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NASA NTRS2001

A Summary of the NASA Fusion Propulsion Workshop 2000

A NASA Fusion Propulsion Workshop was held on Nov. 8 and 9, 2000 at Marshall Space Flight Center (MSFC) in Huntsville, Alabama. A total of 43 papers were presented at the Workshop orally or by posters, covering a broad spectrum of issues related to applying fusion to propulsion. The status of fusion research was reported at the Workshop showing the outstanding scientific research that has been accomplished worldwide in the fusion energy research program. The international fusion research community has demonstrated the scientific principles of fusion creating plasmas with conditions for fusion burn with a gain of order unity: 0.25 in Princeton TFTR, 0.65 in the Joint European Torus, and a Q-equivalent of 1.25 in Japan's JT-60. This research has developed an impressive range of physics and technological capabilities that may be applied effectively to the research of possibly new propulsion-oriented fusion schemes. The pertinent physics capabilities include the plasma computational tools, the experimental plasma facilities, the diagnostics techniques, and the theoretical understanding. The enabling technologies include the various plasma heating, acceleration, and the pulsed power technologies.

Thio, Y. C. Francis↗

DOE OSTI2021

Efficient numerical integration of thermal interaction rates

In many problems in particle cosmology, interaction rates are dominated by 2 ↔ 2 scatterings, or get a substantial contribution from them, given that 1 ↔ 2 and 1 ↔ 3 reactions are phase-space suppressed. We describe an algorithm to represent, regularize, and evaluate a class of thermal 2 ↔ 2 and 1 ↔ 3 interaction rates for general momenta, masses, chemical potentials, and helicity projections. A key ingredient is an automated inclusion of virtual corrections to 1 ↔ 2 scatterings, which eliminate logarithmic and double-logarithmic IR divergences from the real 2 ↔ 2 and 1 ↔ 3 processes. We also review thermal and chemical potential induced contributions that require resummation if plasma particles are ultrarelativistic.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Massively parallel axisymmetric fluid model for streamer discharges

A highly parallelizable fluid plasma simulation tool based upon the first-order drift-diffusion equations is discussed. Atmospheric pressure plasmas have densities and gradients that require small element sizes in order to accurately simulate the plasm resulting in computational meshes on the order of millions to tens of millions of elements for realistic size plasma reactors. To enable simulations of this nature, parallel computing is required and must be optimized for the particular problem. Here, a finite-volume, electrostatic drift-diffusion implementation for low-temperature plasma is discussed. The implementation is built upon the Message Passing Interface (MPI) library in C++ using Object Oriented Programming. The underlying numerical method is outlined in detail and benchmarked against simple streamer formation from other streamer codes. Electron densities, electric field, and propagation speeds are compared with the reference case and show good agreement. Convergence studies are also performed showing a minimal space step of approximately 4 μm required to reduce relative error to below 1% during early streamer simulation times and even finer space steps are required for longer times. Additionally, strong and weak scaling of the implementation are studied and demonstrate the excellent performance behavior of the implementation up to 100 million elements on 1024 processors. Lastly, different advection schemes are compared for the simple streamer problem to analyze the influence of numerical diffusion on the resulting quantities of interest.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

A learned closure method applied to phase mixing in a turbulent gradient-driven gyrokinetic system in simple geometry

We present a new method for formulating closures that learn from kinetic simulation data. We apply this method to phase mixing in a simple gyrokinetic turbulent system – temperature-gradient-driven turbulence in an unsheared slab. The closure, called the learned multi-mode (LMM) closure, is constructed by, first, extracting an optimal basis from a nonlinear kinetic simulation using singular value decomposition. Subsequent nonlinear fluid simulations are projected onto this basis and the results are used to formulate the closure. We compare the closure with other closures schemes over a broad range of the relevant two-dimensional parameter space (collisionality and gradient drive). We find that the turbulent kinetic system produces phase-mixing rates much lower than the linear expectations, which the LMM closure is capable of capturing. We also compare radial heat fluxes. A Hammett–Perkins closure, generalized to include collisional effects, is quite successful throughout the parameter space, producing ${\sim }14\,\%$ root-mean-square (r.m.s.) error. The LMM closure is also very effective: when trained at three (two) points (in a 35 point parameter grid), the LMM closure produces $8\,\%$ ( $12\,\%$ ) r.m.s. errors. The LMM procedure can be readily generalized to other closure problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Fast-ion transport in quasisymmetric equilibria in the presence of a resonant Alfvénic perturbation

