are mostly Ni ions, are reduced at 4.8 V, even though TMs are usually oxidized to maintain charge neutrality upon the removal of Li. It was found that any changes in the crystallographic and electronic structures are mostly reversible down to the sub-surface scale, despite the unexpected reduction of Ni ions. However, after the discharge, traces of the phase transitions remain at the edges of the NMC cathode materials at the scale of a few nanometers (i.e., surface scale). This study demonstrates that the structural modifications in NMC cathode materials are induced by charge as well as discharge at multiple length scales. These changes are nearly reversible after the first cycle, except at the edges of the samples, which should be avoided because these highly localized changes can initiate battery degradation.

25 ENERGY STORAGE↗

DOE OSTI2021

Assembly and Analysis of Cell-Scale Membrane Envelopes

The march toward exascale computing will enable routine molecular simulation of larger and more complex systems, for example, simulation of entire viral particles, on the scale of approximately billions of atoms-a simulation size commensurate with a small bacterial cell. Anticipating the future hardware capabilities that will enable this type of research and paralleling advances in experimental structural biology, efforts are currently underway to develop software tools, procedures, and workflows for constructing cell-scale structures. Herein, we describe our efforts in developing and implementing an efficient and robust workflow for construction of cell-scale membrane envelopes and embedding membrane proteins into them. A new approach for construction of massive membrane structures that are stable during the simulations is built on implementing a subtractive assembly technique coupled with the development of a structure concatenation tool (fastmerge), which eliminates overlapping elements based on volumetric criteria rather than adding successive molecules to the simulation system. Using this approach, we have constructed two "protocells" consisting of MARTINI coarse-grained beads to represent cellular membranes, one the size of a cellular organelle and another the size of a small bacterial cell. The membrane envelopes constructed here remain whole during the molecular dynamics simulations performed and exhibit water flux only through specific proteins, demonstrating the success of our methodology in creating tight cell-like membrane compartments. Extended simulations of these cell-scale structures highlight the propensity for nonspecific interactions between adjacent membrane proteins leading to the formation of protein microclusters on the cell surface, an insight uniquely enabled by the scale of the simulations. We anticipate that the experiences and best practices presented here will form the basis for the next generation of cell-scale models, which will begin to address the addition of soluble proteins, nucleic acids, and small molecules essential to the function of a cell.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Scale Invariance of Hot Spot Formation in TATB High Explosives

Shock-induced detonation of insensitive high explosives based on 1,3,5-triamino-2,4,6-trinitrobenzene starts with formation of hot spots at microstructural defects but has eluded atomistic modeling treatment at micron length scales. To this end, we performed multimicron scale all-atom molecular dynamics (MD) simulations of hot spots that form during the collapse of cylindrical pores with diameters between 10 and 300 nm. Our MD simulations show that hot spots formed at pores larger than 20 nm exhibit temperature fields with scale-invariant features for sizes up to at least 300 nm. Through a continuum-based grain-scale modeling framework, we span and extend beyond the size scales currently accessible to MD and find that hot spot scale invariance is a general feature that arises when the mechanical strength is insensitive to strain rate. Finally, our results demonstrate the applicability of all-atom MD to simulate the complicated dynamical evolution of micron-sized systems and bolster confidence in insights from MD simulations of materials that exhibit strength with negligible rate dependence over the relevant intervals.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Fast Atomic-Scale Chemical Imaging of Crystalline Materials and Dynamic Phase Transformations

