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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

Where and how flares efficiently accelerate charged particles remains an unresolved question. Recent studies revealed that a "magnetic bottle" structure, which forms near the bottom of a large-scale reconnection current sheet above the flare arcade, is an excellent candidate for confining and accelerating charged particles. However, further understanding its role requires linking the various observational signatures to the underlying coupled plasma and particle processes. Here we present the first study combining multi-wavelength observations with data-informed macroscopic magnetohydrodynamics and particle modeling in a realistic eruptive flare geometry. The presence of an above-the-looptop magnetic bottle structure is strongly supported by the observations, which feature not only a local minimum of magnetic field strength but also abruptly slowing down plasma downflows. It also coincides with a compact hard X-ray source and an extended microwave source that bestrides above the flare arcade. Spatially resolved spectral analysis suggests that nonthermal electrons are highly concentrated in this region. Our model returns synthetic emission signatures that are well-matched to the observations. The results suggest that the energetic electrons are strongly trapped in the magnetic bottle region due to turbulence, with only a small fraction managing to escape. The electrons are primarily accelerated by plasma compression and facilitated by a fast-mode termination shock via the Fermi mechanism. Our results provide concrete support for the magnetic bottle as the primary electron acceleration site in eruptive solar flares. They also offer new insights into understanding the previously reported small population of flare-accelerated electrons entering interplanetary space., Comment: 20 pages, 13 figures (12 pages and 10 figures for main text). Accepted for publication in The Astrophysical Journal

Relativistic magnetic turbulence has been proposed as a process for producing nonthermal particles in high-energy astrophysics. The particle energization may be contributed by both magnetic reconnection and turbulent fluctuations, but their interplay is poorly understood. It has been suggested that during magnetic reconnection the parallel electric field dominates the particle acceleration up to the lower bound of the power-law particle spectrum, but recent studies show that electric fields perpendicular to the magnetic field can play an important, if not dominant role. In this study, we carry out fully kinetic particle-in-cell simulations of magnetically dominated decaying turbulence in a relativistic pair plasma. For a fixed magnetization parameter $\sigma_0 = 20$, we find that the injection energy~$\varepsilon_{\rm inj}$ converges with increasing domain size to~$\varepsilon_{\rm inj} \simeq 10 \, m_ec^2$. In contrast, the power-law index, the cut-off energy, and the power-law extent increase steadily with domain size. We trace a large number of particles and evaluate the contributions of the work done by the parallel ($W_\parallel$) and perpendicular ($W_\perp$) electric fields during both the injection phase and the post-injection phase. We find that during the injection phase, the $W_\perp$ contribution increases with domain size, suggesting that it may eventually dominate injection for a sufficiently large domain. In contrast, both components contribute equally during the post-injection phase, insensitive to the domain size. For high energy ($\varepsilon \gg \varepsilon_{\rm inj}$) particles, $W_\perp$ dominates the subsequent energization. These findings may improve our understanding of nonthermal particles and their emissions in astrophysical plasmas., Comment: 11 pages, 7 figures, 1 animation, Submitted to ApJ

We have developed a new computational method to explore astrophysical and heliophysical phenomena, especially those considerably influenced by non-thermal energetic particles. This novel approach considers the backreaction from these energetic particles by incorporating the non-thermal fluid pressure into Magnetohydrodynamics (MHD) equations. The pressure of the non-thermal fluid is evaluated from the energetic particle distribution evolved through Parker's transport equation, which is solved using stochastic differential equations. We implement this method in the HOW-MHD code (Seo \& Ryu 2023), which achieves 5th-order accuracy. We find that without spatial diffusion, the method accurately reproduces the Riemann solution in the hydrodynamic shock tube test when including the non-thermal pressure. Solving Parker's transport equation allows the determination of pressure terms for both relativistic and non-relativistic non-thermal fluids with adiabatic indices $\gamma_{\rm{NT}}=4/3$ and $\gamma_{\rm{NT}}=5/3$, respectively. The method also successfully replicates the Magnetohydrodynamic shock tube test with non-thermal pressure, successfully resolving the discontinuities within a few cells. Introducing spatial diffusion of non-thermal particles leads to marginal changes in the shock but smooths the contact discontinuity. Importantly, this method successfully simulates the energy spectrum of the non-thermal particles accelerated through shock, which includes feedback from the non-thermal population. These results demonstrate that this method is very powerful for studying particle acceleration when a significant portion of the plasma energy is taken by energetic particles., Comment: 15 pages, 8 figures