Significant progress has been made in designing magnetic fields that provide excellent confinement of the guiding-centre trajectories of alpha particles using quasisymmetry (QS). Given the reduction in this transport channel, we assess the impact of resonant Alfvén eigenmodes (AEs) on the guiding-centre motion. The AE amplitudes are chosen to be consistent with experimental measurements and large-scale simulations. We evaluate the drift resonance condition, phase-space island width and island overlap criterion for quasisymmetric configurations. Kinetic Poincaré plots elucidate features of the transport, including stiff transport above a critical perturbation amplitude. Our analysis highlights key departures from the AE-driven transport in tokamaks, such as the avoidance of phase-space island overlap in quasihelical configurations and the enhanced transport due to wide phase-space islands in low magnetic shear configurations. In configurations that are closer to QS, with QS deviations $\delta B/B_0 \lesssim 10^{-3}$ , the transport is primarily driven by the AE, while configurations that are further from QS, $\delta B/B_0 \sim 10^{-2}$ , experience significant transport due to the QS-breaking fields in addition to the AE.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

A Gaussian process based surrogate approach for the optimization of cylindrical targets

Simulating direct-drive inertial confinement experiments presents significant computational challenges, both due to the complexity of the codes required for such simulations and the substantial computational expense associated with target design studies. Machine learning models, and in particular, surrogate models, offer a solution by replacing simulation results with a simplified approximation. In this study, we apply surrogate modeling and optimization techniques that are well established in the existing literature to one-dimensional simulation data of a new cylindrical target design containing deuterium–tritium fuel. These models predict yields without the need for expensive simulations. We find that Bayesian optimization with Gaussian process surrogates enhances sampling efficiency in low-dimensional design spaces but becomes less efficient as dimensionality increases. Nonetheless, optimization routines within two-dimensional and five-dimensional design spaces can identify designs that maximize yield, while also aligning with established physical intuition. Optimization routines, which ignore constraints on hydrodynamic instability growth, are shown to lead to unstable designs in 2D, resulting in yield loss. However, routines that utilize 1D simulations and impose constraints on the in-flight aspect ratio converge on novel cylindrical target designs that are stable against hydrodynamic instability growth in 2D and achieve high yield.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

General kinetic ion-induced electron emission model for metallic walls applied to biased Z-pinch electrodes

A kinetic ion-induced electron emission (IIEE) model for general applications is developed to obtain the emitted electron energy spectrum for a distribution of ion impacts on a metallic surface. We assume an ionization cascade mechanism and use empirical models for the ion and electron stopping powers. The emission spectrum and the secondary electron yield (SEY) are validated for a variety of materials. The IIEE model is used to study the effect of IIEE on the plasma-material interactions of Z-pinch electrodes. Un-magnetized Boltzmann-Poisson simulations are performed for a Z-pinch plasma doubly bounded by two biased copper electrodes with and without IIEE at bias potentials from 0 to 9 kV. At the anode, the SEY decreases from 0 to 1 kV, but then increases at higher bias potentials. At the cathode, the SEY is much larger due to higher energy ion bombardment and grows with bias potential. As the bias potential increases, the emitted cathode electrons are accelerated to higher energies into the domain, collisionally heating the plasma. Above 1 kV, the heating is strong enough to increase the plasma potential. Despite SEY greater than 1, only a classical sheath forms as opposed to a space-charge limited or inverse sheath due to the emitted electron flux not reaching the space charge current saturation limits. Furthermore, the current in the emissionless cases saturates to a value lower than experiment. With IIEE, the current does not saturate and continues to increase with the 4 kV case, matching most closely with the experiment.

