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All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Production flux of sea spray aerosol

Knowledge of the size- and composition-dependent production flux of primary sea spray aerosol (SSA) particles and its dependence on environmental variables is required for modeling cloud microphysical properties and aerosol radiative influences, interpreting measurements of particulate matter in coastal areas and its relation to air quality, and evaluating rates of uptake and reactions of gases in sea spray drops. This review examines recent research pertinent to SSA production flux, which deals mainly with production of particles with r{sub 80} (equilibrium radius at 80% relative humidity) less than 1 {micro}m and as small as 0.01 {micro}m. Production of sea spray particles and its dependence on controlling factors has been investigated in laboratory studies that have examined the dependences on water temperature, salinity, and the presence of organics and in field measurements with micrometeorological techniques that use newly developed fast optical particle sizers. Extensive measurements show that water-insoluble organic matter contributes substantially to the composition of SSA particles with r{sub 80} < 0.25 {micro}m and, in locations with high biological activity, can be the dominant constituent. Order-of-magnitude variation remains in estimates of the size-dependent production flux per white area, the quantity central to formulations of the production flux based on the whitecap method. This variation indicates that the production flux may depend on quantities such as the volume flux of air bubbles to the surface that are not accounted for in current models. Variation in estimates of the whitecap fraction as a function of wind speed contributes additional, comparable uncertainty to production flux estimates.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2012

The role of trace gas flux networks in biogeosciences

Vast networks of meteorological sensors ring the globe, providing continuous measurements of an array of atmospheric state variables such as temperature, humidity, rainfall, and the concentration of carbon dioxide [New etal., 1999; Tans etal., 1996]. These measurements provide input to weather and climate models and are key to detecting trends in climate, greenhouse gases, and air pollution. Yet to understand how and why these atmospheric state variables vary in time and space, biogeoscientists need to know where, when, and at what rates important gases are flowing between the land and the atmosphere. Tracking trace gas fluxes provides information on plant or microbial metabolism and climate-ecosystem interactions. The existence of trace gas flux networks is a relatively new phenomenon, dating back to research in 1984. The first gas flux measurement networks were regional in scope and were designed to track pollutant gases such as sulfur dioxide, ozone, nitric acid, and nitrogen dioxide. Atmospheric observations and model simulations were used to infer the depositional rates of these hazardous chemicals [Fowler etal., 2009; Meyers etal., 1991]. In the late 1990s, two additional trace gas flux measurement networks emerged. One, the United States Trace Gas Network (TRAGNET), was a short-lived effort that measured trace gas emissions from the soil and plants with chambers distributed throughout the country [Ojima etal., 2000]. The other, FLUXNET, was an international endeavor that brought many regional networks together to measure the fluxes of carbon dioxide, water vapor, and sensible heat exchange with the eddy covariance technique [Baldocchi etal., 2001]. FLUXNET, which remains active today, currently includes more than 400 tower sites, dispersed across most of the world's climatic zones and biomes, with sites in North and South America, Europe, Asia, Africa, and Australia. More recently, several specialized networks have emerged, including networks dedicated to urban areas (Urban Fluxnet), nitrogen compounds in Europe (NitroEurope), and methane (MethaneNet). Technical Aspects of Flux Networks Eddy covariance flux measurements are the preferred method by which biogeoscientists measure trace gas exchange between ecosystems and the atmosphere [Baldocchi, 2003].

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

A Remote Sensing Technique to Upscale Methane Emission Flux in a Subtropical Peatland

Abstract Quantification of methane (CH 4 ) gas emission from peat is critical to understand CH 4 budget from natural wetlands under a climate warming scenario. Previous studies have focused on prediction and mapping of CH 4 emission flux using process‐based models, while application of statistical‐empirical models for upscaling spatially sparse in situ measurements is scarce. In this study, we developed an empirical remote sensing upscaling approach to estimate CH 4 emission flux in the Everglades using limited in situ point‐based CH 4 emission flux measurements and Landsat data during 2013–2018. We spatially and temporally linked in situ data with Landsat surface reflectance based on temporally composite data sets and developed an object‐based machine learning framework to model and map CH 4 emission flux. An ensemble analysis of two machine learning models, k ‐Nearest Neighbor ( k ‐NN) and Support Vector Machine (SVM), shows that the upscaling approach is promising for predicting CH 4 emission flux with a R 2 of 0.65 and 0.87 based on a fivefold cross‐validation for a dry season and wet season estimation, respectively. We generated emission flux map products that successfully revealed the spatial and temporal heterogeneity of CH 4 emission within the dominant freshwater marsh ecosystem in the Everglades. We conclude that Landsat is promising for upscaling and monitoring CH 4 emission flux and reducing the uncertainty in emission estimates from wetlands.

