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 article 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).

Previously, using an incompressible von Kármán–Howarth formalism, the behavior of cross-scale energy transfer in magnetic reconnection and turbulence was found to be essentially identical to each other, independent of an external magnetic (guide) field, in the inertial and energy-containing ranges [Adhikari et al., Phys. Plasmas 30, 082904 (2023)]. However, this description did not account for the energy transfer in the dissipation range for kinetic plasmas. In this Letter, we adopt a scale-filtering approach to investigate this previously unaccounted-for energy transfer channel in reconnection. Using kinetic particle-in-cell simulations of antiparallel and component reconnection, we show that the pressure–strain interaction becomes important at scales smaller than the ion inertial length, where the nonlinear energy transfer term drops off. Also, the presence of a guide field makes a significant difference in the morphology of the scale-filtered energy transfer. These results are consistent with kinetic turbulence simulations, suggesting that the pressure strain interaction is the dominant energy transfer channel between electron scales and ion scales.

With the increase in technical capabilities of computer simulation in recent years, it has become feasible to quantify the degradation of fluid scale plasma and electromagnetic energies in favor of increases of internal energies. While it is understood that electromagnetic energy can be exchanged with fluid scale velocities, it is the pressure strain interaction that exchanges energy between fluid motions and internal energy. Here using simulations of both turbulence and reconnection we show that for electrons, the pressure strain and electromagnetic work are closely related and are frequently comparable when appropriate time and spatial averaging is applied. Otherwise, the instantaneous spatial averaged pressure strain and electromagnetic work are nearly equal for slowly evolving systems, like the reconnection case, while they differ significantly in rapidly evolving systems, like the turbulence case. This clarifies the relationship between these two quantities, which are each frequently used as measures of dissipation. The electromagnetic field changes the fluid velocity of each type of plasma particle. Meanwhile, the pressure of each plasma species, interacts with nonuniform fluid velocities to produce heat. The intermediate steps are in general, complicated, but because electrons are so light, a special simplifying approximation holds, equating properly averaged electromagnetic work on electrons to the rate of increase of electron internal energy. This result may help clarify differences in how the reconnection and turbulence communities quantify "dissipation". Time integrated volume averaged electromagnetic work does not formally or generally correspond to dissipation Due to small electron mass, time integrated volume averaged pressure strain and electromagnetic work are nearly equal for electrons Differences between instantaneous electromagnetic work and pressure strain can be considerable, but for electrons, these average to zero

A common approach to assess the nature of energy conversion in a classical fluid or plasma is to compare power densities of the various possible energy conversion mechanisms. A leading research area is quantifying energy conversion for systems that are not in local thermodynamic equilibrium (LTE), as is common in a number of fluid and plasma systems. Here we introduce the "higher-order nonequilibrium term" (HORNET) effective power density, which quantifies the rate of change of departure of a phase space density from LTE. It has dimensions of power density, which allows for quantitative comparisons with standard power densities. We employ particle-in-cell simulations to calculate HORNET during two processes, magnetic reconnection and decaying kinetic turbulence in collisionless magnetized plasmas, that inherently produce non-LTE effects. We investigate the spatial variation of HORNET and the time evolution of its spatial average. By comparing HORNET with power densities describing changes to the internal energy (pressure dilatation, Pi-D, and divergence of the vector heat flux density), we find that HORNET can be a significant fraction of these other measures (8% and 35% for electrons and ions, respectively, for reconnection; up to 67% for both electrons and ions for turbulence), meaning evolution of the system towards or away from LTE can be dynamically important. Applications to numerous plasma phenomena are discussed.

Resolving 3D physics occurring on multiple spatial and temporal scales is difficult with spacecraft and computer simulations alone, but can be studied much more easily with laboratory plasma experiments.This white paper proposes increasing funding for both human and physical infrastructure development in laboratory plasma facilities, as well as educating early career scientists on how to better utilize laboratory experiments in their own research.

Although pressure plays a vital role in the dynamics of the turbulent plasmas, pressure statistics have not been studied as extensively as other plasma properties. The studies that have focused on pressure are mostly based on hydrodynamic turbulence or have been formulated in the nearly incompressible magnetohydrodynamics (NIMHD) framework. However, less attention has been paid to the scaling properties of pressure in kinetic plasma. In this study, we explore the statistics of magnetic, thermal, and total pressure fluctuation in kinetic collisionless turbulence. A 2.5D kinetic particle-in-cell (PIC) simulation of turbulence is used to investigate pressure balance via the evolution of thermal and magnetic pressure. Further, the behavior of thermal, magnetic, and total pressure structure function and their corresponding spectrum is explored. Finally, we evaluate higher-order total pressure structure functions to discuss intermittency and compare the power exponents with higher-order structure functions of velocity and magnetic fluctuations.