Carbon based materials↗

DOE OSTI2024

Overionized plasma in the supernova remnant Sagittarius A East anchored by XRISM observations

Sagittarius A East is a supernova remnant with a unique surrounding environment, as it is located in the immediate vicinity of the supermassive black hole at the Galactic center, Sagittarius A$^{*}$. The X-ray emission of the remnant is suspected to show features of overionized plasma, which would require peculiar evolutionary paths. We report on the first observation of Sagittarius A East with the X-Ray Imaging and Spectroscopy Mission (XRISM). Equipped with a combination of a high-resolution microcalorimeter spectrometer and a large field-of-view CCD imager, we for the first time resolved the Fe xxv K-shell lines into fine structure lines and measured the forbidden-to-resonance intensity ratio to be $1.39 \pm 0.12$, which strongly suggests the presence of overionized plasma. We obtained a reliable constraint on the ionization temperature just before the transition into the overionization state, of $\gt\! 4\:$keV. The recombination timescale was constrained to be $\lt\! 8 \times 10^{11} \:$cm$^{-3}\:$s. The small velocity dispersion of $109 \pm 6\:$km$\:$s$^{-1}$ indicates a low Fe ion temperature $\lt\! 8\:$keV and a small expansion velocity $\lt\! 200\:$km$\:$s$^{-1}$. The high initial ionization temperature and small recombination timescale suggest that either rapid cooling of the plasma via adiabatic expansion from dense circumstellar material or intense photoionization by Sagittarius A$^{*}$ in the past may have triggered the overionization.

galaxy center↗

DOE OSTI2022

Gaussian Mixture Model Solvers for the Boltzmann Equation

This report documents our experience constructing a numerical method for the collisional Boltzmann equation that is capable of accurately capturing the collisionless through strongly collisional limits. We explore three different functional representations and present a detailed account of a numerical method based on a spatially dependent Gaussian mixture model (GMM). The Kullback-Leibler divergence is used as a closeness measure and various expectation maximization (EM) solution algorithms are implemented to find a compact representation in velocity space for distribution functions that exhibit significant non-Maxwellian character. We discuss issues that appear with this representation over a range of Knudsen numbers for a prototypical test problem and demonstrate that the strongly collisional limit recovers a solution to Euler's equations. Looking forward, this approach is broadly applicable to the non-relativistic and relativistic collisional Vlasov equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Do Impulsive Solar-Energetic-Electron (SEE) Events Drive High-Voltage Charging Events on the Nightside of the Moon?

When the Earth’s moon is in the supersonic solar wind, the darkside of the Moon and the lunar plasma wake can be very dangerous charging environments. In the absence of photoelectron emission (dark) and in the absence of cool plasma (wake), the emission or collection of charge to reduce electrical potentials is difficult. Unique extreme charging events may occur during impulsive solar-energetic-electron (SEE) events when the lunar wake is dominated by relativistic electrons, with the potential to charge and differentially charge objects on and above the lunar surface to very-high negative electrical potentials. In this report the geometry of the magnetic connections from the Sun to the lunar nightside are explored; these magnetic connections are the pathways for SEEs from the Sun. Rudimentary charging calculations for objects in the relativistic-electron environment of the lunar wake are performed. To enable these charging calculations, secondary-electron yields for impacts by relativistic electrons are derived. Needed lunar electrical-grounding precautions for SEE events are discussed. Calls are made 1) for future dynamic simulations of the plasma wake in the presence of time-varying SEE-event relativistic electrons and time-varying solar-wind magnetic-field orientations and 2) for future charging calculations in the relativistic-electron wake environment and on the darkside lunar surface.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Low Cost, High Volume, Carbon Fiber Precursor for Plasma Oxidation

