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High energy electrons carry much of a solar flare's energy. Therefore, understanding changes in electron beam distributions during their propagation is crucial. A key focus of this paper is how the co-spatial return current reduces the energy flux carried by these accelerated electrons. We systematically compute this reduction for various beam and plasma parameters relevant to solar flares. Our 1D model accounts for collisions between beam and plasma electrons, return current electric-field deceleration, thermalization in a warm target approximation, and runaway electron contributions. The results focus on the classical (Spitzer) regime, offering a valuable benchmark for energy flux reduction and its extent. Return current losses are only negligible for the lowest nonthermal fluxes. We calculate the conditions for return current losses to become significant and estimate the extent of the modification to the beam's energy flux density. We also calculate two additional conditions which occur for higher injected fluxes: (1) where runaway electrons become significant, and (2) where current-driven instabilities might become significant, requiring a model that self-consistently accounts for them. Condition (2) is relaxed and the energy flux losses are reduced in the presence of runaway electrons. All results are dependent on beam and co-spatial plasma parameters. We also examine the importance of the reflection of beam electrons by the return-current electric field. We show that the interpretation of a number of flares needs to be reviewed to account for the effects of return currents., Comment: 22 pages, 11 figures, Submitted to ApJ

The results of simulations of magnetic reconnection accompanied by electron and proton heating and energization in a macroscale system are presented. Both species form extended powerlaw distributions that extend nearly three decades in energy. The primary drive mechanism for the production of these nonthermal particles is Fermi reflection within evolving and coalescing magnetic flux ropes. While the powerlaw indices of the two species are comparable, the protons overall gain more energy than electrons and their power law extends to higher energy. The power laws roll into a hot thermal distribution at low energy with the transition energy occurring at lower energy for electrons compared with protons. A strong guide field diminishes the production of non-thermal particles by reducing the Fermi drive mechanism. In solar flares, proton power laws should extend down to 10's of keV, far below the energies that can be directly probed via gamma-ray emission. Thus, protons should carry much more of the released magnetic energy than expected from direct observations., Comment: 14 pages, 8 figures

Simulations have played a critical role in the advancement of our knowledge of magnetic reconnection. However, due to the inherently multiscale nature of reconnection, it is impossible to simulate all physics at all scales. For this reason, a wide range of simulation methods have been crafted to study particular aspects and consequences of magnetic reconnection. This chapter reviews many of these methods, laying out critical assumptions, numerical techniques, and giving examples of scientific results. Plasma models described include magnetohydrodynamics (MHD), Hall MHD, Hybrid, kinetic particle-in-cell (PIC), kinetic Vlasov, Fluid models with embedded PIC, Fluid models with direct feedback from energetic populations, and the Rice Convection Model (RCM)., Comment: Chapter 5.2 of ISSI Book on Magnetic Reconnection, submitted to Space Science Reviews

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 of 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., Comment: Submitted to Space Science Reviews. This is a review paper as an outcome of the 2022 Magnetic Reconnection Workshop in the International Space Science Institute

A set of equations are developed that extend the macroscale magnetic reconnection simulation model kglobal to include particle ions. The extension from earlier versions of kglobal, which included only particle electrons, requires the inclusion of the inertia of particle ions in the fluid momentum equation, which was not required in the electron-only model. The new equations will facilitate the exploration of the simultaneous non-thermal energization of ions and electrons during magnetic reconnection in macroscale systems. Numerical tests of the propagation of Alfv\'en waves in a plasma with anisotropic electron and ion pressure are presented to benchmark the new model., Comment: 10 pages, 2 figures

We conduct two-dimensional particle-in-cell simulations to investigate the scattering of electron heat flux by self-generated oblique electromagnetic waves. The heat flux is modeled as a bi-kappa distribution with a T_parallel > T_perp temperature anisotropy maintained by continuous injection at the boundaries. The anisotropic distribution excites oblique whistler waves and filamentary-like Weibel instabilities. Electron velocity distributions taken after the system has reached a steady state show that these in stabilities inhibit the heat flux and drive the total distributions towards isotropy. Electron trajectories in velocity space show a circular-like diffusion along constant energy surfaces in the wave frame. The key parameter controlling the scattering rate is the average speed, or drift speed vd, of the heat flux compared with the electron Alfven speed vAe, with higher drift speeds producing stronger fluctua tions and a more significant reduction of the heat flux. Reducing the density of the electrons carrying the heat flux by 50% does not significantly affect the scattering rate. A scaling law for the electron scattering rate versus vd/vAe is deduced from the simulations. The implications of these results for understanding energetic electron transport during solar flare energy release are discussed.

