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DOE OSTI2026

Closure models for the feedback of energetic particles on plasma turbulence

Energetic particles interact with the plasma surrounding them, resonating with certain types of plasma waves to stabilize them while destabilizing others, and changing the character of the background turbulence in ways that have not been fully quantified or understood. Interaction with the turbulent background plasma is key to the acceleration of many types of energetic particles including high-energy cosmic rays, solar energetic particles, and pick-up ions. The acceleration of particles is a process that would ideally be described by a kinetic model, a type of model that follows a probability distribution function (PDF) for all particles in 7-dimensional (x, y, z, v x , v y , v z , t) space. Because of the high dimensionality of a kinetic model, simulations that solve kinetic equations use the largest computational resources currently available, and are yet unable to simulate a realistic number of particles, reach the large scales necessary for astrophysical problems, and use high-precision numerical methods. Two available alternatives to kinetic plasma models have been explored for this problem, with limited success. One is a multi-fluid model produced by a cumulant discarding closure, which evolves coupled equations for the velocity, magnetic field, and internal energy for both the background plasma and the fluid of energetic particles. However, simulations that solve multi-fluid magnetohydrodynamic (MHD) equations are able to include the interaction with energetic particles only in crude ways, typically as an add-on pressure term. The second alternative is to use a hybrid method to couple a fluid description of the background plasma to a kinetic model or a Fokker–Planck model for the energetic particles. These methods are hampered by the physical modeling of the coupling. In this work, we develop a new model, which follows the PDF for all particles; this can be viewed as a step toward physical realism above a multi-fluid MHD model, while also being more computationally efficient than a kinetic model. The equations we develop model both the background plasma and the energetic particles self-consistently. Over the last decade, similar PDF methods have been developed to a high level of sophistication to model reactive flows and turbulent combustion for engineering applications. For treatment of the feedback of the energetic particles on a background plasma, a PDF closure approach should evaluate the mean characteristics, including the density, with better statistical quality than will particle-sampling procedures.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Safety First: Stability and Dissipation of Line-tied Force-free Flux Tubes in Magnetized Coronae

Abstract Magnetized plasma columns and extended magnetic structures with both footpoints anchored to a surface layer are an important building block of astrophysical dissipation models. Current loops shining in X-rays during the growth of plasma instabilities are observed in the corona of the Sun and are expected to exist in highly magnetized neutron star magnetospheres and accretion disk coronae. For varying twist and system sizes, we investigate the stability of line-tied force-free flux tubes and the dissipation of twist energy during instabilities using linear analysis and time-dependent force-free electrodynamics simulations. Kink modes ( m = 1) and efficient magnetic energy dissipation develop for plasma safety factors q ≲ 1, where q is the inverse of the number of magnetic field line windings per column length. Higher-order fluting modes ( m > 1) can distort equilibrium flux tubes for q > 1 but induce significantly less dissipation. In our analysis, the characteristic pitch μ ˜ 0 of flux-tube field lines determines the growth rate ( ∝ μ ˜ 0 3 ) and minimum wavelength of the kink instability ( ∝ μ ˜ 0 − 1 ). We use these scalings to determine a minimum flux tube length for the growth of the kink instability for any given μ ˜ 0 . By drawing analogies to idealized magnetar magnetospheres with varying regimes of boundary shearing rates, we discuss the expected impact of the pitch-dependent growth rates for magnetospheric dissipation in magnetar conditions.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Nuclear Uncertainties Associated with the Nucleosynthesis in Ejecta of a Black Hole Accretion Disk

Abstract The simulation of heavy element nucleosynthesis requires input from yet-to-be-measured nuclear properties. The uncertainty in the values of these off-stability nuclear properties propagates to uncertainties in the predictions of elemental and isotopic abundances. However, for any given astrophysical explosion, there are many different trajectories, i.e., temperature and density histories, experienced by outflowing material, and thus different nuclear properties can come into play. We consider combined nucleosynthesis results from 460,000 trajectories from a black hole accretion disk and find the spread in elemental predictions due solely to unknown nuclear properties to be a factor of a few. We analyze this relative spread in model predictions due to nuclear variations and conclude that the uncertainties can be attributed to a combination of properties in a given region of the abundance pattern. We calculate a cross-correlation between mass changes and abundance changes to show how variations among the properties of participating nuclei may be explored. Our results provide further impetus for measurements of multiple quantities on individual short-lived neutron-rich isotopes at modern experimental facilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