Zhang, Caiyun↗
DOE OSTI2024

fluxfinder: An R Package for Reproducible Calculation and Initial Processing of Greenhouse Gas Fluxes From Static Chamber Measurements

Fluxes of greenhouse gases are a critical component of the earth's natural climate, but anthropogenic emissions have created an imbalance and resulted in global climate change. Quantifying the emission of these gases is vital to our understanding of their sources and sinks, both natural and anthropogenic. The static chamber method, in which a system of interest is enclosed, and gas concentrations are measured over time, is widely used to estimate fluxes of greenhouse gases. With the development of instruments such as infrared gas analyzers (IRGAs) supporting high-frequency concentration data, there is a growing need for open-source workflows to calculate fluxes. Here we present fluxfinder, an R package designed to support reproducible calculations and processing of greenhouse gas fluxes measured with the static chamber method. The package includes raw data file parsing from widely used IRGAs, metadata matching, unit conversion, flux estimations, and initial quality assurance/quality control (QA/QC). Diagnostic graphical plots provide a transparent way to differentiate between measurement issues and nonlinear behavior. The package is also designed to be easily integrated with the gasfluxes package for further fitting of nonlinear concentration-time models, allowing alternative or additional flux QA/QC. The fluxfinder package offers a flexible workflow that is easily adaptable to promote open and reproducible greenhouse gas flux estimations.

Wilson, Stephanie J.↗
DOE OSTI2025

Direct Observations of Surface Fluxes and Air‐Sea Exchange Coefficients in Low Winds Using a Small Uncrewed Aircraft System

In the marine boundary layer, the exchange of momentum, heat, and moisture occurs between the atmosphere and ocean. Since it is too dangerous for a crewed aircraft to fly close to the ocean surface to directly obtain these measurements, a sUAS (small Uncrewed Aircraft System) is one of the only viable options. On 24 March 2023 a Black Swift Technologies S0 sUAS was deployed from the NOAA P-3 on a calm clear day off the west coast of Florida. For 23 min at the end of the mission, the sUAS flew 8 straight line legs with an average length of 2.15 km, at roughly 10 m above the ocean surface, with wind speeds between 3.0 and 4.5 m s −1 . For the first time over the open ocean using a sUAS, the 4-Hz wind and thermodynamic data was used to calculate surface momentum flux, sensible heat flux, and latent flux using both direct covariance methods and the bulk aerodynamic formulas. Since all the flux quantities can be found using both direct and indirect methods, we are able to calculate the exchange coefficients of momentum flux (C D ), latent heat flux (C E ), and sensible heat flux (C H ) with results that are generally in good agreement with previous studies over the same wind speed range. This study demonstrates the ability of sUAS to measure air-sea interactions. Future intention is to use sUAS to obtain similar measurements in high wind events such as hurricanes which could better help understand hurricane intensification and improve model physics.

Deloach, Christopher J. [Embry-Riddle Aeronautical↗
DOE OSTI2023

Multiquanta flux jumps in superconducting fractal

We study the magnetic field response of millimeter scale fractal Sierpinski gaskets (SG) assembled of superconducting equilateral triangular patches. Directly imaged quantitative induction maps reveal hierarchical periodic filling of enclosed void areas with multiquanta magnetic flux, which jumps inside the voids in repeating bundles of individual flux quanta Φ 0 . The number N s of entering flux quanta in different triangular voids of the SG is proportional to the linear size s of the void, while the field periodicity of flux jumps varies as 1/s. We explain this behavior by modeling the triangular voids in the SG with effective superconducting rings and by calculating their response following the London analysis of persistent currents, J s , induced by the applied field H a and by the entering flux. With changing H a , J s reaches a critical value in the vertex joints that connect the triangular superconducting patches and allows the giant flux jumps into the SG voids through phase slips or multiple Abrikosov vortex transfer across the vertices. The unique flux behavior in superconducting SG patterns, may be used to design tunable low-loss resonators with multi-line high-frequency spectrum for microwave technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Benchmarking gyrokinetic simulations in a toroidal flux-tube

