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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