Light weighting with carbon fiber is critical to improving the energy efficiency of wind turbines, airplanes, and automobiles, but the high cost of carbon fiber continues to limit market growth and applications. Half of this cost is in the raw materials. For the carbon fiber market to reach the next level of adoption, the cost of both the raw materials and conversion must be reduced. This project considered the combination of low-cost, textile-grade precursors combined with the increased efficiency of plasma oxidation to greatly reduce the cost of carbon fiber. The primary objective of this project was to make industrial-grade carbon fiber (550 ksi tensile strength, 35 Msi tensile modulus) from textile-grade PAN precursors, something that cannot be achieved with conventional oxidation and to date has not been achieved with any technology. To accomplish this, the project team iteratively optimized the process conditions in the plasma oxidation and carbonization stages to maximize the tensile properties of the resultant carbon fibers. This involved implementing experimental designs for both stages, whereby process conditions (e.g. temperature) were varied and correlated to fiber properties. Samples of oxidized PAN fibers (OPFs) were prepared using a small pilot-scale plasma oxidation oven at 4XTechnologies (4XT). The thermal, chemical, and physical properties of OPF samples were analyzed by the University of Tennessee (UTK) and Oak Ridge National Laboratory (ORNL). The OPF samples were then converted to carbon fiber by subsequent low- and high-temperature carbonization using a lab-scale furnace at ORNL. The resultant carbon fibers were tested for tensile strength also at ORNL, and the results were fed back into the experimental design. Of the hundreds of carbon fiber samples produced over the course of the project, the best sample had an average break strength of 479 ksi and modulus of 33 Msi. While the best tensile properties achieved fell short of the final project targets of 550 ksi for break strength and 35 Msi for modulus, the team demonstrated the potential to produce industrial-grade carbon fiber using textile-grade precursors. The best performing fiber samples had tensile properties that are 87% of the goal for tensile strength and 94% of the goal for tensile modulus. With additional optimization work, it is likely that the targets could be achieved, since only a fraction of the process parameter space was explored during this project. 4XT and its affiliate (4M) have already secured funding through private equity, and there is a CRADA (Cooperative Research and Development Agreement) project currently underway with the Carbon Fiber Technology Center (CFTF) at ORNL to continue this research. Additionally, while not an original goal of the project, the carbon fibers for most samples had diameters >8.5μm. This is considerably larger than commercially available carbon fiber products, which can impart unique properties to the composites (e.g. increased compressive strength) and decrease manufacturing costs even further. Moreover, these fibers were oxidized with plasma oxidation using residence times ranging <60mins, which would be considered fast for normal diameter fibers, but it is as much as 5x faster when factoring in the diameter of the fibers.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Thermal and kinematic properties of ejecta in SN1987A revealed by XRISM

We present an analysis of high-resolution spectra from the shock-heated plasmas in SN 1987A, based on an observation using the Resolve instrument onboard the X-Ray Imaging and Spectroscopy Mission (XRISM). The 1.7–10 keV Resolve spectra are accurately represented by a single-component, plane-parallel shock plasma model, with a temperature of $2.84_{-0.08}^{+0.09}$ keV and an ionization parameter of $2.64_{-0.45}^{+0.58}$ × $10^{11}\,\,{\rm s\,\, cm}^{-3}$. The Resolve spectra are also well reproduced by the 3D magneto-hydrodynamic simulation presented by Orlando et al. (2020, A&A, 636, A22) suggesting substantial contribution from the ejecta. The metal abundances obtained with Resolve align with the Large Magellanic Cloud value, indicating that the X-rays in 2024 originate from “non-metal-rich” shock-heated ejecta and the reverse shock has not reached the inner metal-rich region of ejecta. Doppler widths of the atomic lines from Si, S, and Fe correspond to velocities of 1500–1700 km s$^{-1}$, where the thermal broadening effects in this non-metal-rich plasma are negligible. Therefore, the line broadening seen in Resolve spectra is determined by the large bulk motion of ejecta. For reference, we determined a $90\%$ upper limit on non-thermal emission from a pulsar wind nebula at $4.3 \times 10^{-13}$ erg cm$^{-2}$ s$^{-1}$ in the 2–10 keV range, aligning with NuSTAR findings by Greco et al. (2022, ApJ, 931, 132). Additionally, we searched for the $^{44}$Sc K line feature and found a $1\sigma$ upper limit of $1.0 \times 10^{-6}$ photons cm$^{-2}$ s$^{-1}$, which translates to an initial $^{44}$Ti mass of approximately $2 \times 10^{-4}\, M_{\odot }$, consistent with previous X-ray to soft gamma-ray observations (Boggs et al. 2015, Science, 348, 670; Grebenev et al. 2012, Nature, 490, 373; Leising 2006, ApJ, 651, 1019).