All the dataset used in the paper and the python codes used to plot the figures can be found here.

The effect of an external guide field on the turbulence-like properties of magnetic reconnection is studied using five different 2.5D kinetic particle-in-cell (PIC) simulations. The magnetic energy spectrum is found to exhibit a slope of approximately −5/3 in the inertial range, independent of the guide field. On the contrary, the electric field spectrum in the inertial range steepens more with the guide field and approaches a slope of −5/3. In addition, spectral analysis of the different terms of the generalized Ohm's law is performed and found to be consistent with PIC simulations of turbulence and MMS observations. Finally, the guide field effect on the energy transfer behavior is examined using the von Kármán–Howarth (vKH) equation based on incompressible Hall-MHD. The general characteristics of the vKH equation with constant rate of energy transfer in the inertial range are consistent in all the simulations. This suggests that the qualitative behavior of energy spectrum and energy transfer in reconnection are similar to that of turbulence, indicating that reconnection fundamentally involves an energy cascade.

Anisotropic electron heating during electron-only magnetic reconnection with a large guide magnetic field is directly measured in a laboratory plasma through in situ measurements of electron velocity distribution functions. Electron heating preferentially parallel to the magnetic field is localized to one separatrix, and anisotropies of 1.5 are measured. The mechanism for electron energization is identified as the parallel reconnection electric field because of the anisotropic nature of the heating and spatial localization. These characteristics are reproduced in a 2D particle-in-cell simulation and are also consistent with numerous magnetosheath observations. A measured increase in the perpendicular temperature along both separatrices is not reproduced by our 2D simulations. This work has implications for energy partition studies in magnetosheath and laboratory reconnection.

Pressure is an important parameter in plasma turbulence. Historically, pressure fluctuations have been studied extensively via density in the nearly incompressible (NI) magnetohydrodynamic (MHD) framework1-3. However, the statistics of mechanical and total pressure in kinetic plasmas have not been explored much. In this study, we examine the statistics of mechanical and total pressure using a 2.5D particle-in-cell (PIC) simulation of plasma turbulence4. As turbulence is fully developed in the system, it is found that the magnetic and thermal pressure display a negative correlation keeping the total pressure about constant, consistent with MHD behavior. This negative correlation is observed locally in regions near the current sheets and justified by the nature of the joint probability distribution of the two5. Further, pressure spectra are calculated for magnetic, thermal and total pressure. The thermal and magnetic pressure spectra exhibit a slope of -5/3 in the inertial range, while the total pressure spectrum exhibits a slope of -7/3 in agreement with hydrodynamic scaling, influenced by the cross-spectral contribution of the individual pressures. Finally, the implications of the local structures of pressure to intermittency are discussed using probability distribution functions and scale dependent kurtosis.1. Montgomery, D., Brown M. R., and Matthaeus W. H. "Density fluctuation spectra in magnetohydrodynamic turbulence"JGR: Space Physics A1 (1987): 282-284.2. Matthaeus, W. H., Brown M. R., "Nearly incompressible magnetohydrodynamics at low Mach number"The Physics of Fluids 12 (1988): 3634-3644.3. Matthaeus, W. H., et al. "Nearly incompressible magnetohydrodynamics, pseudosound, and solar wind fluctuations" JGR: Space Physics A4 (1991): 5421-5435.4. Adhikari, S., et al. "Energy transfer in reconnection and turbulence" Physical Review E 6 (2021): 065206.5. Adhikari S., et al. “Statistics of Total Pressure in Kinetic Plasma Turbulence" ESS Open Archive (2023).

In this study we explore the statistics of pressure fluctuations in kinetic collisionless turbulence. A 2.5D kinetic particle-in-cell (PIC) simulation of decaying turbulence is used to investigate pressure balance via the evolution of thermal and magnetic pressure in a plasma with beta of order unity. We also discuss the behavior of thermal, magnetic and total pressure structure functions and their corresponding wavenumber spectra. The total pressure spectrum exhibits a slope of -7/3 extending for about a decade in the ion-inertial range. In contrast, shallower -5/3 spectra are characteristic of the magnetic pressure and thermal pressure. The steeper total pressure spectrum is a consequence of cancellation caused by density-magnetic field magnitude anticorrelation. Further, we evaluate higher order total pressure structure functions in an effort to discuss intermittency and compare the power exponents with higher order structure functions of velocity and magnetic fluctuations. Finally, applications to astrophysical systems are also discussed.