A flux-tube model is implemented in the global turbulence code GEM [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 839 (2007)] in order to facilitate benchmarking with Eulerian codes. The global GEM assumes the magnetic equilibrium to be completely given. The initial flux-tube implementation simply selects a radial location as the center of the flux-tube and a radial size of the flux-tube, sets all equilibrium quantities (B, ∇B, etc.) to be equal to the values at the center of the flux-tube, and retains only a linear radial profile of the safety factor needed for boundary conditions. This implementation shows disagreement with Eulerian codes in linear simulations. An alternative flux-tube model based on a complete local equilibrium solution of the Grad-Shafranov equation [J. Candy, Plasma Phys. Controlled Fusion 51, 105009 (2009)] is then implemented. This results in better agreement between Eulerian codes and the particle-in-cell (PIC) method. The PIC algorithm based on the v{sub ||}-formalism [J. Reynders, Ph.D. dissertation, Princeton University, 1992] and the gyrokinetic ion/fluid electron hybrid model with kinetic electron closure [Y. Chan and S. E. Parker, Phys. Plasmas 18, 055703 (2011)] are also implemented in the flux-tube geometry and compared with the direct method for both the ion temperature gradient driven modes and the kinetic ballooning modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

The role of non-equilibrium fluxes in the relaxation processes of the linear chemical master equation

We propose a non-equilibrium thermodynamical description in terms of the Chemical Master Equation (CME) to characterize the dynamics of a chemical cycle chain reaction among m different species. These systems can be closed or open for energy and molecules exchange with the environment, which determines how they relax to the stationary state. Closed systems reach an equilibrium state (characterized by the detailed balance condition (D.B.)), while open systems will reach a non-equilibrium steady state (NESS). The principal difference between D.B. and NESS is due to the presence of chemical fluxes. In the D.B. condition the fluxes are absent while for the NESS case, the chemical fluxes are necessary for the state maintaining. All the biological systems are characterized by their “far from equilibrium behavior,” hence the NESS is a good candidate for a realistic description of the dynamical and thermodynamical properties of living organisms. In this work we consider a CME written in terms of a discrete Kolmogorov forward equation, which lead us to write explicitly the non-equilibrium chemical fluxes. For systems in NESS, we show that there is a non-conservative “external vector field” whose is linearly proportional to the chemical fluxes. We also demonstrate that the modulation of these external fields does not change their stationary distributions, which ensure us to study the same system and outline the differences in the system's behavior when it switches from the D.B. regime to NESS. We were interested to see how the non-equilibrium fluxes influence the relaxation process during the reaching of the stationary distribution. By performing analytical and numerical analysis, our central result is that the presence of the non-equilibrium chemical fluxes reduces the characteristic relaxation time with respect to the D.B. condition. Within a biochemical and biological perspective, this result can be related to the “plasticity property” of biological systems and to their capabilities to switch from one state to another as is observed during synaptic plasticity, cell fate determination, and differentiation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

The appearance and propagation of filaments in the private flux region in Mega Amp Spherical Tokamak

The transport of particles via intermittent filamentary structures in the private flux region (PFR) of plasmas in the MAST tokamak has been investigated using a fast framing camera recording visible light emission from the volume of the lower divertor, as well as Langmuir probes and IR thermography monitoring particle and power fluxes to plasma-facing surfaces in the divertor. The visible camera data suggest that, in the divertor volume, fluctuations in light emission above the X-point are strongest in the scrape-off layer (SOL). Conversely, in the region below the X-point, it is found that these fluctuations are strongest in the PFR of the inner divertor leg. Detailed analysis of the appearance of these filaments in the camera data suggests that they are approximately circular, around 1–2 cm in diameter, but appear more elongated near the divertor target. The most probable toroidal quasi-mode number is between 2 and 3. These filaments eject plasma deeper into the private flux region, sometimes by the production of secondary filaments, moving at a speed of 0.5–1.0 km/s. Probe measurements at the inner divertor target suggest that the fluctuations in the particle flux to the inner target are strongest in the private flux region, and that the amplitude and distribution of these fluctuations are insensitive to the electron density of the core plasma, auxiliary heating and whether the plasma is single-null or double-null. It is found that the e-folding width of the time-average particle flux in the PFR decreases with increasing plasma current, but the fluctuations appear to be unaffected. At the outer divertor target, the fluctuations in particle and power fluxes are strongest in the SOL.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Dislocation confinement in the growth of Na flux GaN on metalorganic chemical vapor deposition-GaN