Chemical imaging at the atomic-scale provides a useful real-space approach to chemically investigate solid crystal structures, and has been recently demonstrated in aberration corrected scanning transmission electron microscopy (STEM). Atomic-scale chemical imaging by STEM using energy-dispersive X-ray spectroscopy (EDS) offers easy data interpretation with a one-to-one correspondence between image and structure but has a severe shortcoming due to the poor efficiency of X-ray generation and collection. As a result, it requires a long acquisition time of typical > few 100 seconds, limiting its potential applications. Here we describe the development of an atomic-scale STEM EDS chemical imaging technique that cuts the acquisition time to one or a few seconds, efficiently reducing the acquisition time by more than 100 times. This method was demonstrated using LaAlO 3 (LAO) as a model crystal. Applying this method to the study of phase transformation induced by electron-beam radiation in a layered lithium transition-metal (TM) oxide, i.e., Li[Li 0.2 Ni 0.2 Mn 0.6 ]O 2 (LNMO), a cathode materials for lithium-ion batteries, we obtained a time-series of the atomic-scale chemical imaging, showing the transformation progressing by preferably jumping of Ni atoms from the TM layers into the Li-layers. The new capability offers an opportunity for temporal, atomic-scale chemical mapping of crystal structures for the investigation of materials susceptible to electron irradiation as well as phase transformation and dynamics at the atomic-scale.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Predicting Outcomes of Nanoparticle Attachment by Connecting Atomistic, Interfacial, Particle, and Aggregate Scales

Predicting nanoparticle aggregation and attachment phenomena requires a rigorous understanding of the interplay among crystal structure, particle morphology, surface chemistry, solution conditions, and interparticle forces, yet no comprehensive picture exists. We used an integrated suite of experimental, theoretical, and simulation methods to resolve the effect of solution pH on the aggregation of boehmite nanoplatelets, a case study with important implications for the environmental management of legacy nuclear waste. Real-time observations showed that the particles attach preferentially along the (010) planes at pH 8.5 and the (101) planes at pH 11. To rationalize these results, we established the connection between key physicochemical phenomena across the relevant length scales. Starting from molecular-scale simulations of surface hydroxyl reactivity, we developed an interfacial-scale model of the corresponding electrostatic potentials, with subsequent particle-scale calculations of the resulting driving forces allowing successful prediction of the attachment modes. Finally, we scaled these phenomena to understand the collective structure at the aggregate-scale . Here, our results indicate that facet-specific differences in surface chemistry produce heterogeneous surface charge distributions that are coupled to particle anisotropy and shape-dependent hydrodynamic forces, to play a key role in controlling aggregation behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Life-Cycle Assessment of Alternative Pyrolysis-Based Transport Fuels: Implications of Upgrading Technology, Scale, and Hydrogen Requirement

In an effort to diversify liquid fuel supply and address climate change, there are ongoing studies on the use of biomass as a renewable source of energy. Bio-oil produced from fast pyrolysis of biomass is a promising substitute for fossil fuels that can meet climate change mitigation goals, spur rural economies, and diversify liquid fuel supply. However, for bio-oil to be used as a transportation fuel, it requires upgrading to remove oxygen present in the oil. Hydrodeoxygenation (HDO) is one means of upgrading fast pyrolysis oil, however, one of its main limitations is a large hydrogen requirement. We evaluate an alternative electrochemical deoxygenation (EDOx) method that uses catalytic electrode membranes on a ceramic, oxygen permeable support, to generate hydrogen in-situ for deoxygenation at the cathode and remove oxygen at the anode. We analyze the life cycle greenhouse gas (GHG) emissions and scale effects of gas-phase upgrading pyrolysis oil (300 metric tons per day (MTPD)) using EDOx, which reduces energy needs for condensing the pyrolysis gas to bio-oil prior to deoxygenation. The dispersed woody biomass can be accessed and thus more efficiently used if a small scale process is used to densify and stabilize the bio-oil product. We evaluate two configurations of the small-scale deoxygenation, full electrochemical deoxygenation (EDOx), which removes 100% of oxygen present in the bio-oil and partial EDOx, which removes 96% of oxygen present in the bio-oil and compare them to the large scale (2000 MTPD) deoxygenation (HDO). The partial EDOx process has the lowest total GHG emissions of 4.95 gCO2 eq. and 7.43 gCO2 eq. per MJ of a vehicle operated with diesel and gasoline respectively compared to full EDOx (8.36 g CO2 eq. diesel, 10.86 g CO2 eq. gasoline) and HDO (39 gCO2 eq. per MJ for diesel and gasoline). In addition, with the EDOx processes, we can site 10 times more small-scale pyrolysis upgrading sites compared to HDO, suggesting that small-scale on-site partial or full deoxygenation can reach more inaccessible forest biomass resources.