ISM: supernova remnants↗

DOE OSTI2025

Achievement of highly radiating plasma in negative triangularity and effect of reactor-relevant seeded impurities on confinement and transport

The first achievement of highly radiating plasmas in negative triangularity (NT) is shown with an operational space featuring high core radiation at high Greenwald fraction obtained with the injection of reactor-relevant seeded gases. These NT shape diverted discharges reach high values of normalized plasma pressure ( β N > 2) at high radiation fraction with no edge localized modes (ELMs) and a simultaneous reduction of the divertor heat flux. Here, we demonstrate that as long as the impurity level in the core is kept low to avoid excessive fuel dilution and impurity accumulation, integration of NT configuration with high radiation fraction not only is achievable but it can lead to confinement improvement with stabilization effects originating from collisionality, E × B shear and profiles changes due to impurity radiation cooling. The underlying physics mechanism is robust and reproducible and holds for a variety of impurity species. The absence of the requirement to stay in H-mode translates in a higher core radiation fraction potentially allowed in NT shape effectively mitigating the power exhaust issue. The results presented here demonstrate a path to high performance, ELM free and highly radiative regime with reactor-relevant seeding gases making this regime a potential new scenario for reactor design.

confinement improvement↗

DOE OSTI2022

Optimization of Backscatter and Symmetry for Laser Fusion Experiments Using Multiple Tunable Wavelengths

A new additional wavelength-tuning capability has been implemented on the National Ignition Facility (NIF) laser allowing for unprecedented control of crossed-beam energy transfer (CBET) between all groups of beams for better performance of indirect-drive inertial confinement fusion (ICF) ignition experiments. In particular, this advance allows for negation and reversal of flow-induced CBET and the rebalancing of the intensity of different groups of beams within an indirect-drive (ICF) hohlraum. The experiments conducted at the NIF using a 1.1 MJ laser pulse with peak power of 390 TW demonstrate this high level of control through measurements of the precise changes to stimulated Brillouin scattering, typically driven by flow-induced CBET at the end of the pulse. Additionally, this new capability is shown to be able to predictably control gold-wall plasma expansion in the target driven by early-time flow-induced CBET. Estimates of early-time CBET from the wall expansion are shown to be consistent with simulation expectations. This new additional capability to control symmetry and backscatter expands the design space of current experiments and provides extra margin for increased laser energy in near-future experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

A Data-driven, Physics-based Transport Model of Solar Energetic Particles Accelerated by Coronal Mass Ejection Shocks Propagating through the Solar Coronal and Heliospheric Magnetic Fields

Abstract In an effort to develop computational tools for predicting radiation hazards from solar energetic particles (SEPs), we have created a data-driven physics-based particle transport model to calculate the injection, acceleration, and propagation of SEPs from coronal mass ejection (CME) shocks traversing through the solar corona and interplanetary magnetic fields. The model runs on an input of corona and heliospheric plasma and magnetic field configuration from a magnetohydrodynamic model driven by solar photospheric magnetic field measurements superposed with observed CME shocks determined from coronagraph images. SEP source particles are injected at the shock using the result of diffusive shock acceleration formulation from a characteristic obliquity-dependent injection from a heated solar wind thermal tail population. With several advanced computation techniques involving stochastic simulation and integration, the model obtains the particle intensity at any location in interplanetary space through the rigorous solution to the time-dependent 5D focus transport equation in the phase space that includes perpendicular diffusion. We apply the model to the 2011 November 3 CME event. The calculation results reproduce multispacecraft SEP observations at Earth and STEREO-B reasonably well without normalization of particle flux. The observations at STEREO-A can be reproduced by rescaling particle energy or modified energy dependence of particle diffusion coefficients. This circumsolar SEP event seen by spacecraft at Earth, STEREO-A, and STEREO-B at widely separated longitudes can be explained by diffusive shock acceleration by a single CME shock with a moderate speed.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2023

CME Propagation Through the Heliosphere: Status and Future of Observations and Model Development