Understanding plasma turbulence requires a synthesis of experiments, observations, theory, and simulations. In the case of kinetic plasmas such as the solar wind, the lack of collisions renders the fluid closures such as viscosity meaningless and one needs to resort to higher order fluid models or kinetic models. Typically, the computational expense in such models is managed by simulating artificial values of certain parameters such as the ratio of the Alfv\'en speed to the speed of light ($v_A/c$) or the relative mass ratio of ions and electrons ($m_i/m_e$). Although, typically care is taken to use values as close as possible to realistic values within the computational constraints, these artificial values could potentially introduce unphysical effects. These unphysical effects could be significant at sub-ion scales, where kinetic effects are the most important. In this paper, we use the ten-moment fluid model in the Gkeyll framework to perform controlled numerical experiments, systematically varying the ion-electron mass ratio from a small value down to the realistic proton-electron mass ratio. We show that the unphysical mass ratio has a significant effect on the kinetic range dynamics as well as the heating of both the plasma species. The dissipative process for both ions and electrons become more compressive in nature, although the ions remain nearly incompressible in all cases. The electrons move from being dominated by incompressive viscous like heating/dissipation, to very compressive heating/dissipation dominated by compressions/rarefactions. While the heating change is significant for the electrons, a mass ratio of $m_i/m_e \sim 250$ captures the asymptotic behaviour of electron heating., Comment: 13 pages (including bibliography), 11 figures and 2 tables

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-xline 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 leads 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 $\beta$ ($\ll1$) 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 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 run into 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., Comment: 15 pages, 11 figures

The formation of jets in black hole accretion systems is a long-standing problem. It has been proposed that a jet can be formed by extracting the rotation energy of the black hole ("BZ-jet") or the accretion flow ("disk-jet"). While both models can produce collimated relativistic outflows, neither has successfully explained the observed jet morphology. By employing general relativistic magnetohydrodynamic simulations, and considering nonthermal electrons accelerated by magnetic reconnection that is likely driven by magnetic eruption in the underlying accretion flow, we obtain images by radiative transfer calculations and compared them to millimeter observations of the jet in M87. We find that the BZ-jet originating from a magnetically arrested disk around a high-spin black hole can well reproduce the jet morphology, including its width and limb-brightening feature., Comment: 46 pages, 20 figures, 3 tables, published in Science Advances on 22 Mar 2024. arXiv admin note: substantial text overlap with arXiv:2206.05661

Diffusion coefficients of energetic charged particles in turbulent magnetic fields are a fundamental aspect of diffusive transport theory but remain incompletely understood. In this work, we use quasi-linear theory to evaluate the spatial variation of the parallel diffusion coefficient $\kappa_\parallel$ from the measured magnetic turbulence power spectra in the inner heliosphere. We consider the magnetic field and plasma velocity measurements from Parker Solar Probe made during Orbits 5-13. The parallel diffusion coefficient is calculated as a function of radial distance from 0.062 to 0.8 AU, and the particle energy from 100 keV to 1GeV. We find that $\kappa_\parallel$ increases exponentially with both heliocentric distance and energy of particles. The fluctuations in $\kappa_\parallel$ are related to the episodes of large-scale magnetic structures in the solar wind. By fitting the results, we also provide an empirical formula of $\kappa_{\parallel}=(5.16\pm1.22) \times 10^{18} \: r^{1.17\pm0.08} \: E^{0.71\pm 0.02} \; (cm^2/s)$ in the inner heliosphere which can be used as a reference in studying the transport and acceleration of solar energetic particles as well as the modulation of cosmic rays., Comment: Accepted to ApJ

Magnetic reconnection occurs ubiquitously in the universe and is often invoked to explain fast energy release and particle acceleration in high-energy astrophysics. The study of relativistic magnetic reconnection in the magnetically dominated regime has surged over the past two decades, revealing the physics of fast magnetic reconnection and nonthermal particle acceleration. Here we review these recent progresses, including the magnetohydrodynamic and collisionless reconnection dynamics as well as particle energization. The insights in astrophysical reconnection strongly connect to the development of magnetic reconnection in other areas, and further communication is greatly desired. We also provide a summary and discussion of key physics processes and frontier problems, toward a better understanding to the roles of magnetic reconnection in high-energy astrophysics., Comment: Space Science Reviews in press. This is a review paper as an outcome of the 2022 Magnetic Reconnection Workshop in the International Space Science Institute