We have demonstrated a GaN growth technique in the Na flux method to confine c-, (a+c)-, and a-type dislocations around the interface between a Na flux GaN crystal and a GaN layer grown by metalorganic chemical vapor deposition (MOCVD) on a (0001) sapphire substrate. Transmission electron microscopy (TEM) clearly revealed detailed interface structures and dislocation behaviors that reduced the density of vertically aligned dislocations threading to the Na flux GaN surface. Submicron-scale voids were formed at the interface above the dislocations with a c component in MOCVD-GaN, while no such voids were formed above the a-type dislocations. The penetration of the dislocations with a c component into Na flux GaN was, in most cases, effectively blocked by the presence of the voids. Although some dislocations with a c component in the MOCVD-GaN penetrated into the Na flux GaN, their propagation direction changed laterally through the voids. On the other hand, the a-type dislocations propagated laterally and collectively near the interface, when these dislocations in the MOCVD-GaN penetrated into the Na flux GaN. These results indicated that the dislocation propagation behavior was highly sensitive to the type of dislocation, but all types of dislocations were confined to within several micrometers region of the Na flux GaN from the interface. The cause of void formation, the role of voids in controlling the dislocation behavior, and the mechanism of lateral and collective dislocation propagation are discussed on the basis of TEM results.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Feedback system for divertor impurity seeding based on real-time measurements of surface heat flux in the Alcator C-Mod tokamak

Mitigation of the intense heat flux to the divertor is one of the outstanding problems in fusion energy. One technique that has shown promise is impurity seeding, i.e., the injection of low-Z gaseous impurities (typically N 2 or Ne) to radiate and dissipate the power before it arrives to the divertor target plate. To this end, the Alcator C-Mod team has created a first-of-its-kind feedback system to control the injection of seed gas based on real-time surface heat flux measurements. Surface thermocouples provide real-time measurements of the surface temperature response to the plasma heat flux. The surface temperature measurements are inputted into an analog computer that “solves” the 1-D heat transport equation to deliver accurate, real-time signals of the surface heat flux. The surface heat flux signals are sent to the C-Mod digital plasma control system, which uses a proportional–integral–derivative (PID) algorithm to control the duty cycle demand to a pulse width modulated piezo valve, which in turn controls the injection of gas into the private flux region of the C-Mod divertor. This paper presents the design and implementation of this new feedback system as well as initial results using it to control divertor heat flux.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Multiple striated heat fluxes patterns on the EAST first wall generated by lower hybrid wave absorption in the scrape-off layer

Multiple striated heat fluxes on the EAST first wall are observed with lower hybrid wave (LHW) heating on the EAST device. Our analysis indicates that the heat source for the striated heat flux is from LHW absorption in the scrape-off layer (SOL). Magnetic field line tracing from the front of the LHW antenna grills is in good agreement with the striated heat flux profile. In addition the relative intensity of the LHW absorption in the SOL is consistent with the measured striated heat flux. However, the heat flux at inner strike points and outer strike points significantly decreased when the ion cyclotron resonance frequency (ICRF) wave was switched off, while there was no change for the striated heat flux, suggests that the striated heat flux is independent on the injected power to the core plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Measurements of multiple heat flux components at the divertor target by using surface eroding thermocouples (invited)