A More Precise Measurement of the Radius of PSR J0740+6620 Using Updated NICER Data

PSR J0740+6620 is the neutron star with the highest precisely determined mass, inferred from radio observations to be 2.08 ± 0.07 M ⊙ . Measurements of its radius therefore hold promise to constrain the properties of the cold, catalyzed, high-density matter in neutron star cores. Previously, Miller et al. and Riley et al. reported measurements of the radius of PSR J0740+6620 based on Neutron Star Interior Composition Explorer (NICER) observations accumulated through 2020 April 17, and an exploratory analysis utilizing NICER background estimates and a data set accumulated through 2021 December 28 was presented in Salmi et al. Here we report an updated radius measurement, derived by fitting models of X-ray emission from the neutron star surface to NICER data accumulated through 2022 April 21, totaling ~1.1 Ms additional exposure compared to the data set analyzed in Miller et al. and Riley et al., and to data from XMM-Newton observations. We find that the equatorial circumferential radius of PSR J0740+6620 is ${12.92}_{-1.13}^{+2.09}$ km (68% credibility), a fractional uncertainty ~83% the width of that reported in Miller et al., in line with statistical expectations given the additional data. If we were to require the radius to be less than 16 km, as was done in Salmi et al., then our 68% credible region would become $R={12.76}_{-1.02}^{+1.49}$ km, which is close to the headline result of Salmi et al. Our updated measurements, along with other laboratory and astrophysical constraints, imply a slightly softer equation of state than that inferred from our previous measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Combined Pre-supernova Alert System with KamLAND and Super-Kamiokande

Preceding a core-collapse supernova (CCSN), various processes produce an increasing amount of neutrinos of all flavors characterized by mounting energies from the interior of massive stars. Among them, the electron antineutrinos are potentially detectable by terrestrial neutrino experiments such as KamLAND and Super-Kamiokande (SK) via inverse beta decay interactions. Once these pre-supernova (pre-SN) neutrinos are observed, an early warning of the upcoming CCSN can be provided. In light of this, KamLAND and SK, both located in the Kamioka mine in Japan, have been monitoring pre-SN neutrinos since 2015 and 2021, respectively. Recently, we performed a joint study between KamLAND and SK on pre-SN neutrino detection. A pre-SN alert system combining the KamLAND detector and the SK detector was developed and put into operation, which can provide a supernova alert to the astrophysics community. Fully leveraging the complementary properties of these two detectors, the combined alert is expected to resolve a pre-SN neutrino signal from a 15 M ⊙ star within 510 pc of the Earth at a significance level corresponding to a false alarm rate of no more than 1 per century. For a Betelgeuse-like model with optimistic parameters, it can provide early warnings up to 12 hr in advance.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Periodic Gamma-Ray Modulation of the Blazar PG 1553+113 Confirmed by Fermi-LAT and Multiwavelength Observations

A 2.1 yr periodic oscillation of the gamma-ray flux from the blazar PG 1553+113 has previously been tentatively identified in ∼7 yr of data from the Fermi Large Area Telescope. After 15 yr of Fermi sky-survey observations, doubling the total time range, we report >7 cycle gamma-ray modulation with an estimated significance of 4σ against stochastic red noise. Independent determinations of oscillation period and phase in the earlier and the new data are in close agreement (chance probability <0.01). Pulse timing over the full light curve is also consistent with a coherent periodicity. Multiwavelength new data from Swift X-Ray Telescope, Burst Alert Telescope, and UVOT, and from KAIT, Catalina Sky Survey, All-Sky Automated Survey for Supernovae, and Owens Valley Radio Observatory ground-based observatories as well as archival Rossi X-Ray Timing Explorer satellite-All Sky Monitor data, published optical data of Tuorla, and optical historical Harvard plates data are included in our work. Optical and radio light curves show clear correlations with the gamma-ray modulation, possibly with a nonconstant time lag for the radio flux. We interpret the gamma-ray periodicity as possibly arising from a pulsational accretion flow in a sub-parsec binary supermassive black hole system of elevated mass ratio, with orbital modulation of the supplied material and energy in the jet. Other astrophysical scenarios introduced include instabilities, disk and jet precession, rotation or nutation, and perturbations by massive stars or intermediate-mass black holes in polar orbit.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Plasma Dynamics and Nonthermal Particle Acceleration in 3D Nonrelativistic Magnetic Reconnection