Heliophysics theory and modeling build understanding from fundamental principles to motivate, interpret, and predict observations. Together with observational analysis, they constitute a comprehensive scientific program in heliophysics. As observations and data analysis become increasingly detailed, it is critical that theory and modeling develop more quantitative predictions and iterate with observations. Advanced theory and modeling can inspire and greatly improve the design of new instruments and increase their chance of success. In addition, in order to build physics-based space weather forecast models, it is important to keep developing and testing new theories, and maintaining constant communications with theory and modeling. Maintaining a sustainable effort in theory and modeling is critically important to heliophysics. We recommend that all funding agencies join forces and consider expanding current and creating new theory and modeling programs--especially, 1. NASA should restore the HTMS program to its original support level to meet the critical needs of heliophysics science; 2. a Strategic Research Model program needs to be created to support model development for next-generation basic research codes; 3. new programs must be created for addressing mission-critical theory and modeling needs; and 4. enhanced programs are urgently required for training the next generation of theorists and modelers., Comment: White paper submitted to Heliophysics 2024 Decadal Survey

Electron ring velocity space distributions have previously been seen in numerical simulations of magnetic reconnection exhausts and have been suggested to be caused by the magnetization of the electron outflow jet by the compressed reconnected magnetic fields [Shuster et al., ${\it Geophys.~Res.~Lett.}, {\bf 41}$, 5389 (2014)]. We present a theory of the dependence of the major and minor radii of the ring distributions solely in terms of upstream (lobe) plasma conditions, thereby allowing a prediction of the associated temperature and temperature anisotropy of the rings in terms of upstream parameters. We test the validity of the prediction using 2.5-dimensional particle-in-cell (PIC) simulations with varying upstream plasma density and temperature, finding excellent agreement between the predicted and simulated values. We confirm the Shuster et al. suggestion for the cause of the ring distributions, and also find that the ring distributions are located in a region marked by a plateau, or shoulder, in the reconnected magnetic field profile. The predictions of the temperature are consistent with observed electron temperatures in dipolarization fronts, and may provide an explanation for the generation of plasma with temperatures in the 10s of MK in super-hot solar flares. A possible extension of the model to dayside reconnection is discussed. Since ring distributions are known to excite whistler waves, the present results should be useful for quantifying the generation of whistler waves in reconnection exhausts., Comment: Accepted for publication in Journal of Geophysical Research: Space Physics

We analyze the structure and evolution of ribbons from the M7.3 SOL2014-04-18T13 flare using ultraviolet (UV) images from IRIS and SDO/AIA, magnetic data from SDO/HMI, hard X-ray (HXR) images from RHESSI, and light curves from Fermi/GBM, in order to infer properties of coronal magnetic reconnection. As the event progresses, two flare ribbons spread away from the magnetic polarity inversion line. The width of the newly brightened front along the extension of the ribbon is highly intermittent in both space and time, presumably reflecting non-uniformities in the structure and/or dynamics of the flare current sheet. Furthermore, the ribbon width grows most rapidly in regions exhibiting concentrated non-thermal HXR emission, with sharp increases slightly preceding the HXR bursts. The light curve of the ultraviolet emission matches the HXR light curve at photon energies above 25 keV. In other regions the ribbon-width evolution and light curves do not temporally correlate with the HXR emission. This indicates that the production of non-thermal electrons is highly non-uniform within the flare current sheet. Our results suggest a strong connection between the production of non-thermal electrons and the locally enhanced perpendicular extent of flare ribbon fronts, which in turn reflects inhomogeneous structure and/or reconnection dynamics of the current sheet. Despite this variability, the ribbon fronts remain nearly continuous, quasi-one-dimensional features. Thus, although the reconnecting coronal current sheets are highly structured, they remain quasi-two-dimensional and the magnetic energy release occurs systematically, rather than stochastically, through the volume of reconnecting magnetic flux.

The formation, development and impact of slow shocks in the upstream region of reconnecting current layers are explored. Slow shocks have been documented in the upstream region of magnetohydrodynamic (MHD) simulations of magnetic reconnection as well as in similar simulations with the {\it kglobal} kinetic macroscale simulation model. They are therefore a candidate mechanism for preheating the plasma that is injected into the current layers that facilitate magnetic energy release in solar flares. Of particular interest is their potential role in producing the hot thermal component of electrons in flares. During multi-island reconnection, the formation and merging of flux ropes in the reconnecting current layer drives plasma flows and pressure disturbances in the upstream region. These pressure disturbances steepen into slow shocks that propagate along the reconnecting component of the magnetic field and satisfy the expected Rankine-Hugoniot jump conditions. Plasma heating arises from both compression across the shock and the parallel electric field that develops to maintain charge neutrality in a kinetic system. Shocks are weaker at lower plasma $\beta $, where shock steepening is slow. While these upstream slow shocks are intrinsic to the dynamics of multi-island reconnection, their contribution to electron heating remains relatively minor compared with that from Fermi reflection and the parallel electric fields that bound the reconnection outflow., Comment: 9 pages and 5 figures

The first self-consistent simulations of electron acceleration during magnetic reconnection in a macroscale system are presented. Consistent with solar flare observations the spectra of energetic electrons take the form of power-laws that extend more than two decades in energy. The drive mechanism for these nonthermal electrons is Fermi reflection in growing and merging magnetic flux ropes. A strong guide field is found to suppress the production of nonthermal electrons by weakening the Fermi drive mechanism. For a weak guide field the total energy content of nonthermal electrons dominates that of the hot thermal electrons even though their number density remains small. Our results are benchmarked with the hard x-ray, radio and extreme ultra-violet (EUV) observations of the X8.2-class solar flare on September 10, 2017.