The ISWAT (International Space Weather Action Teams) heliosphere clusters H1 and H2 have a focus on interplanetary space and its characteristics, especially on the large-scale co-rotating and transient structures impacting Earth. Solar wind stream interaction regions, generated by the interaction between high-speed solar wind originating in large-scale open coronal magnetic fields and slower solar wind from closed magnetic fields, are regions of compressed plasma and magnetic field followed by high-speed streams that recur at the ~27 day solar rotation period. Short-term reconfigurations of the lower coronal magnetic field generate flare emissions and provide the energy to accelerate enormous amounts of magnetised plasma and particles in the form of coronal mass ejections into interplanetary space. The dynamic interplay between these phenomena changes the configuration of interplanetary space on various temporal and spatial scales which in turn influences the propagation of individual structures. While considerable efforts have been made to model the solar wind, we outline the limitations arising from the rather large uncertainties in parameters inferred from observations that make reliable predictions of the structures impacting Earth difficult. Moreover, the increased complexity of interplanetary space as solar activity rises in cycle 25 is likely to pose a challenge to these models. Combining observational and modeling expertise will extend our knowledge of the relationship between these different phenomena and the underlying physical processes, leading to improved models and scientific understanding and more-reliable space-weather forecasting. The current paper summarizes the efforts and progress achieved in recent years, identifies open questions, and gives an outlook for the next 5–10 years. It acts as basis for updating the existing COSPAR roadmap by Schrijver et al. (2015), as well as providing a useful and practical guide for peer-users and the next generation of space weather scientists.

Space weather↗

NASA NTRS2023

A Data-driven, Physics-based Transport Model of Solar Energetic Particles Accelerated by Coronal Mass Ejection Shocks Propagating through the Solar Coronal and Heliospheric Magnetic Fields

In an effort to develop computational tools for predicting radiation hazards from solar energetic particles (SEPs), we have created a data-driven physics-based particle transport model to calculate the injection, acceleration, and propagation of SEPs from coronal mass ejection (CME) shocks traversing through the solar corona and interplanetary magnetic fields. The model runs on an input of corona and heliospheric plasma and magnetic field configuration from a magnetohydrodynamic model driven by solar photospheric magnetic field measurements superposed with observed CME shocks determined from coronagraph images. SEP source particles are injected at the shock using the result of diffusive shock acceleration formulation from a characteristic obliquity-dependent injection from a heated solar wind thermal tail population. With several advanced computation techniques involving stochastic simulation and integration, the model obtains the particle intensity at any location in interplanetary space through the rigorous solution to the time-dependent 5D focus transport equation in the phase space that includes perpendicular diffusion. We apply the model to the 2011 November 3 CME event. The calculation results reproduce multispacecraft SEP observations at Earth and STEREO-B reasonably well without normalization of particle flux. The observations at STEREO-A can be reproduced by rescaling particle energy or modified energy dependence of particle diffusion coefficients. This circumsolar SEP event seen by spacecraft at Earth, STEREO-A, and STEREO-B at widely separated longitudes can be explained by diffusive shock acceleration by a single CME shock with a moderate speed.

Solar energetic particles↗

NASA NTRS2015

Mission Oriented Support and Theory (MOST) for MMS -- The Goddard Space Flight Center/University of California Los Angeles Interdisciplinary Science Program

The MOST IDS team was tasked with focusing on two general areas: The first was to participate with the Fast Plasma Investigation (FPI) team in the development of virtual detectors that model the instrument responses of the MMS FPI sensors. The virtual instruments can be 'flown through' both simulation data (from magnetohydrodynamic, hybrid, and kinetic simulations) and Cluster and THEMIS spacecraft data. The goal is to determine signatures of magnetic reconnection expected during the MMS mission. Such signatures can serve as triggers for selection of burst mode downloads. The chapter contributed by the FPI team covers that effort in detail and, therefore, most of that work has not been included here. The second area of emphasis, and the one detailed in this chapter, was to build on past and present knowledge of magnetic reconnection and its physical signatures. Below we describe intensive analyses of Cluster and THEMIS data together with theoretical models and simulations that delineate the plasma signatures that surround sites of reconnection, including the effects of turbulence as well as the detailed kinetic signatures that indicate proximity to reconnection sites. In particular, we point out that particles are energized in several regions, not only at the actual site of reconnection.

Goldstein, Melvyn L.↗