bio-oil hydrotreating, Biomass, deoxygenation, sol↗

DOE OSTI2023

Incorporating the Effect of Large‐Scale Vertical Motion on Convection Through Convective Mass Flux Adjustment in E3SMv2

Abstract Recent observational studies suggest that the large‐scale dynamical forcing (vertical motion) plays important roles in deep convection development. In this study we propose a convective mass flux adjustment (MAdj) approach to represent the dynamical effects of large‐scale vertical motion on convection in the Department of Energy's Energy Exascale Earth System Model version 2 (E3SMv2). With MAdj, convection is enhanced (suppressed) when there is large‐scale ascending (descending) motion at the planetary boundary layer top. The coupling of convection with large‐scale circulation significantly improves the simulation of climate variability in E3SMv2 across multiple scales from the diurnal cycle, convectively coupled equatorial waves, to the Madden‐Julian Oscillation (MJO). The standard E3SMv2 tends to simulate overly weak diurnal amplitude of precipitation and overly weak variance of convectively coupled equatorial Kelvin and westward inertio‐gravity (WIG) waves. It also fails to simulate the essential characteristics of the MJO: continuous eastward propagation. With MAdj, the amplitude of diurnal cycle of precipitation is systematically increased and its probability density distribution is much closer to observations. The MAdj can also simulate more realistic eastward propagation of the MJO and much stronger convectively coupled Kelvin and WIG waves. Moreover, the MAdj approach slightly improves the climatology simulations in precipitation, cloud, radiation, circulation, temperature, and moisture fields, with overall root‐mean‐square error (RMSE) of major climatological fields reduced by about 2%. The MAdj approach suppresses excessive grid‐scale precipitation, reducing precipitation wet biases over South China Sea, Philippine Sea, Himalayas, and South Pacific Convergence Zone in western Pacific in summer.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

A Robust Estimate of Continental-Scale Terrestrial Carbon Sinks Using GOSAT XCO 2 Retrievals

Satellite XCO 2 retrievals could improve the estimates of surface carbon fluxes, but it remains unknown on what scales these estimates are robust. Here, we use the time-dependent Bayesian synthesis top-down method and prior net ecosystem exchanges (NEEs) from 12 terrestrial biosphere models (TBMs) to infer the monthly carbon fluxes of 51 land regions with constraints by GOSAT XCO 2 retrievals. We find that the uncertainty (standard deviation of 12 TBMs) reduction rates (uncertainty reduction rate (URR)) decrease significantly at decreasing spatial scales. On the continental-scale, the mean URR is about 57%, and the annual and seasonal cycle estimates of NEE are rather robust. The evaluation shows that the posterior CO 2 concentrations are significantly improved at the continental scale. Our study suggests that the GOSAT XCO 2 can only promise a robust continental-scale NEE estimate and improving the XCO 2 accuracy is an effective way to achieve robust estimates on smaller scales under current spatial coverage.

58 GEOSCIENCES↗

DOE OSTI2025

Representing Fine‐Scale Topographic Effects on Surface Radiation Balance in Hyper‐Resolution Land Surface Models