Understanding plasma dynamics and nonthermal particle acceleration in 3D magnetic reconnection has been a long-standing challenge. In this paper, we explore these problems by performing large-scale fully kinetic simulations of multi-X-line plasmoid reconnection with various parameters in both the weak- and strong-guide-field regimes. In each regime, we have identified its unique 3D dynamics that lead to field-line chaos and efficient acceleration, and we have achieved nonthermal acceleration of both electrons and protons into power-law spectra. The spectral indices agree well with a simple Fermi acceleration theory that includes guide-field dependence. In the low-guide-field regime, the flux rope kink instability governs the 3D dynamics for efficient acceleration. The weak dependence of the spectra on the ion-to-electron mass ratio and β ($\ll$1) implies that the particles are sufficiently magnetized for Fermi acceleration in our simulations. While both electrons and protons are injected at reconnection exhausts, protons are primarily injected by perpendicular electric fields through Fermi reflections and electrons are injected by a combination of perpendicular and parallel electric fields. The magnetic power spectra agree with in situ magnetotail observations, and the spectral index may reflect a reconnection-driven size distribution of plasmoids instead of the Goldreich–Sridhar vortex cascade. As the guide field becomes stronger, the oblique flux ropes of large sizes capture the main 3D dynamics for efficient acceleration. Intriguingly, the oblique flux ropes can also experience flux rope kink instability, to drive extra 3D dynamics. This work has broad implications for 3D reconnection dynamics and particle acceleration in heliophysics and astrophysics.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Electron Influence on the Parallel Proton Firehose Instability in 10-moment, Multifluid Simulations

Instabilities driven by pressure anisotropy play a critical role in modulating the energy transfer in space and astrophysical plasmas. For the first time, we simulate the evolution and saturation of the parallel proton firehose instability using a multifluid model without adding artificial viscosity. These simulations are performed using a 10-moment, multifluid model with local and gradient relaxation heat-flux closures in high-β proton–electron plasmas. When these higher-order moments are included and pressure anisotropy is permitted to develop in all species, we find that the electrons have a significant impact on the saturation of the parallel proton firehose instability, modulating the proton pressure anisotropy as the instability saturates. Even for lower β's more relevant to heliospheric plasmas, we observe a pronounced electron energization in simulations using the gradient relaxation closure. Our results indicate that resolving the electron pressure anisotropy is important to correctly describe the behavior of multispecies plasma systems.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Tearing-mediated Alfvénic Turbulence in a Relativistic Plasma

In astrophysical relativistic plasmas, Alfvénic turbulence exists across a wide range of scales. Similar to a nonrelativistic case, this turbulence can be influenced by the tearing instability. We argue that in an ultrarelativistic pair plasma the tearing effects become significant at the critical scale given by ${a}_{t}\sim {d}_{\mathrm{rel}}{\left({L}_{\perp }/{d}_{\mathrm{rel}}\right)}^{n/(4+5n)}$, where L ⊥ represents the outer scale of the turbulence and d rel the relativistic electron inertial scale. Here n = 1 corresponds to the Harris magnetic configurations, while n = 2 applies to localized (non-Harris) magnetic profiles of turbulence-generated current sheets. Below the critical scale, the energy spectrum of magnetic fluctuations steepens to W(k)dk ∝ k -(7n+2)/3n dk. However, this happens only when $\tilde{\sigma }\ll {\left({L}_{\perp }/{d}_{\mathrm{rel}}\right)}^{(2+4n)/(4+5n)}$, where $\tilde{\sigma }$ is the magnetization parameter based on the magnetic fluctuations. If the opposite inequality holds, the Alfvénic cascade is instead affected by charge starvation at scales below ${a}_{\mathrm{ch}}\sim {d}_{\mathrm{rel}}{\left({d}_{\mathrm{rel}}/{L}_{\perp }\right)}^{1/3}{\tilde{\sigma }}^{2/3}$, and the energy spectrum becomes steeper than W(k)dk ∝ k -3 dk. When d rel is replaced by its nonrelativistic equivalent, our results agree with the nonrelativistic analysis of N. F. Loureiro & S. Boldyrev (2018). In the Harris case n = 1, they agree with the recent relativistic studies by I. Demidov & Y. Lyubarsky.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Multifrequency Models of Black Hole Photon Rings from Low-luminosity Accretion Disks