Solar flares and coronal mass ejections are interrelated phenomena that together are known as solar eruptive events. These are the main drivers of space weather and understanding their origins is a primary goal of Heliophysics. In this white paper, we advocate for the allocation of sufficient resources to bring together experts in observations and modeling to construct and test next generation data-driven models of solar eruptive events. We identify the key components necessary for constructing comprehensive end-to-end models including global scale 3D MHD resolving magnetic field evolution and reconnection, small scale simulations of particle acceleration in reconnection exhausts, kinetic scale transport of flare-accelerated particles into the lower solar atmosphere, and the radiative and hydrodynamics responses of the solar atmosphere to flare heating. Using this modeling framework, long-standing questions regarding how solar eruptive events release energy, accelerate particles, and heat plasma can be explored. To address open questions in solar flare physics, we recommend that NASA and NSF provide sufficient research and analysis funds to bring together a large body of researchers and numerical tools to tackle the end-to-end modeling framework that we outline. Current dedicated theory and modeling funding programs are relatively small scale and infrequent; funding agencies must recognize that modern space physics demands the use of both observations and modeling to make rapid progress., Comment: White paper submitted to the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033; 9 pages, 4 figures

Ground level enhancements (GLEs) are extreme solar energetic particle (SEP) events that are of particular importance in space weather. In solar cycle 24, two GLEs were recorded on 2012 May 17 (GLE 71) and 2017 September 10 (GLE 72), respectively, by a range of advanced modern instruments. Here we conduct a comparative analysis of the two events by focusing on the effects of large-scale magnetic field configuration near active regions on particle acceleration and release. Although the active regions both located near the western limb, temporal variations of SEP intensities and energy spectra measured in-situ display different behaviors at early stages. By combining a potential field model, we find the CME in GLE 71 originated below the streamer belt, while in GLE 72 near the edge of the streamer belt. We reconstruct the CME shock fronts with an ellipsoid model based on nearly simultaneous coronagraph images from multi-viewpoints, and further derive the 3D shock geometry at the GLE onset. The highest-energy particles are primarily accelerated in the shock-streamer interaction regions, i.e., likely at the nose of the shock in GLE 71 and the eastern flank in GLE 72, due to quasi-perpendicular shock geometry and confinement of closed fields. Subsequently, they are released to the field lines connecting to near-Earth spacecraft when the shocks move through the streamer cusp region. This suggests that magnetic structures in the corona, especially shock-streamer interactions, may have played an important role in the acceleration and release of the highest-energy particles in the two events., Comment: Accepted for publication in ApJ

Particles are accelerated to very high, non-thermal energies during explosive energy-release phenomena in space, solar, and astrophysical plasma environments. While it has been established that magnetic reconnection plays an important role in the dynamics of Earth's magnetosphere, it remains unclear how magnetic reconnection can further explain particle acceleration to non-thermal energies. Here we review recent progress in our understanding of particle acceleration by magnetic reconnection in Earth's magnetosphere. With improved resolutions, recent spacecraft missions have enabled detailed studies of particle acceleration at various structures such as the diffusion region, separatrix, jets, magnetic islands (flux ropes), and dipolarization front. With the guiding-center approximation of particle motion, many studies have discussed the relative importance of the parallel electric field as well as the Fermi and betatron effects. However, in order to fully understand the particle acceleration mechanism and further compare with particle acceleration in solar and astrophysical plasma environments, there is a need for further investigation of, for example, energy partition and the precise role of turbulence., Comment: Submitted to Space Science Reviews; Revised on July 21, 2023

Understanding the nature of energetic particles in the solar atmosphere is one of the most important outstanding problems in heliophysics. Flare-accelerated particles compose a huge fraction of the flare energy budget; they have large influences on how events develop; they are an important source of high-energy particles found in the heliosphere; and they are the single most important corollary to other areas of high-energy astrophysics. Despite the importance of this area of study, this topic has in the past decade received only a small fraction of the resources necessary for a full investigation. For example, NASA has selected no new Explorer-class instrument in the past two decades that is capable of examining this topic. The advances that are currently being made in understanding flare-accelerated electrons are largely undertaken with data from EOVSA (NSF), STIX (ESA), and NuSTAR (NASA Astrophysics). This is despite the inclusion in the previous Heliophysics decadal survey of the FOXSI concept as part of the SEE2020 mission, and also despite NASA's having invested heavily in readying the technology for such an instrument via four flights of the FOXSI sounding rocket experiment. Due to that investment, the instrumentation stands ready to implement a hard X-ray mission to investigate flare-accelerated electrons. This white paper describes the scientific motivation for why this venture should be undertaken soon., Comment: White paper submitted to the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033; 15 pages, 5 figures