Land surface models are increasingly used to simulate land surface processes at hyper-spatial resolutions (e.g., ∼1 km). As model resolution increases, grid-scale topographic effects on surface radiation fluxes and their interactions between adjacent grids become more pronounced. However, current land surface models routinely neglect the fine-scale topographic effects on surface radiation balance. This study developed physically-based and computationally-efficient parameterizations (fineTOP) that explicitly resolve fine-scale topographic effects on downward shortwave and longwave radiation as well as land surface radiative properties. The newly developed parameterizations were implemented and tested in the Energy Exascale Earth System Model (E3SM) Land Model (ELM). Multi-decadal km-resolution ELM simulations over the California Sierra Nevada show that fine-scale topography significantly impacts the surface energy balance and snow processes across seasons. Slope determines the magnitude of topographic effects, while aspect controls their sign. For slopes larger than 30°, topography-induced change in annual surface temperature can be as large as 3.3 K. Regionally, the mean value and standard deviation of topography-induced changes in annual surface temperature are −0.22 ± 0.38 K and +0.25 ± 0.37 K over north-facing and south-facing slopes, respectively. Topography-induced changes in surface radiative properties account for 3.5% ± 13.8% of total topographic effects on annual net radiation. With fineTOP, ELM captures the aspect-dependence of snow cover fraction, snow water equivalent, and land surface temperature found in MODIS satellite observations and a snow reanalysis data set, while the default ELM fails to capture this phenomenon. The enhanced capability to represent fine-scale topographic effects on surface radiation balance can be used to advance understanding of the role of fine-scale topography in land surface processes and land-atmosphere interactions over mountainous regions.

Hao, Dalei [Pacific Northwest National Laboratory ↗

DOE OSTI2019

Bioinspired design of flexible armor based on chiton scales

Man-made armors often rely on rigid structures for mechanical protection, which typically results in a trade-off with flexibility and maneuverability. Chitons, a group of marine mollusks, evolved scaled armors that address similar challenges. Many chiton species possess hundreds of small, mineralized scales arrayed on the soft girdle that surrounds their overlapping shell plates. Ensuring both flexibility for locomotion and protection of the underlying soft body, the scaled girdle is an excellent model for multifunctional armor design. Here we conduct a systematic study of the material composition, nanomechanical properties, three-dimensional geometry, and interspecific structural diversity of chiton girdle scales. Moreover, inspired by the tessellated organization of chiton scales, we fabricate a synthetic flexible scaled armor analogue using parametric computational modeling and multi-material 3D printing. This approach allows us to conduct a quantitative evaluation of our chiton-inspired armor to assess its orientation-dependent flexibility and protection capabilities.

Science & Technology - Other Topics↗

DOE OSTI2014

Contact kinematics of biomimetic scales

Dermal scales, prevalent across biological groups, considerably boost survival by providing multifunctional advantages. Here, we investigate the nonlinear mechanical effects of biomimetic scale like attachments on the behavior of an elastic substrate brought about by the contact interaction of scales in pure bending using qualitative experiments, analytical models, and detailed finite element (FE) analysis. Our results reveal the existence of three distinct kinematic phases of operation spanning linear, nonlinear, and rigid behavior driven by kinematic interactions of scales. The response of the modified elastic beam strongly depends on the size and spatial overlap of rigid scales. The nonlinearity is perceptible even in relatively small strain regime and without invoking material level complexities of either the scales or the substrate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Self-consistent implementation of meta-GGA functionals for the ONETEP linear-scaling electronic structure package

Accurate and computationally efficient exchange-correlation functionals are critical to the successful application of linear-scaling density functional theory (DFT). Local and semi-local functionals of the density are naturally compatible with linear-scaling approaches, having a general form which assumes the locality of electronic interactions and which can be efficiently evaluated by numerical quadrature. Presently, the most sophisticated and flexible semi-local functionals are members of the meta-generalized-gradient approximation (meta-GGA) family, and depend upon the kinetic energy density, τ, in addition to the charge density and its gradient. In order to extend the theoretical and computational advantages of τ-dependent meta-GGA functionals to large-scale DFT calculations on thousands of atoms, we have implemented support for τ-dependent meta-GGA functionals in the ONETEP program. In this paper we lay out the theoretical innovations necessary to implement τ-dependent meta-GGA functionals within ONETEP's linear-scaling formalism. We present expressions for the gradient of the τ-dependent exchange-correlation energy, necessary for direct energy minimization. We also derive the forms of the τ-dependent exchange-correlation potential and kinetic energy density in terms of the strictly localized, self-consistently optimized orbitals used by ONETEP. To validate the numerical accuracy of our self-consistent meta-GGA implementation, we performed calculations using the B97M-V and PKZB meta-GGAs on a variety of small molecules. Using only a minimal basis set of self-consistently optimized local orbitals, we obtain energies in excellent agreement with large basis set calculations performed using other codes. Lastly, to establish the linear-scaling computational cost and applicability of our approach to large-scale calculations, we present the outcome of self-consistent meta-GGA calculations on amyloid fibrils of increasing size, up to tens of thousands of atoms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Multi-scale transport in the DIII-D ITER baseline scenario with direct electron heating and projection to ITER