Images of black holes encode both astrophysical and gravitational properties. Detecting highly lensed features in images can differentiate between these two effects. We present an accretion disk emission model coupled to the Adaptive Analytical Ray Tracing (AART) code that allows a fast parameter space exploration of black hole photon ring images produced from synchrotron emission from 10 to 670 GHz. As an application, we systematically study several disk models and compute their total flux density, average radii, and optical depth. The model parameters are chosen around fiducial values calibrated to general relativistic magnetohydrodynamic (GRMHD) simulations and observations of M87*. For the parameter space studied, we characterize the transition between optically thin and thick regimes and the frequency at which the first photon ring is observable. Our results highlight the need for careful definitions of photon ring radius in the image domain, as in certain models the highly lensed photon ring is dimmer than the direct emission at certain angles. We find that at low frequencies the ring radii are set by the electron temperature, while at higher frequencies the magnetic field strength plays a more significant role, demonstrating how multifrequency analysis can also be used to infer plasma parameters. Lastly, we show how our implementation can qualitatively reproduce multifrequency black hole images from GRMHD simulations when adding time variability to our disk model through Gaussian random fields. This approach provides a new method for simulating observations from the Event Horizon Telescope and the proposed Black Hole Explorer space mission.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

VERITAS and Multiwavelength Observations of the Blazar B3 2247+381 in Response to an IceCube Neutrino Alert

While the sources of the diffuse astrophysical neutrino flux detected by the IceCube Neutrino Observatory are still largely unknown, one of the promising methods to improve our understanding of them is investigating the potential temporal and spatial correlations between neutrino alerts and the electromagnetic radiation from blazars. We report on the multiwavelength target-of-opportunity observations of the blazar B3 2247+381, taken in response to an IceCube multiplet alert for a cluster of muon neutrino events compatible with the source location between 2022 May 20 and 2022 November 10. B3 2247+381 was not detected with VERITAS during this time period. The source was found to be in a low-flux state in the optical, ultraviolet, and gamma-ray bands for the time interval corresponding to the neutrino event, but was detected in the hard X-ray band with NuSTAR during this period. We find the multiwavelength spectral energy distribution is described well using a simple one-zone leptonic synchrotron self-Compton radiation model. Moreover, assuming the neutrinos originate from hadronic processes within the jet, the neutrino flux would be accompanied by a photon flux from the cascade emission, and the integrated photon flux required in such a case would significantly exceed the total multiwavelength fluxes and the VERITAS upper limits presented here. The lack of flaring activity observed with VERITAS, combined with the low multiwavelength flux levels, as well as the significance of the neutrino excess being at a 3σ level (uncorrected for trials), makes B3 2247+381 an unlikely source of the IceCube multiplet. We conclude that the neutrino excess is likely a background fluctuation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

How Does Feedback Affect the Star Formation Histories of Galaxies?