Particles are accelerated to very high, non-thermal energies during explosive energy-release phenomena in space, solar, and astrophysical plasma environments. In the case of solar flares, it has been established that magnetic reconnection plays an important role for releasing the magnetic energy, but it remains unclear if or how magnetic reconnection can further explain particle acceleration during flares. Here we argue that the key issue is the lack of understanding of the precise context of particle acceleration but it can be overcome, in the near future, by performing imaging-spectroscopy in soft X-rays (SXRs). Such observations should be complemented by observations in other wavelengths such as extreme-ultraviolets (EUVs), microwaves, hard X-rays (HXRs), and gamma-rays. Also, numerical simulations will be crucial for further narrowing down the particle acceleration mechanism in the context revealed by the observations. Of all these efforts, imaging-spectroscopy in SXRs, if successfully applied to large limb flares, will be a milestone in our challenge of understanding electron acceleration in solar flares and beyond, i.e. the Plasma Universe., Comment: White paper submitted to the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033; 10 pages, 2 figures

Many questions remain about the compressibility of solar wind turbulence with respect to its origins and properties. Low plasma beta (ratio of thermal to magnetic pressure) environments allow for the easier generation of compressible turbulence, enabling study of the relationship between density fluctuations and turbulent Mach number. Utilizing Parker Solar Probe plasma data, we examine the normalized proton density fluctuations $\langle \delta n_p^2 \rangle ^{1/2}/\langle n_p\rangle = \delta {n_p}_{rms}/\langle n_p\rangle$ as a function of turbulent Mach number $M_t$ conditioned on plasma beta and cross helicity. With consideration of statistical error in the parameters computed from in-situ data, we find a general result that $\delta {n_p}_{rms}/\langle n_p\rangle \sim M_t^{1.18 \pm 0.04}$, consistent with both linear-wave theory, and nearly-incompressible turbulence in an inhomogeneous background field. We compare observational results conditioned on plasma beta and cross helicity with 3D magnetohydrodynamic simulations, and observe rather significant similarities with respect to how those parameters affect the proportionality between density fluctuations and turbulent Mach number. This study further investigates the complexity of compressible turbulence as viewed by the density scaling relationship, and may help better understand the compressible environment of the near-Sun solar wind., Comment: 8 pages, 3 figures, 1 table, submitted to ApJL

The past decade has seen an outstanding development of nonthermal particle acceleration in magnetic reconnection in magnetically-dominated systems, with clear signatures of power-law energy distributions as a common outcome of first-principles kinetic simulations. Here we propose a semi-analytical model for systematically investigating nonthermal particle acceleration in reconnection. We show particle energy distributions are well determined by particle injection, acceleration, and escape processes. Using a series of kinetic simulations, we accurately evaluate the energy- and time-dependent model coefficients. The resulting spectral characteristics, including the spectral index and lower and upper bounds of the power-law distribution, agree well with the simulation results. Finally, we apply the model to predict the power-law indices and break energies in astrophysical reconnection systems., Comment: 13 pages, 7 figures, published by ApJL

Blazar emission is dominated by nonthermal radiation processes that are highly variable across the entire electromagnetic spectrum. Turbulence, which can be a major source of nonthermal particle acceleration, can widely exist in the blazar emission region. The Turbulent Extreme Multi-Zone (TEMZ) model has been widely used to describe turbulent radiation signatures. Recent particle-in-cell (PIC) simulations have also revealed the stochastic nature of the turbulent emission region and particle acceleration therein. However, radiation signatures have not been systematically studied via first-principle-integrated simulations. In this paper, we perform combined PIC and polarized radiative transfer simulations to study synchrotron emission from magnetic turbulence in the blazar emission region. We find that the multi-wavelength flux and polarization are generally characterized by stochastic patterns. Specifically, the variability time scale and average polarization degree (PD) are governed by the correlation length of the turbulence. Interestingly, magnetic turbulence can result in polarization angle (PA) swings with arbitrary amplitudes and duration, in either directions, that are not associated to changes in flux or PD. Surprisingly, these swings, which are of stochastic nature, can appear either bumpy or smooth, although large amplitude swings ($>180^{\circ}$) are very rare as expected. Our radiation and polarization signatures from first-principle-integrated simulations are consistent with the TEMZ model., Comment: 19 pages, 17 figures, accepted by ApJ