A new computational model, kglobal, is being developed to explore energetic electron production via magnetic reconnection in macroscale systems. The model is based on the discovery that the production of energetic electrons during reconnection is controlled by Fermi reflection in large-scale magnetic fields and not by parallel electric fields localized in kinetic scale boundary layers. Thus, the model eliminates these boundary layers. However, although the parallel electric fields that develop around the magnetic x-line and associated separatrices are not important in producing energetic electrons, there is a large scale electric field that kickstarts the heating of low-energy electrons and drives the cold-electron return current that accompanies escaping energetic electrons in open systems. This macroscale electric field is produced by magnetic-field-aligned gradients in the electron pressure. We have upgraded kglobal to include this large-scale electric field while maintaining energy conservation. The new model is tested by exploring the dynamics of electron acoustic modes which develop as a consequence of the presence of two electron species: hot kinetic and cold fluid electrons. Remarkably, the damping of electron acoustic modes is accurately captured by kglobal. Additionally, it has been established that kglobal correctly describes the dynamics of the interaction of the parallel electric field with escaping hot electrons through benchmarking simulations with the Particle-In-Cell (PIC) code p3d., Comment: 7 pages, 3 figures, double columns

We describe a systematic development of kinetic entropy as a diagnostic in fully kinetic particle-in-cell (PIC) simulations and use it to interpret plasma physics processes in heliospheric, planetary, and astrophysical systems. First, we calculate kinetic entropy in two forms -- the ``combinatorial'' form related to the logarithm of the number of microstates per macrostate and the ``continuous'' form related to $f \ln f$, where $f$ is the particle distribution function. We discuss the advantages and disadvantages of each and discuss subtleties about implementing them in PIC codes. Using collisionless PIC simulations that are two-dimensional in position space and three-dimensional in velocity space, we verify the implementation of the kinetic entropy diagnostics and discuss how to optimize numerical parameters to ensure accurate results. We show the total kinetic entropy is conserved to three percent in an optimized simulation of anti-parallel magnetic reconnection. Kinetic entropy can be decomposed into a sum of a position space entropy and a velocity space entropy, and we use this to investigate the nature of kinetic entropy transport during collisionless reconnection. We find the velocity space entropy of both electrons and ions increases in time due to plasma heating during magnetic reconnection, while the position space entropy decreases due to plasma compression. This project uses collisionless simulations, so it cannot address physical dissipation mechanisms; nonetheless, the infrastructure developed here should be useful for studies of collisional or weakly collisional heliospheric, planetary, and astrophysical systems. Beyond reconnection, the diagnostic is expected to be applicable to plasma turbulence and collisionless shocks., Comment: 20 pages, 7 figures

The structure of dipolarization jets with finite width in the dawn-dusk direction relevant to magnetic reconnection in the Earth's magnetotail is explored with particle-in-cell simulations. We carry out Riemann simulations of the evolution of the jet in the dawn-dusk, north-south plane to investigate the dependence of the jet structure on the jet width in the dawn-dusk direction. We find that the magnetic field and Earth-directed ion flow structure depend on the dawn-dusk width. A reversal in the usual Hall magnetic field near the center of the current sheet on the dusk side of larger jets is observed. For small widths, the maximum velocity of the Earthward flow is significantly reduced below the theoretical limit of the upstream Alfv\'en speed. However, the ion flow speed approaches this limit once the width exceeds the ion Larmor radius based on the normal magnetic field, $B_z$.

The acceleration of solar flare ions during magnetic reconnection is explored via particle-in-cell simulations that self-consistently follow the motions of both protons and $\alpha$ particles. We demonstrate that the dominant ion heating during reconnection with a guide field (a magnetic component perpendicular to the reconnection plane) results from pickup behavior during the entry into reconnection exhausts. In contrast with anti-parallel reconnection, the temperature increment is dominantly transverse, rather than parallel, to the local magnetic field. The comparison of protons and alphas reveals a mass-to-charge ($M/Q$) threshold in pickup behavior that favors heating of high $M/Q$ ions over protons, which is consistent with impulsive flare observations., Comment: Revised based on reviewer's comments; text clarified and references added

Recent full-particle simulations of electron-positron reconnection have revealed that the Weibel instability plays an active role in controlling the dynamics of the current layer and maintaining fast reconnection. A four-beam model is developed to explore the development of the instability within a narrow current layer characteristic of reconnection. The problem is reduced to two coupled second-order differential equations, whose growing eigenmodes are obtained via both asymptotic approximations and finite difference methods. Full particle simulations confirm the linear theory and help probe the nonlinear development of the instability. The current layer broadening in the reconnection outflow jet is linked to the scattering of high-velocity streaming particles in the Weibel-generated, out-of-plane magnetic field.