Star formation in galaxies is regulated by the interplay of a range of processes that shape the multiphase gas in the interstellar and circumgalactic media. Using the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) suite of cosmological simulations, we study the effects of varying feedback and cosmology on the average star formation histories (SFHs) of galaxies at z ∼ 0 across the IllustrisTNG, SIMBA, and ASTRID galaxy formation models. We find that galaxy SFHs in all three models are sensitive to changes in stellar feedback, which affect the efficiency of baryon cycling and the rates at which central black holes grow, whereas the effects of varying active galactic nucleus (AGN) feedback depend on model-specific implementations of black hole seeding, accretion, and feedback. We also find strong interaction terms that couple stellar and AGN feedback, usually by regulating the amount of gas available for the central black hole to accrete. Using a double power law to describe the average SFHs, we derive a general set of equations relating the shape of the SFHs to physical quantities like baryon fraction and black hole mass across all three models. We find that a single set of equations (albeit with different coefficients) can describe the SFHs across all three CAMELS models, with cosmology dominating the SFH at early times, followed by halo accretion, and feedback and baryon cycling at late times. Galaxy SFHs provide a novel, complementary probe to constrain cosmology and feedback, and can connect the observational constraints from current and upcoming galaxy surveys with the physical mechanisms responsible for regulating galaxy growth and quenching.

Iyer, Kartheik G. [Columbia Univ., New York, NY (U↗

DOE OSTI2026

The Thermal and Kinematic Sunyaev–Zeldovich Effect in Galaxy Clusters and Filaments Using Multifrequency Temperature Maps of the Cosmic Microwave Background: A399–A401 Cluster Pair Case Study

We present a multifrequency and multi-instrument methodology to study the physical properties of galaxy clusters and cosmic filaments using cosmic microwave background observations. Our approach enables simultaneous measurement of both the thermal (tSZ) and kinematic Sunyaev–Zeldovich (kSZ) effects, incorporates relativistic corrections, and models astrophysical foregrounds such as thermal dust emission. We do this by jointly fitting a single physical model across multiple maps from multiple instruments at different frequencies, rather than fitting a model to a single Compton-y map. We demonstrate the success of this method by fitting the A399–A401 galaxy cluster pair and filament system using archival data from the Planck satellite and new, targeted deep data from the Atacama Cosmology Telescope, covering 11 different frequencies over 14 maps from 30 GHz to 545 GHz. Our tSZ results are consistent with previous work using Compton-y maps. We measure the line-of-sight peculiar velocities of the cluster–filament system using the kSZ effect and find statistical uncertainties on individual cluster peculiar velocities of ≲600 km s −1 , which are competitive with current state-of-the-art measurements. Additionally, we measure the optical depth of the filament component with a signal-to-noise of 8.5σ and reveal hints of its morphology. This modular approach is well-suited for application to future instruments across a wide range of millimeter and submillimeter wavebands.

Gill, Ajay S. [National Research Council of Canada↗

DOE OSTI2025

PROTOCALC, a W -band Polarized Calibrator for Cosmic Microwave Background Telescopes: Application to Simons Observatory and CLASS

Current- and next-generation cosmic microwave background (CMB) experiments will measure polarization anisotropies with unprecedented sensitivities. The need for high precision in these measurements underscores the importance of gaining a comprehensive understanding of instrument properties, with a particular emphasis on the study of the beam properties, and especially their polarization characteristics and the measurement of the polarization angle. In this context, a major challenge lies in the scarcity of millimeter polarized astrophysical sources with sufficient brightness and calibration knowledge to meet the stringent accuracy requirements of future CMB missions. This led to the development of a drone-borne calibration source designed for the frequency band centered on approximately 90 GHz, matching a commonly used channel in ground-based CMB measurements. The Prototype Calibrator for Cosmology, PROTOCALC, has undergone thorough in-lab testing, and its properties have been subsequently modeled through simulation software integrated into the standard Simons Observatory analysis pipeline. Moreover, the PROTOCALC system has been tested in the field, having been deployed twice on calibration campaigns with CMB telescopes in the Atacama Desert. The data collected constrain the roll angle of the source with a statistical accuracy of 0$^°_•$045.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Multimessengers from the Radioactive Decay of r -process Nuclei