Solar flares and the often associated solar eruptive events serve as an outstanding laboratory to study the magnetic reconnection and the associated energy release and conversion processes under plasma conditions difficult to reproduce in the laboratory, and with considerable spatiotemporal details not possible elsewhere in the universe. In the past decade, thanks to advances in multi-wavelength imaging spectroscopy, as well as developments in theories and numerical modeling, significant progress has been made in improving our understanding of solar flare/eruption energy release. In particular, broadband imaging spectroscopy at microwave wavelengths offered by the Expanded Owens Valley Solar Array (EOVSA) has enabled the revolutionary capability of measuring the time-evolving coronal magnetic fields at or near the flare reconnection region. However, owing to EOVSA's limited dynamic range, imaging fidelity, and angular resolution, such measurements can only be done in a region around the brightest source(s) where the signal-to-noise is sufficiently large. In this white paper, after a brief introduction to the outstanding questions and challenges pertinent to magnetic energy release in solar flares and eruptions, we will demonstrate how a next-generation radio facility with many (~100-200) antenna elements can bring the next revolution by enabling high dynamic range, high fidelity broadband imaging spectropolarimetry along with a sub-second time resolution and arcsecond-level angular resolution. We recommend to prioritize the implementation of such a ground-based instrument within this decade. We also call for facilitating multi-wavelength, multi-messenger observations and advanced numerical modeling in order to achieve a comprehensive understanding of the "system science" of solar flares and eruptions., Comment: Science white paper submitted to the 2024 Solar and Space Physics Decadal Survey. All submitted white papers (including this one) are available at https://www.nationalacademies.org/our-work/decadal-survey-for-solar-and-space-physics-heliophysics-2024-2033

The acceleration and transport of energetic electrons during solar flares is one of the outstanding topics in solar physics. Recent X-ray and radio imaging and spectroscopy observations have provided diagnostics of the distribution of nonthermal electrons and suggested that, in certain flare events, electrons are primarily accelerated in the loop-top and likely experience trapping and/or scattering effects. By combining the focused particle transport equation with magnetohydrodynamic (MHD) simulations of solar flares, we present a macroscopic particle model that naturally incorporates electron acceleration and transport. Our simulation results indicate that the physical processes such as turbulent pitch-angle scattering can have important impacts on both electron acceleration in the loop-top and transport in the flare loop, and their influences are highly energy dependent. A spatial-dependent turbulent scattering with enhancement in the loop-top can enable both efficient electron acceleration to high energies and transport of abundant electrons to the footpoints. We further generate spatially resolved synthetic hard X-ray (HXR) emission images and spectra, revealing both the loop-top and footpoint HXR sources. Similar to the observations, we show that the footpoint HXR sources are brighter and harder than the loop-top HXR source. We suggest that the macroscopic particle model provides new insights into understanding the connection between the observed loop-top and footpoint nonthermal emission sources by combining the particle model with dynamically evolving MHD simulations of solar flares., Comment: Accepted for publication in ApJL

We present a 2D kinematic model to study the acceleration of solar energetic particles (SEPs) at a shock driven by a coronal mass ejection. The shock is assumed to be spherical about an origin that is offset from the center of the Sun. This leads to a spatial and temporal evolution of the angle between the magnetic field and shock normal direction ($\theta_{Bn}$) as it propagates through the Parker spiral magnetic field from the lower corona to 1 AU. We find that the high-energy SEP intensity varies significantly along the shock front due to the evolution of $\theta_{Bn}$. Generally, the west flank of the shock preferentially accelerates particles to high energies compared to the east flank and shock nose. This can be understood in terms of the rate of acceleration, which is higher at the west flank. Double power-law energy spectra are reproduced in our model as a consequence of the local acceleration and transport effects. These results will help better understand the evolution of SEP acceleration and provide new insights into large SEP events observed by multi-spacecraft, especially those close to the Sun, such as Parker Solar Probe and Solar Orbiter.

Magnetic reconnection in the relativistic regime has been proposed as an important process for the efficient production of nonthermal particles and high-energy emissions. Using fully kinetic particle-in-cell simulations, we investigate how guide-field strength and domain size affect characteristic spectral features and acceleration processes. We study two stages of acceleration: energization up until the injection energy $\gamma_{\rm inj}$ and further acceleration that generates a power-law spectrum. Stronger guide fields increase the power-law index and $\gamma_{\rm inj}$, which suppresses acceleration efficiency. These quantities seemingly converge with increasing domain size, suggesting that our findings can be extended to large-scale systems. We find that three distinct mechanisms contribute to acceleration during injection: particle streaming along the parallel electric field, Fermi reflection, and the pickup process. Fermi and pickup processes, related to the electric field perpendicular to the magnetic field, govern the injection for weak guide fields and larger domains. Meanwhile, parallel electric fields are important for injection in the strong guide field regime. In the post-injection stage, we find that perpendicular electric fields dominate particle acceleration in the weak guide field regime, whereas parallel electric fields control acceleration for strong guide fields. These findings will help explain the nonthermal acceleration and emissions in high-energy astrophysics, including black hole jets and pulsar wind nebulae., Comment: 27 pages, 15 figures, accepted for publication to The Astrophysical Journal