The Surface Eroding Thermocouple (SETC) is a robust diagnostic utilized in DIII-D to provide fast, edge-localized modes (ELMs) resolved heat flux measurements, in particular in geometric regions that are too shadowed for traditional infrared thermography. In order to further investigate the power dissipation in the divertor region, a combination of flush-mounted and recessed SETCs was developed to assess the effect on surface heating from non-charged particles at the divertor target. Utilizing the Divertor Materials Evaluation System sample exposure platform, the first demonstration of the feasibility of using this new method to distinguish between the heat flux from charged particles and that from neutrals and radiative heating was achieved. This paper details the process of using the combination of flush SETCs and recessed SETCs to measure the multiple heat flux components at the divertor target and further discusses how to determine two important ratios, α (ratio of heat flux from charged particles deposit on recessed SETC to that deposit on flush SETC) and β (ratio of heat flux from non-charged particles deposit on recessed SETC to that deposit on flush SETC), in the estimation of the heat flux from non-charged particle sources. Using a time dependent ratio α, it was found that ~50% of the total incident heat flux is attributable to the non-charged particles in the fully detached open divertor in DIII-D. Finally, the new application of similar SETC diagnostics in the Small Angle Slot divertor with a V-like configuration and partial tungsten coated surface (SAS-VW) is also introduced.

47 OTHER INSTRUMENTATION↗
DOE OSTI2011

EVOLUTION OF SPINNING AND BRAIDING HELICITY FLUXES IN SOLAR ACTIVE REGION NOAA 10930

The line-of-sight magnetograms from Solar Optical Telescope Narrowband Filter Imager observations of NOAA Active Region 10930 have been used to study the evolution of spinning and braiding helicities over a period of five days starting from 2006 December 9. The north (N) polarity sunspot was the follower and the south (S) polarity sunspot was the leader. The N-polarity sunspot in the active region was rotating in the counterclockwise direction. The rate of rotation was small during the first two days of observations and it increased up to 8 Degree-Sign hr{sup -1} on the third day of the observations. On the fourth and fifth days it remained at 4 Degree-Sign hr{sup -1} with small undulations in its magnitude. The sunspot rotated about 260 Degree-Sign in the last three days. The S-polarity sunspot did not complete more than 20 Degree-Sign in five days. However, it changed its direction of rotation five times over a period of five days and injected both the positive and negative type of spin helicity fluxes into the corona. Through the five days, both the positive and negative sunspot regions injected equal amounts of spin helicity. The total injected helicity is predominantly negative in sign. However, the sign of the spin and braiding helicity fluxes computed over all the regions were reversed from negative to positive five times during the five-day period of observations. The reversal in spinning helicity flux was found before the onset of the X3.4-class flare, too. Though, the rotating sunspot has been observed in this active region, the braiding helicity has contributed more to the total accumulated helicity than the spinning helicity. The accumulated helicity is in excess of -7 Multiplication-Sign 10{sup 43} Mx{sup 2} over a period of five days. Before the X3.4-class flare that occurred on 2006 December 13, the rotation speed and spin helicity flux increased in the S-polarity sunspot. Before the flare, the total injected helicity was larger than -6 Multiplication-Sign 10{sup 43} Mx{sup 2}. The observed reversal in the sign of spinning and braiding helicity fluxes could be the signature of the emergence of a twisted flux tube, which acquires the writhe of an opposite sign. The magnetic cloud associated with the ejected mass has carried about -7 Multiplication-Sign 10{sup 41} Mx{sup 2} of helicity. A time integration of helicity flux of about 1.2 hr integrated backward in time of the observation of the coronal mass ejection is sufficient for this event.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Energy propagation by transverse waves in multiple flux tube systems using filling factors

In the last few years, it has been found that transverse waves are present at all times in coronal loops or spicules. Their energy has been estimated with an expression derived for bulk Alfvén waves in homogeneous media, with correspondingly uniform wave energy density and flux. The kink mode, however, is localized in space with the energy density and flux dependent on the position in the cross-sectional plane. The more relevant quantities for the kink mode are the integrals of the energy density and flux over the cross-sectional plane. The present paper provides an approximation to the energy propagated by kink modes in an ensemble of flux tubes by means of combining the analysis of single flux tube kink oscillations with a filling factor for the tube cross-sectional area. This finally allows one to compare the expressions for energy flux of Alfvén waves with an ensemble of kink waves. We find that the correction factor for the energy in kink waves, compared to the bulk Alfvén waves, is between f and 2f, where f is the density filling factor of the ensemble of flux tubes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Simulation study of solar plasma eruptions caused by interactions between emerging flux and coronal arcade fields