The radioactive β-decay of nuclei synthesized in the rapid neutron capture process (r-process) releases a variety of particles, including electrons, γ-rays, neutrinos, and neutrons. These particles provide a rich set of multimessenger signals that carry information about the astrophysical environments where neutron-rich nucleosynthesis occurs. In this work, we calculate from first principles the emission spectra resulting from the β-decay of r-process nuclei. Our approach incorporates detailed nuclear structure and decay data to model the energy distributions of each particle species. We couple the spectra with a nuclear reaction network simulation to obtain the temporal evolution of these distributions. We find that the emission distributions vary significantly in time and are nonthermal, with substantial average energies. We investigate these nuclear signals as a direct probe of heavy element formation and show that they are complementary observables to kilonova.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

A closer look in the mirror: reflections on the matter/dark matter coincidence

We argue that the striking similarity between the cosmic abundances of baryons and dark matter, despite their very different astrophysical behavior, strongly motivates the scenario in which dark matter resides within a rich dark sector parallel in structure to that of the standard model. The near cosmic coincidence is then explained by an approximate ℤ$_{2}$ exchange symmetry between the two sectors, where dark matter consists of stable dark neutrons, with matter and dark matter asymmetries arising via parallel WIMP baryogenesis mechanisms. Taking a top-down perspective, we point out that an adequate ℤ$_{2}$ symmetry necessitates solving the electroweak hierarchy problem in each sector, without our committing to a specific implementation. A higher-dimensional realization in the far UV is presented, in which the hierarchical couplings of the two sectors and the requisite ℤ$_{2}$-breaking structure arise naturally from extra-dimensional localization and gauge symmetries. We trace the cosmic history, paying attention to potential pitfalls not fully considered in previous literature. Residual ℤ$_{2}$-breaking can very plausibly give rise to the asymmetric reheating of the two sectors, needed to keep the cosmological abundance of relativistic dark particles below tight bounds. We show that, despite the need to keep inter-sector couplings highly suppressed after asymmetric reheating, there can naturally be order-one couplings mediated by TeV scale particles which can allow experimental probes of the dark sector at high energy colliders. Massive mediators can also induce dark matter direct detection signals, but likely at or below the neutrino floor.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Crosstalk Effects in Microwave SQUID Multiplexed TES Bolometer Readout

Transition-edge sensor (TES) bolometers are broadly used for background-limited astrophysical measurements from the far-infrared to mm-waves. Many planned future instruments require increasingly large detector arrays, but their scalability is limited by their cryogenic readout electronics. Microwave SQUID multiplexing offers a highly capable scaling solution through the use of inherently broadband circuitry, enabling readout of hundreds to thousands of channels per microwave line. As with any multiplexing technique, the channelization mechanism gives rise to electrical crosstalk which must be understood and controlled so as to not degrade the instrument sensitivity. Here, in this study, we explore implications relevant for TES bolometer array applications, focusing in particular on upcoming mm-wave observatories such as the Simons Observatory and AliCPT. We model the relative contributions of the various underlying crosstalk mechanisms, evaluate the difference between fixed-tone and tone-tracking readout systems, and discuss ways in which crosstalk nonlinearity will complicate on-sky measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Ohm’s Law, the Reconnection Rate, and Energy Conversion in Collisionless Magnetic Reconnection

Magnetic reconnection is a ubiquitous plasma process that transforms magnetic energy into particle energy during eruptive events throughout the universe. Reconnection not only converts energy during solar flares and geomagnetic substorms that drive space weather near Earth, but it may also play critical roles in the high energy emissions from the magnetospheres of neutron stars and black holes. In this review article, we focus on collisionless plasmas that are most relevant to reconnection in many space and astrophysical plasmas. Guided by first-principles kinetic simulations and spaceborne in-situ observations, we highlight the most recent progress in understanding this fundamental plasma process. We start by discussing the non-ideal electric field in the generalized Ohm’s law that breaks the frozen-in flux condition in ideal magnetohydrodynamics and allows magnetic reconnection to occur. We point out that this same reconnection electric field also plays an important role in sustaining the current and pressure in the current sheet and then discuss the determination of its magnitude (i.e., the reconnection rate), based on force balance and energy conservation. This approach to determining the reconnection rate is applied to kinetic current sheets with a wide variety of magnetic geometries, parameters, and background conditions. We also briefly review the key diagnostics and modeling of energy conversion around the reconnection diffusion region, seeking insights from recently developed theories. Finally, future prospects and open questions are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