Magnetic reconnection drives multi-species particle acceleration broadly in space and astrophysics. We perform the first 3D hybrid simulations (fluid electrons, kinetic ions) that contain sufficient scale separation to produce nonthermal heavy-ion acceleration, with fragmented flux ropes critical for accelerating all species. We demonstrate the acceleration of all ion species (up to Fe) into power-law spectra with similar indices, by a common Fermi acceleration mechanism. The upstream ion velocities influence the first Fermi reflection for injection. The subsequent onsets of Fermi acceleration are delayed for ions with lower charge-mass ratios (Q/M), until growing flux ropes magnetize them. This leads to a species-dependent maximum energy/nucleon $\propto(Q/M)^\alpha$. These findings are consistent with in-situ observations in reconnection regions, suggesting Fermi acceleration as the dominant multi-species ion acceleration mechanism., Comment: version accepted by Physical Review Letters

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

Recently, Sironi (PRL, 128, 145102; S22) reported the correlation between particles accelerated into high energy and their crossings of regions with electric field larger than magnetic field (E>B regions) in kinetic simulations of relativistic magnetic reconnection. They claim that electric fields in E>B regions (for a vanishing guide field) dominate in accelerating particles to the injection energy. S22 presented test-particle simulations showing that if particle energies are reset to low energies in E>B regions, efficient injection is suppressed. This Comment re-examines these claims by analyzing a simulation resembling the reference case in S22. We show that during crossings E>B acceleration only contributes a small fraction to the injection energy as E>B regions only host particles for a short duration. The energization before any E>B crossings has a comparable contribution, indicating E>B regions are not unique in pre-accelerating particles. A new test-particle simulation shows that zero-outing electric fields in E>B regions does not strongly influence the injection. We suggest that the procedure used in S22 to exclude E>B acceleration partly removes acceleration outside E>B regions, leading to a false conclusion., Comment: 2 pages, 1 figure

The formation of jets in black hole accretion systems is a long-standing problem. It has been proposed that a jet can be formed by extracting the rotation energy of the black hole ("BZ-jet") or the accretion flow ("disk-jet"). While both models can produce collimated relativistic outflows, neither has successfully explained the observed jet morphology. In this paper, by employing general relativistic magnetohydrodynamic simulations, and considering nonthermal electrons accelerated by magnetic reconnection driven by kink instability of the jet, we have obtained images by radiative transfer calculations and compared them to millimeter observations of the jet in M87. We find that the BZ-jet originated from a magnetically arrested disk around a high-spin black hole can well reproduce the jet morphology, including its width and limb-brightening feature., Comment: We would like to submit a new article with the same research question as this article. We have made significant modifications in the following two aspects. We have constructed a more refined and accurate theoretical model and greatly improved the resolution of the simulation. Republishing a new version avoids confusion and misleading readers

Particle acceleration during magnetic reconnection is a long-standing topic in space, solar and astrophysical plasmas. Recent 3D particle-in-cell simulations of magnetic reconnection show that particles can leave flux ropes due to 3D field-line chaos, allowing particles to access additional acceleration sites, gain more energy through Fermi acceleration, and develop a power-law energy distribution. This 3D effect does not exist in traditional 2D simulations, where particles are artificially confined to magnetic islands due to their restricted motions across field lines. Full 3D simulations, however, are prohibitively expensive for most studies. Here, we attempt to reproduce 3D results in 2D simulations by introducing ad hoc pitch-angle scattering to a small fraction of the particles. We show that scattered particles are able to transport out of 2D islands and achieve more efficient Fermi acceleration, leading to a significant increase of energetic particle flux. We also study how the scattering frequency influences the nonthermal particle spectra. This study helps achieve a complete picture of particle acceleration in magnetic reconnection.

The X8.2-class limb flare on September 10, 2017 is among the best studied solar flare events owing to its great similarity to the standard flare model and the broad coverage by multiple spacecraft and ground-based observations. These multiwavelength observations indicate that electron acceleration and transport are efficient in the reconnection and flare looptop regions. However, there lacks a comprehensive model for explaining and interpreting the multi-faceted observations. In this work, we model the electron acceleration and transport in the early impulsive phase of this flare. We solve the Parker transport equation that includes the primary acceleration mechanism during magnetic reconnection in the large-scale flare region modeled by MHD simulations. We find that electrons are accelerated up to several MeV and fill a large volume of the reconnection region, similar to the observations shown in microwaves. The electron spatial distribution and spectral shape in the looptop region agree well with those derived from the microwave and hard X-ray emissions before magnetic islands grow large and dominate the acceleration. Future emission modelings using the electron maps will enable direct comparison with microwave and hard X-ray observations. These results shed new light on the electron acceleration and transport in a broad region of solar flares within a data-constrained realistic flare geometry., Comment: 19 pages, 8 figures, accepted to ApJ