Over the past few decades, the relationship between turbulence and reconnection has emerged as a subject of interest. For example, various properties of reconnection have been studied in different turbulent environments using plasma simulations. In other approaches, reconnection is studied as a subsidiary process occurring in turbulence. Turbulent features are also studied as consequences of instabilities associated with large scale reconnection. Only recently, we have attempted to answer some of the fundamental questions such as: “What are the turbulent-like features of laminar magnetic reconnection?”, "Is magnetic reconnection fundamentally an energy cascade?" both related to the interplay between reconnection and turbulence. Using 2.5D particle in cell simulations, we have found that laminar magnetic reconnection in a quasi-steady phase exhibits a Kolmogorov-like power spectrum. Most notably, the energy transfer process in magnetic reconnection is also found to be similar to that of a turbulent system suggesting that reconnection involves an energy cascade. The reconnection rate is correlated to both the magnetic energy spectrum in the ion-scales and the cascade of energy. Further, similarities between reconnection and turbulence in terms of the electric field spectrum, their components, and pressure-strain interaction will be highlighted.

``Exact'' laws for evaluating cascade rates, tracing back to the Kolmogorov ``4/5'' law, have been extended to many systems of interest including magnetohydrodynamics (MHD), and compressible flows of the magnetofluid and ordinary fluid types. It is understood that implementations may be limited by the quantity of available data and by the lack of turbulence symmetry. Assessment of the accuracy and feasibility of such ``third-order'' (or Yaglom) relations is most effectively accomplished by examining the von Karman-Howarth equation in increment form, a framework from which the third-order laws are derived as asymptotic approximations. Using this approach, we examine the context of third-order laws for incompressible MHD in some detail. The simplest versions rely on the assumption of isotropy and the presence of a well-defined inertial range, while related procedures generalize the same idea to arbitrary rotational symmetries. Conditions for obtaining correct and accurate values of the dissipation rate from these laws based on several sampling and fitting strategies are investigated using results from simulations. The questions we address are of particular relevance to sampling of solar wind turbulence by one or more spacecraft.

Reconnection and turbulence are two of the most commonly observed dynamical processes in plasmas, but their relationship is still not fully understood. Using 2.5D kinetic particle-in-cell simulations of both strong turbulence and reconnection, we compare the cross-scale transfer of energy in the two systems by analyzing the generalization of the von Kármán Howarth equations for Hall magnetohydrodynamics, a formulation that subsumes the third-order law for steady energy transfer rates. Even though the large scale features are quite different, the finding is that the decomposition of the energy transfer is structurally very similar in the two cases. In the reconnection case, the time evolution of the energy transfer also exhibits a correlation with the reconnection rate. These results provide explicit evidence that reconnection dynamics fundamentally involves turbulence-like energy transfer.

Reconnection and turbulence are two of the most commonly observed dynamical processes in plasmas, but their relationship is still not fully understood. Using 2.5D kinetic particle-in-cell simulations of both strong turbulence and reconnection, we compare the cross-scale transfer of energy in the two systems by analyzing the generalization of the von Kármán Howarth equations for Hall magnetohydrodynamics, a formulation that subsumes the third-order law for steady cascade rates. Even though the large scale features are quite different, the finding is that the decomposition of the energy transfer is structurally very similar in the two cases. In the reconnection case, the time evolution of the energy transfer also exhibits a correlation with the reconnection rate. These results provide explicit evidence that reconnection itself is fundamentally an energy cascade process.

Earth and Space Science Open Archive Presented WorkOpen AccessYou are viewing the latest version by default [v1]Reconnection as an Energy CascadeAuthorsSubashAdhikariSee all authors Subash AdhikariCorresponding Author• Submitting AuthorDepartment of Physics and Astronomy, University of Delawareview email addressThe email was not providedcopy email address

The spectral properties associated with laminar, anti-parallel reconnection are examined using a 2.5D kinetic particle in cell (PIC) simulation. Both the reconnection rate and the energy spectrum exhibit three distinct phases: an initiation phase where the reconnection rate grows, a quasi-steady phase, and a declining phase where both the reconnection rate and the energy spectrum decrease. During the steady phase, the energy spectrum exhibits approximately a double power-law behavior, with a slope near -5/3 at wavenumbers smaller than the inverse ion inertial length, and a slope steeper than -8/3 for larger wavenumbers up to the inverse electron inertial length. This behavior is consistent with a Kolmogorov energy cascade and implies that laminar reconnection may fundamentally be an energy cascade process. Consistent with this idea is that the reconnection rate exhibits a rough correlation with the energy spectrum at wave numbers near the inverse ion inertial length. The 2D spectrum is strongly anisotropic with most energy associated with the wave vector direction normal to the current sheet. Reconnection acts to isotropize the energy spectrum, reducing the Shebalin angle from an initial value of 70 degrees to about 48 degrees (nearly isotropic) by the end of the simulation.