Multi-scale fluctuations measured by turbulence diagnostics spanning long and short wavelength spatial scales impact energy confinement and the scale-lengths of plasma kinetic profiles in the DIII-D ITER baseline scenario with direct electron heating. Contrasting discharge phases with ECH + neutral beam injection (NBI) and NBI only at similar rotation reveal higher energy confinement and lower fluctuations when only NBI heating is used. Modeling of the core transport with TGYRO using the TGLF turbulent transport model and NEO neoclassical transport reproduces the experimental profile changes upon application of direct electron heating and indicates that multi-scale transport mechanisms are responsible for changes in the temperature and density profiles. Intermediate and high-k fluctuations appear responsible for the enhanced electron thermal flux, and intermediate-k electron modes produce an inward particle pinch that increases the inverse density scale length. Projection to ITER is performed with TGLF and indicates a density profile that has a finite scale length due to intermediate-k electron modes at low collisionality and increases the fusion gain. Finally, for a range of E×B shear, the dominant mechanism that increases fusion performance is suppression of outward low-k particle flux and increased density peaking.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2019

Scaling methods for accelerating kinetic Monte Carlo simulations of chemical reaction networks

Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. In this work, we present a new acceleration algorithm based on adaptive and heterogeneous scaling of reaction rates and stoichiometric coefficients. The algorithm is conceptually related to the commonly used idea of accelerating a stochastic simulation by considering a subvolume λΩ (0 < λ < 1) within a system of interest, which reduces the number of reaction events per unit time occurring in a simulation by a factor 1/λ at the cost of greater error in unbiased estimates of first moments and biased overestimates of second moments. Our new approach offers two unique benefits. First, scaling is adaptive and heterogeneous, which eliminates the pitfall of overaggressive scaling. Second, there is no need for an a priori classification of populations as discrete or continuous (as in a hybrid method), which is problematic when discreteness of a chemical species changes during a simulation. The method requires specification of only a single algorithmic parameter, N c , a global critical population size above which populations are effectively scaled down to increase simulation efficiency. The method, which we term partial scaling, is implemented in the open-source BioNetGen software package. We demonstrate that partial scaling can significantly accelerate simulations without significant loss of accuracy for several published models of biological systems. Finally, these models characterize activation of the mitogen-activated protein kinase ERK, prion protein aggregation, and T-cell receptor signaling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Scalings pertaining to current sheet disruption mediated by the plasmoid instability

Analytic scaling relations are derived for a phenomenological model of the plasmoid instability in an evolving current sheet, including the effects of reconnection outflow. Two scenarios are considered, where the plasmoid instability can be triggered either by an injected initial perturbation or by the natural noise of the system (here referred to as the system noise). The two scenarios lead to different scaling relations because the initial noise decays when the linear growth of the plasmoid instability is not sufficiently fast to overcome the advection loss caused by the reconnection outflow, whereas the system noise represents the lowest level of fluctuations in the system. The leading order approximation for the current sheet width at disruption takes the form of a power law multiplied by a logarithmic factor, and from that, the scaling relations for the wavenumber and the linear growth rate of the dominant mode are obtained. When the effects of the outflow are neglected, the scaling relations agree, up to the leading order approximation, with previously derived scaling relations based on a principle of least time. As a result, the analytical scaling relations are validated with numerical solutions of the model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