Magnetic reconnection is a ubiquitous astrophysical process that rapidly converts magnetic energy into some combination of plasma flow energy, thermal energy, and non-thermal energetic particles, including energetic electrons. Various reconnection acceleration mechanisms in different low-$\beta$ (plasma-to-magnetic pressure ratio) and collisionless environments have been proposed theoretically and studied numerically, including first- and second-order Fermi acceleration, betatron acceleration, parallel electric field acceleration along magnetic fields, and direct acceleration by the reconnection electric field. However, none of them have been heretofore confirmed experimentally, as the direct observation of non-thermal particle acceleration in laboratory experiments has been difficult due to short Debye lengths for \textit{in-situ} measurements and short mean free paths for \textit{ex-situ} measurements. Here we report the direct measurement of accelerated non-thermal electrons from low-$\beta$ magnetically driven reconnection in experiments using a laser-powered capacitor coil platform. We use kiloJoule lasers to drive parallel currents to reconnect MegaGauss-level magnetic fields in a quasi-axisymmetric geometry. The angular dependence of the measured electron energy spectrum and the resulting accelerated energies, supported by particle-in-cell simulations, indicate that the mechanism of direct electric field acceleration by the out-of-plane reconnection electric field is at work. Scaled energies using this mechanism show direct relevance to astrophysical observations. Our results therefore validate one of the proposed acceleration mechanisms by reconnection, and establish a new approach to study reconnection particle acceleration with laboratory experiments in relevant regimes., Comment: 13 pages, 6 figures

Recent observations have shown that in many large solar energetic particle (SEP) events the event-integrated differential spectra resemble double power laws. We perform numerical modeling of particle acceleration at coronal shocks propagating through a streamer-like magnetic field by solving the Parker transport equation, including protons and heavier ions. We find that for all ion species the energy spectra integrated over the simulation domain can be described by a double power law, and the break energy depends on the ion charge-to-mass ratio as $E_B \sim (Q/A)^\alpha$, with $\alpha$ varying from 0.16 to 1.2 by considering different turbulence spectral indices. We suggest that the double power law distribution may emerge as a result of the superposition of energetic particles from different source regions where the acceleration rates differ significantly due to particle diffusion. The diffusion and mixing of energetic particles could also provide an explanation for the increase of Fe/O at high energies as observed in some SEP events. Although further mixing processes may occur, our simulations indicate that either power-law break or rollover can occur near the Sun and predict that the spectral forms vary significantly along the shock front, which may be examined by upcoming near-Sun SEP measurements from Parker Solar Probe and Solar Orbiter., Comment: Accepted for publication in The Astrophysical Journal Letters

A number of double coronal X-ray sources have been observed during solar flares by RHESSI, where the two sources reside at different sides of the inferred reconnection site. However, where and how are these X-ray-emitting electrons accelerated remains unclear. Here we present the first model of the double coronal hard X-ray (HXR) sources, where electrons are accelerated by a pair of termination shocks driven by bi-directional fast reconnection outflows. We model the acceleration and transport of electrons in the flare region by numerically solving the Parker transport equation using velocity and magnetic fields from the macroscopic magnetohydrodynamic simulation of a flux rope eruption. We show that electrons can be efficiently accelerated by the termination shocks and high-energy electrons mainly concentrate around the two shocks. The synthetic HXR emission images display two distinct sources extending to $>$100 keV below and above the reconnection region, with the upper source much fainter than the lower one. The HXR energy spectra of the two coronal sources show similar spectral slopes, consistent with the observations. Our simulation results suggest that the flare termination shock can be a promising particle acceleration mechanism in explaining the double-source nonthermal emissions in solar flares., Comment: Accepted for publication in ApJ

Various systems can be modeled as a point-like explosion of ionized debris into a magnetized, collisionless background plasma -- including astrophysical examples, active experiments in space, and laser-driven laboratory experiments. Debris streaming from the explosion parallel to the magnetic field may drive multiple resonant and non-resonant ion-ion beam instabilities, some of which can efficiently couple the debris energy to the background and may even support the formation of shocks. We present a large-scale hybrid (kinetic ions + fluid electrons) particle-in-cell (PIC) simulation, extending hundreds of ion inertial lengths from a 3-D explosion, that resolves these instabilities. We show that the character of these instabilities differs notably from the 1-D equivalent by the presence of unique transverse structure. Additional 2-D simulations explore how the debris beam length, width, density, and speed affect debris-background coupling, with implications for the generation of quasi-parallel shocks., Comment: 21 pages, 10 figures, the article has been accepted by Physics of Plasmas (2021)