We investigate the triggering mechanisms of plasma eruptions in the solar atmosphere due to interactions between emerging flux and coronal arcade fields by using two-dimensional MHD simulations. We perform parameter surveys with respect to arcade field height, magnetic field strength, and emerging flux location. Our results show that two possible mechanisms exist, and which mechanism is dominant depends mostly on emerging flux location. One mechanism appears when the location of emerging flux is close to the polarity inversion line (PIL) of an arcade field. This mechanism requires reconnection between the emerging flux and the arcade field, as pointed out by previous studies. The other mechanism appears when the location of emerging flux is around the edge of an arcade field. This mechanism does not require reconnection between the emerging flux and the arcade field but does demand reconnection in the arcade field above the PIL. Furthermore, we found that the eruptive condition for this mechanism can be represented by a simple formula.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

THE X-RAY FLUX DISTRIBUTION OF SAGITTARIUS A* AS SEEN BY CHANDRA

We present a statistical analysis of the X-ray flux distribution of Sgr A* from the Chandra X-Ray Observatory's 3 Ms Sgr A* X-ray Visionary Project in 2012. Our analysis indicates that the observed X-ray flux distribution can be decomposed into a steady quiescent component, represented by a Poisson process with rate Q = (5.24 ± 0.08) × 10{sup –3} counts s{sup –1}, and a variable component, represented by a power law process (dN/dF∝F {sup –ξ}, ξ=1.92{sub −0.02}{sup +0.03}). This slope matches our recently reported distribution of flare luminosities. The variability may also be described by a log-normal process with a median unabsorbed 2-8 keV flux of 1.8{sub −0.6}{sup +0.8}×10{sup −14} erg s{sup –1} cm{sup –2} and a shape parameter σ = 2.4 ± 0.2, but the power law provides a superior description of the data. In this decomposition of the flux distribution, all of the intrinsic X-ray variability of Sgr A* (spanning at least three orders of magnitude in flux) can be attributed to flaring activity, likely in the inner accretion flow. We confirm that at the faint end, the variable component contributes ∼10% of the apparent quiescent flux, as previously indicated by our statistical analysis of X-ray flares in these Chandra observations. Our flux distribution provides a new and important observational constraint on theoretical models of Sgr A*, and we use simple radiation models to explore the extent to which a statistical comparison of the X-ray and infrared can provide insights into the physics of the X-ray emission mechanism.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A KINETIC TRANSPORT THEORY FOR PARTICLE ACCELERATION AND TRANSPORT IN REGIONS OF MULTIPLE CONTRACTING AND RECONNECTING INERTIAL-SCALE FLUX ROPES

Simulations of particle acceleration in turbulent plasma regions with multiple contracting and merging (reconnecting) magnetic islands emphasize the key role of temporary particle trapping in island structures for the efficient acceleration of particles to form hard power-law spectra. Statistical kinetic transport theories have been developed that capture the essential physics of particle acceleration in multi-island regions. The transport theory of Zank et al. is further developed by considering the acceleration effects of both the mean and the variance of the electric fields induced by the dynamics of multiple inertial-scale flux ropes. A focused transport equation is derived that includes new Fokker-Planck terms for particle scattering and stochastic acceleration due to the variance in multiple flux-rope magnetic fields, plasma flows, and reconnection electric fields. A Parker transport equation is also derived in which a new expression for momentum diffusion appears, combining stochastic acceleration by particle scattering in the mean multi-flux-rope electric fields with acceleration by the variance in these electric fields. Test particle acceleration is modeled analytically considering drift acceleration by the variance in the induced electric fields of flux ropes in the slow supersonic, radially expanding solar wind. Hard power-law spectra occur for sufficiently strong inertial-scale flux ropes with an index modified by adiabatic cooling, solar wind advection, and diffusive escape from flux ropes. Flux ropes might be sufficiently strong behind interplanetary shocks where the index of suprathermal ion power-law spectra observed in the supersonic solar wind can be reproduced.

79 ASTRONOMY AND ASTROPHYSICS↗