It is commonly believed that blazar jets are relativistic magnetized plasma outflows from supermassive black holes. One key question is how the jets dissipate magnetic energy to accelerate particles and drive powerful multi-wavelength flares. Relativistic magnetic reconnection has been proposed as the primary plasma physical process in the blazar emission region. Recent numerical simulations have shown strong acceleration of nonthermal particles that may lead to multi-wavelength flares. Nevertheless, previous works have not directly evaluated $\gamma$-ray signatures from first-principle simulations. In this paper, we employ combined particle-in-cell and polarized radiation transfer simulations to study multi-wavelength radiation and optical polarization signatures under the leptonic scenario from relativistic magnetic reconnection. We find harder-when-brighter trends in optical and {\it Fermi-LAT} $\gamma$-ray bands as well as closely correlated optical and $\gamma$-ray flares. The optical polarization angle swings are also accompanied by $\gamma$-ray flares with trivial time delays. Intriguingly, we find highly variable synchrotron self Compton signatures due to inhomogeneous particle distributions during plasmoid mergers. This feature may result in fast $\gamma$-ray flares or orphan $\gamma$-ray flares under the leptonic scenario, complementary to the frequently considered mini-jet scenario. It may also infer neutrino emission with low secondary synchrotron flux under the hadronic scenario, if plasmoid mergers can accelerate protons to very high energy., Comment: 16 pages, 12 figures. Accepted by ApJ

We propose a model for interpreting highly variable ion composition ratios in solar energetic particles (SEP) events recently observed by Parker Solar Probe (PSP) at $0.3 - 0.45$ astronomical unit. We use numerical simulations to calculate SEP propagation in a turbulent interplanetary magnetic field with a Kolmogorov power spectrum from large scale down to the gyration scale of energetic particles. We show that when the source regions of different species are offset by a distance comparable to the size of the source regions, the observed energetic particle composition He/H can be strongly variable over more than two orders of magnitude, even if the source ratio is at the nominal value. Assuming a $^3$He/$^4$He source ratio of $10 \%$ in impulsive $^3$He-rich events and the same spatial offset of the source regions, the $^3$He/$^4$He ratio at observation sites also vary considerably. The variability of the ion composition ratios depends on the radial distance, which can be tested by observations made at different radial locations. We discuss the implication of these results on the variability of ion composition of impulsive events and on further PSP and Solar Orbiter observations close to the Sun., Comment: 10 pages, 5 figures, ApJ accepted

We perform 2.5D particle-in-cell simulations of decaying turbulence in the presence of a guide (out-of-plane) background magnetic field. The fluctuating magnetic field initially consists of Fourier modes at low wavenumbers (long wavelengths). With time, the electromagnetic energy is converted to plasma kinetic energy (bulk flow+thermal energy) at the rate per unit volume of ${\pp J}\cdot{\pp E}$ for current density ${\pp J}$ and electric field ${\pp E}$. Such decaying turbulence is well known to evolve toward a state with strongly intermittent plasma current. Here we decompose the electric field into components that are irrotational, ${\pp E}_{\rm ir}$, and solenoidal (divergence-free), ${\pp E}_{\rm so}$. ${\pp E}_{\rm ir}$ is associated with charge separation, and ${\pp J}\cdot{\pp E}_{\rm ir}$ is a rate of energy transfer between ions and electrons with little net change in plasma kinetic energy. Therefore, the net rate of conversion of electromagnetic energy to plasma kinetic energy is strongly dominated by ${\pp J}\cdot{\pp E}_{\rm so}$, and for a strong guide magnetic field, this mainly involves the component ${\pp E}_{\rm so,\parallel}$ parallel to the total magnetic field ${\pp B}$. We examine various indicators of the spatial distribution of the energy transfer rate {\bf J$_\parallel\cdot$E$_{so,\parallel}$}, which relates to magnetic reconnection, the best of which are 1) the ratio of the out-of-plane electric field to the in-plane magnetic field, 2) the out-of-plane component of the non-ideal electric field, and 3) the magnitude of the estimate of current helicity.

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 coupling between a rapidly expanding cloud of ionized debris and an ambient magnetized plasma is revisited with a hybrid (kinetic ion/fluid electron) simulation code that allows a study over a wide range of plasma parameters. Over a specified range of hypothetical conditions, simple scaling laws in terms of the total debris mass and explosion speed are derived and verified for the maximal size of the debris cloud and the fraction of debris that free-streams from the burst along the magnetic field. The amount of debris that escapes from the burst with minimal coupling to the background magnetic field increases with the debris gyroradius. Test cases with two different debris species--including a heavy minority species with a relatively large gyroradius--highlight how the collisionless coupling of the debris depends on the single-particle trajectories as well as the overall conservation of energy and momentum., Comment: To appear in JGR: Space Physics